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 the following statements in respect of five candidates P, Q, R, S and T. Two statements are true and one statement is false.
True Statement : One of P and Q was selected for the job.
False Statement : At least one of R and S was selected for the job.
True Statement : At most two of R, S and T were selected for the job.
Which of the following conclusions can be drawn ?
- 1. At least four were selected for the job.
- 2. S was selected for the job.
Select the correct answer using the code given below :
Answer (d) & explanation
Neither conclusion follows (d). Step 1: the false statement is "at least one of R and S was selected". If it is false, then neither R nor S was selected. So conclusion 2 (S was selected) is wrong. Step 2: only one of P and Q was selected, and T may or may not be. So at most 2 people were selected. Step 3: so conclusion 1 (at least four selected) is wrong too. Options (a), (b) and (c) fail.
Tip: the opposite of "at least one" is "none". Turning the false statement into its opposite is the key step.
the negation of 'at least one' is 'none', not 'only one'.
Answer as per the official UPSC answer key.
If 7 ⊕ 9 ⊕ 10 = 8, 9 ⊕ 11 ⊕ 30 = 5, 11 ⊕ 17 ⊕ 21 = 13, what is the value of 23 ⊕ 4 ⊕ 15 ?
Answer (a) & explanation
The value is 6 (a). Step 1: find the rule from the examples. Add the three numbers, then add the digits of the sum. Step 2: 7 + 9 + 10 = 26 → 2 + 6 = 8. 9 + 11 + 30 = 50 → 5. 11 + 17 + 21 = 49 → 4 + 9 = 13. The rule works for all three. Step 3: 23 + 4 + 15 = 42 → 4 + 2 = 6. Options (b), (c) and (d) do not follow this rule.
Tip: for made-up symbols, test simple operations (sum, product, digit sum) on all examples. The rule must fit every one.
Answer as per the official UPSC answer key.
Question : Is p greater than q ?
Statement-1: p × q is greater than zero.
Statement-2: p2 is greater than q2.
Which one of the following is correct in respect of the above Question and the Statements ?
Answer (d) & explanation
The question cannot be answered even with both statements (d). Step 1: Statement-1: p × q is positive, so p and q have the same sign. Step 2: Statement-2: p² > q², so p is farther from zero than q. Step 3: together: both positive, like 3 and 2, gives p > q. Both negative, like −3 and −2, gives p < q. Two different answers, so the data are not enough. Options (a), (b) and (c) fail.
Tip: squares hide signs. Always test negative numbers in data sufficiency questions involving squares.
squaring hides the sign. Negatives reverse the order.
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Answer as per the official UPSC answer key.
Read the passage
In India, a majority of farmers are marginal and small, less educated and possess low adaptive capabilities to climate change, perhaps because of credit and other constraints. So, one cannot expect autonomous adaptation to climate change. Even if it was possible, it would not be sufficient to offset losses from climate change. To deal with this, adaptation to climate change is paramount, alongside a fast mitigation response. Another solution is to have a planned or policy-driven adaptation, which would require the government to come up with policy recommendations. Perception is a necessary pre-requisite for adaptation. Whether farmers are adapting agricultural practices to climate change depends on whether they perceive it or not. However, this is not always enough for adaptation. It is important how a farmer perceives the risks associated with climate change.
Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage ?
Answer (c) & explanation
The message is that farmers' risk perceptions matter for motivating adaptation (c). Step 1: the passage says perception is a "necessary pre-requisite" for adaptation. Step 2: it ends with its key point: "It is important how a farmer perceives the risks" of climate change. That is (c). Step 3: option (a) says adaptation is only the government's job; the passage mentions policy as just one solution. Option (b) is not discussed. Option (d) says mitigation is not possible, but the passage calls for "a fast mitigation response".
Tip: the last line of a passage often carries its main message. Check options with "only" or "not possible" against the text.
Answer as per the official UPSC answer key.
Read the passage
Food consumption patterns have changed substantially in India over the past few decades. This has resulted in the disappearance of many nutritious foods such as millets. While food grain production has increased over five times since independence, it has not sufficiently addressed the issue of malnutrition. For long, the agriculture sector focussed on increasing food production particularly staples, which led to lower production and consumption of indigenous traditional crops/grains, fruits and other vegetables, impacting food and nutrition security in the process. Further, intensive, monoculture agriculture practices can perpetuate the food and nutrition security problem by degrading the quality of land, water and food derived through them.
Based on the above passage, the following assumptions have been made :
- 1. To implement the Sustainable Development Goals and to achieve zero-hunger goal, monoculture agriculture practices are inevitable even if they do not address malnutrition.
- 2. Dependence on a few crops has negative consequences for human health and the ecosystem.
- 3. Government policies regarding food planning need to incorporate nutritional security.
- 4. For the present monoculture agriculture practices, farmers receive subsidies in various ways and government offers remunerative prices for grains and therefore they do not tend to consider crop diversity.
Which of the above assumptions are valid ?
Answer (b) & explanation
Assumptions 2 and 3 are valid (b). Step 1: the passage says monoculture degrades the quality of land, water and food. So depending on a few crops harms health and the ecosystem (2). Step 2: it says grain output rose five times but did not fix malnutrition. So food planning must include nutritional security (3). Step 3: assumption 1 calls monoculture inevitable, which goes against the passage. Assumption 4, about subsidies and prices, is never mentioned. So options (a), (c) and (d) fail.
Tip: 2023 was the International Year of Millets, led by India at the UN. Millets are exactly the "disappearing nutritious foods" this passage mentions.
Answer as per the official UPSC answer key.
A rectangular floor measures 4 m in length and 2·2 m in breadth. Tiles of size 140 cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor ?
Answer (d) & explanation
1. Floor = 400 cm × 220 cm. One tile = 140 cm × 60 cm.
2. Neat rows (all tiles the same way) fit only 8 tiles.
3. Mixing the two directions in a staggered (pinwheel) pattern, as in the figure, fits 9 tiles.
4. 10 cannot fit: across the 220 cm width the tiles can fill at most 200 cm (140 + 60), so a strip of floor is always left empty and there is room for only 9.
don't stop at the neat grid answer 8. "Any orientation" is a hint to mix them.
Answer as per the official UPSC answer key.
Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following :
- 1. p + q + r – s – t is definitely even.
- 2. 2p + q + 2r – 2s + t is definitely odd.
Which of the above statements is/are correct ?
Answer (a) & explanation
Only statement 1 is correct (a). Step 1: subtracting a number has the same odd-even effect as adding it. So p + q + r − s − t has the same parity as the sum of all five. Step 2: the five include two odd numbers, and two odds make an even sum. So statement 1 is always even, and true. Step 3: in 2p + q + 2r − 2s + t, the doubled terms are even. The parity depends on q + t, which depends on which numbers are odd. So it is not definitely odd. Options (b), (c) and (d) fail.
Tip: for odd-even questions, ignore the signs and any doubled terms. Just count the odd numbers left.
Answer as per the official UPSC answer key.
Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements :
- 1. The number of possible values of p is 5.
- 2. The number of possible values of q is 6.
Which of the above statements is/are correct ?
Answer (c) & explanation
Both statements are correct (c). Step 1: pp = 11p, so 11(p + q + r) = tt0 = 110t. So p + q + r = 10t: either 10 or 20. Step 2: sum 10 with p < q < r: (1, 2, 7), (1, 3, 6), (1, 4, 5), (2, 3, 5). Sum 20: (3, 8, 9), (4, 7, 9), (5, 6, 9), (5, 7, 8). Step 3: p takes 1, 2, 3, 4, 5 (five values). q takes 2, 3, 4, 6, 7, 8 (six values). So options (a), (b) and (d) fail.
Tip: repeated-digit numbers like pp are 11 × p. Spotting this turns the puzzle into a simple sum.
Answer as per the official UPSC answer key.
Let P, Q, R, S and T be five statements such that :
- I. If P is true, then both Q and S are true.
- II. If R and S are true, then T is false.
Which of the following can be concluded ?
- 1. If T is true, then at least one of P and R must be false.
- 2. If Q is true, then P is true.
Select the correct answer using the code given below :
Answer (a) & explanation
Only conclusion 1 follows (a). Step 1: suppose T is true. By rule II, R and S cannot both be true. If S is false, then by rule I, P must be false (P true would make S true). If R is false, we are done. Either way, P or R is false. So conclusion 1 follows. Step 2: rule I says "if P then Q". This does not give "if Q then P". So conclusion 2 does not follow. Step 3: options (b), (c) and (d) fail.
Tip: "If A then B" also gives "if not B then not A". It never gives "if B then A".
reversing an 'if … then' (Q → P) is the classic mistake. Only the contrapositive (not Q → not P) is safe.
Answer as per the official UPSC answer key.
Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible ?
Answer (c) & explanation
12 values of x are possible (c). Step 1: 7x is always divisible by x. So 7x + 96 is divisible by x only if x divides 96. Step 2: 96 = 2⁵ × 3. Step 3: the number of divisors = (5 + 1) × (1 + 1) = 12. So x can be any of 12 values: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96. Options (a), (b) and (d) miscount.
Tip: to count divisors, write the number as a product of prime powers. Add 1 to each power and multiply.
Answer as per the official UPSC answer key.
Question : Is (p + q – r) greater than (p – q + r), where p, q and r are integers ?
Statement-1: (p – q) is positive.
Statement-2: (p – r) is negative.
Which one of the following is correct in respect of the above Question and the Statements ?
Answer (c) & explanation
Both statements together are needed (c). Step 1: simplify the question first. p + q − r > p − q + r means 2q > 2r, that is, is q > r? Step 2: Statement-1 says p − q is positive, so q < p. Statement-2 says p − r is negative, so p < r. Neither alone links q and r. Step 3: together: q < p < r, so q < r. The question gets a definite "no". A definite "no" still answers it, so (c). Options (a), (b) and (d) fail.
Tip: always simplify the question before reading the statements. A firm "no" counts as an answer in data sufficiency.
Answer as per the official UPSC answer key.
Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make?
Answer (d) & explanation
The maximum is 45 attempts (d). Step 1: think of the unluckiest case. First he picks every non-red shoe: 9 + 8 = 17 pairs = 34 shoes. Step 2: still unlucky, he then picks all 10 red shoes of the same foot (say all left shoes): 34 + 10 = 44. Step 3: the next shoe must be a red right shoe, which makes a pair. So 45 picks at most. Option (c), 44, stops one short. Options (a) and (b) ignore the left-right problem.
Tip: shoes have a left and a right, unlike socks. In worst-case questions, always ask what "a pair" really needs.
(c) 44 forgets that ten left shoes still do not make a pair.
Answer as per the official UPSC answer key.
A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements :
- 1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175.
- 2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167.
Which of the above statements is/are correct ?
Answer (c) & explanation
Both statements are correct (c). Step 1: think of the worst case. To avoid completing any colour, take one less than each group: 13 + 19 + 25 + 27 + 37 + 53 = 174. The next ball must complete a group, so n = 175 (statement 1 true). Step 2: to miss a colour as long as possible, take every ball except the smallest group (14 black): 180 − 14 = 166. Step 3: the next ball must be black, so m = 167 (statement 2 true). Options (a), (b) and (d) fail.
Tip: worst-case questions: give the unlucky picker everything except what you need, then add one.
for 'one of each colour', the worst case leaves out the smallest group, not the largest.
Answer as per the official UPSC answer key.
There are five persons P, Q, R, S and T each one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1. Task-2 must be assigned to either R or S. In how many ways can the assignment be done ?
Answer (d) & explanation
There are 24 ways (d). Step 1: Task-2 must go to R or S: 2 ways. Step 2: Task-1 cannot go to P, Q or the person who got Task-2. So only 2 people are left for it: 2 ways. Step 3: the other 3 tasks go to the remaining 3 people in 3 × 2 × 1 = 6 ways. Total = 2 × 2 × 6 = 24. Options (a), (b) and (c) miss a factor.
Tip: fill the most restricted task first. Then each later choice becomes simple counting.
Answer as per the official UPSC answer key.
Consider the following in respect of prime number p and composite number c.
- 1. (p + c)/(p – c) can be even.
- 2. 2p + c can be odd.
- 3. pc can be odd.
Which of the statements given above are correct ?
Answer (d) & explanation
All three statements can be true (d). Step 1: "can be" needs only one example each. Step 2: statement 1: p = 11, c = 9. (11 + 9) ÷ (11 − 9) = 20 ÷ 2 = 10, which is even. Statement 2: c = 9. 2p is even, and even + 9 is odd. Step 3: statement 3: p = 3, c = 9. 3 × 9 = 27, odd. So options (a), (b) and (c) fail.
Tip: remember that composite numbers can be odd (9, 15, 21). Many "can be" traps assume composites are even.
Answer as per the official UPSC answer key.
What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated ?
Answer (a) & explanation
The sum is 7998 (a). Step 1: below 2000, the first digit must be 1. The other digits 2, 3 and 4 can be arranged in 3 × 2 × 1 = 6 ways. Step 2: thousands place: 6 numbers × 1000 = 6000. Step 3: each of 2, 3, 4 sits twice in each of the other three places: (2 + 3 + 4) × 2 × 111 = 1998. Total = 6000 + 1998 = 7998. Options (b), (c) and (d) miscount.
Tip: for sums of arranged numbers, handle the fixed digit separately, then use (sum of digits) × (times each appears) × 111.
Answer as per the official UPSC answer key.
A cuboid of dimensions 7 cm × 5 cm × 3 cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7 cm × 5 cm, 5 cm × 3 cm, 7 cm × 3 cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1 cm. Which of the following statements is/are correct ?
- 1. There are exactly 15 small cubes with no paint on any face.
- 2. There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green.
Select the correct answer using the code given below :
Answer (a) & explanation
Only statement 1 is correct (a). Step 1: unpainted cubes form the inner block: (7 − 2) × (5 − 2) × (3 − 2) = 5 × 3 × 1 = 15. So statement 1 is true. Step 2: blue faces (7 × 3) and green faces (5 × 3) meet along the four edges of length 3 cm. Step 3: each such edge has 3 − 2 = 1 middle cube with exactly those two colours. Four edges give 4 cubes, not 6. So statement 2 is false. Options (b), (c) and (d) fail.
Tip: two coloured faces meet along an edge. Cubes with exactly two colours on an edge = edge length − 2 (the corners have three colours).
corner cubes have three painted faces, so leave them out when you count 'exactly two'.
Answer as per the official UPSC answer key.
If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q)(r + s)?
Answer (b) & explanation
The greatest value is 225 (b). Step 1: to make the product big, use the four largest digits: 9, 8, 7, 6. Their total is 30. Step 2: for a fixed total, a product of two parts is largest when the parts are equal. So make each bracket 15: 9 + 6 and 8 + 7. Step 3: 15 × 15 = 225. Option (a), 230, is impossible. Option (c), 224 = 16 × 14, is slightly less. Option (d), 221 = 17 × 13, is less again.
Tip: for a fixed sum, the product is greatest when the numbers are as close as possible.
Answer as per the official UPSC answer key.
In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.
Question: How many persons attended the party ?
Statement-1: 50 persons took milk.
Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.
Which one of the following is correct in respect of the above Question and the Statements ?
Answer (a) & explanation
Statement-2 alone answers it, but Statement-1 alone does not (a). Step 1: people who took tea or coffee = 75 + 60 − 15 = 120. No milk-taker takes tea, so total = 120 + (people who took milk only). Step 2: Statement-1 says 50 took milk. But some of them may also take coffee, so "milk only" is unknown. Not enough. Step 3: Statement-2: total = 5 × (milk only). So 120 + m = 5m, giving m = 30 and total = 150. Options (b), (c) and (d) fail.
Tip: in Venn questions, ask which region the given number covers. "Took milk" is not the same as "took milk only".
Answer as per the official UPSC answer key.
In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots?
Answer (b) & explanation
1. Choose how many sixes and fours. The singles then fill up the rest of the 25, so they never cause a problem.
2. 0 sixes: fours can be 0 to 6 (up to 24 runs). That is 7 ways.
3. 1 six: 19 runs left, fours 0 to 4. 5 ways.
4. 2 sixes: 13 left, fours 0 to 3. 4 ways.
5. 3 sixes: 7 left, fours 0 or 1. 2 ways.
6. 4 sixes: 1 left, no four. 1 way.
7. Total: 7 + 5 + 4 + 2 + 1 = 19.
Answer as per the official UPSC answer key.