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.
There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these points as vertices and taking the diameter as one side of the triangle?
Answer (a) & explanation
24 right-angled triangles can be drawn (a). Step 1: an angle in a semicircle is always a right angle. So any triangle with a diameter as one side is right-angled. Step 2: eight equally spaced points form 4 diameters (each point has one opposite point). Step 3: each diameter can join any of the other 6 points to make a triangle. 4 × 6 = 24. Options (b), (c) and (d) miscount the diameters or the third points.
Tip: remember the circle rule: the angle in a semicircle is 90°. It turns this geometry question into simple counting.
Answer as per the official UPSC answer key.
Read the passage
Unless the forces and tendencies which are responsible for destroying the country’s environment are checked in the near future and afforestation of denuded areas is taken up on a massive scale, the harshness of the climatic conditions and soil erosion by wind and water will increase to such an extent that agriculture, which is the mainstay of our people, will gradually become impossible. The desert countries of the world and our own desert areas in Rajasthan are a grim reminder of the consequences of large-scale deforestation. Pockets of desert-like landscape are now appearing in other parts of the country including the Sutlej-Ganga Plains and the Deccan Plateau. Where only a few decades back there used to be lush green forests with perennial streams and springs, there is only brown earth, bare of vegetation, without any water in the streams and springs except in the rainy season.
According to the passage given above, deforestation and denudation will ultimately lead to which of the following?
- 1. Depletion of soil resource
- 2. Shortage of land for the common man
- 3. Lack of water for cultivation
Select the correct answer using the code given below.
Answer (c) & explanation
Statements 1 and 3 are the outcomes (c). Step 1: the passage warns of "soil erosion by wind and water", which depletes the soil (1). Step 2: it describes streams and springs without water except in the rains. So water for farming runs short (3). Step 3: a shortage of land for the common man (2) is never mentioned. The passage talks of land turning to desert, not of people lacking land. So options (a), (b) and (d) fail.
Tip: deforestation leads to desertification. Note the passage's examples: Rajasthan's desert, and pockets of desert-like land in the Sutlej-Ganga plains and the Deccan.
Answer as per the official UPSC answer key.
How many seconds in total are there in x weeks, x days, x hours, x minutes and x seconds?
Answer (d) & explanation
The total is 694861x seconds (d). Step 1: 1 week = 604800 s, 1 day = 86400 s, 1 hour = 3600 s, 1 minute = 60 s, plus 1 s. Step 2: add them: 604800 + 86400 + 3600 + 60 + 1 = 694861. So the total is 694861x. Step 3: options (a) and (b) leave out the week. Option (c), 694860x, forgets the last x seconds.
Tip: a quick check: "+ x seconds" makes the answer end in 1, which leaves (b) or (d). One week alone is over 6 lakh seconds, so (d).
Answer as per the official UPSC answer key.
Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number :
- 1. p × q can be an odd number.
- 2. q/p can be a prime number.
- 3. p + q can be a prime number.
Which of the above statements are correct?
Answer (d) & explanation
All three statements are correct (d). Step 1: "can be" needs just one example each. Step 2: statement 1: take p = 3 (prime) and q = 9 (composite). 3 × 9 = 27, odd. Statement 2: p = 2 and q = 6. 6 ÷ 2 = 3, a prime. Step 3: statement 3: p = 2 and q = 9. 2 + 9 = 11, a prime. So options (a), (b) and (c) fail.
Tip: for "can be" statements, look for one working example. Remember 2 is the only even prime, which often helps.
Answer as per the official UPSC answer key.
Read the passage
The poverty line is quite unsatisfactory when it comes to grasping the extent of poverty in India. It is not only because of its extremely narrow definition of ‘who is poor’ and the debatable methodology used to count the poor, but also because of a more fundamental assumption underlying it. It exclusively relies on the notion of poverty as insufficient income or insufficient purchasing power. One can better categorize it by calling it income poverty. If poverty is ultimately about deprivations affecting human well-being, then income poverty is only one aspect of it. Poverty of a life, in our view, lies not merely in the impoverished state in which the person actually lives, but also in the lack of real opportunity given by social constraints as well as personal circumstances—to choose other types of living. Even the relevance of low incomes, meagre possessions, and other aspects of what are standardly seen as economic poverty relate ultimately to their role in curtailing capabilities, i.e., their role in severely restricting the choices people have to lead variable and valued lives.
What does the author mean by ‘poverty of a life’?
Answer (a) & explanation
'Poverty of a life' means all deprivations, from lack of income and lack of real opportunities (a). Step 1: the passage says poverty of a life lies "not merely in the impoverished state" a person lives in. Step 2: it lies "also in the lack of real opportunity" to choose other ways of living. Both parts appear in (a). Step 3: option (b) covers only the impoverished state. Option (c), missed opportunities, leaves out income. Option (d) adds "permanently", which the passage never says.
Tip: "not merely X but also Y" means the answer must include both X and Y. Options with only one half are traps.
Answer as per the official UPSC answer key.
Aman started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1·25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is
Answer (d) & explanation
The village clock is 5 minutes fast (d). Step 1: let the outward drive take t minutes. The return route is 1.25 times longer at twice the speed, so it takes 1.25 ÷ 2 = 0.625t. Step 2: by the home clock, he was away 14:30 to 16:00 = 90 minutes. So t + 25 + 0.625t = 90, giving 1.625t = 65 and t = 40. Step 3: he truly reached the village at 14:30 + 40 = 15:10. The village clock showed 15:15, so it is 5 minutes fast. Options (a), (b) and (c) fail.
Tip: use only the reliable clock for time intervals. Then compare the true arrival time with what the other clock showed.
Answer as per the official UPSC answer key.
The sum of three consecutive integers is equal to their product. How many such possibilities are there?
Answer (c) & explanation
There are three such sets (c). Step 1: integers include 0 and negative numbers. Try small sets in a row. Step 2: 1, 2, 3: sum 6, product 6. Works. −1, 0, 1: sum 0, product 0. Works. −3, −2, −1: sum −6, product −6. Works. Step 3: bigger sets fail; for 2, 3, 4 the sum is 9 but the product is 24. The product grows much faster. So there are three. Option (a) counts only positive numbers.
Tip: "integers" means negatives and zero too. UPSC often hides extra answers there.
integers include zero and negatives. If you check only natural numbers, you find just one.
Answer as per the official UPSC answer key.
Consider the Question and two Statements given below :
Question : Is Z brother of X?
Statement-1 : X is a brother of Y and Y is a brother of Z.
Statement-2 : X, Y and Z are siblings.
Which one of the following is correct in respect of the Question and the Statements?
Answer (d) & explanation
Even both statements together are not enough (d). Step 1: Statement-1 says X is a brother of Y and Y is a brother of Z. So X and Y are male. Step 2: Statement-2 says all three are siblings, which we already know. Step 3: neither statement tells us Z's gender. Z could be X's brother or sister. So the question cannot be answered. Options (a), (b) and (c) fail.
Tip: in relation questions, "brother of Z" tells you the speaker's gender, not Z's. Always check if the gender of the person asked about is given.
'Y is a brother of Z' tells you Y's gender, not Z's.
Answer as per the official UPSC answer key.
24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
Answer (d) & explanation
The data are inadequate (d). Step 1: we are not told how fast a man works compared with a woman. Step 2: if men work faster, the new team (fewer men, more women) is slower, taking more than 30 days. If women work faster, it is quicker. If both work at the same rate, it takes the same 30 days. Step 3: since the answer changes with that one missing fact, we cannot decide. Option (a) assumes equal rates. Option (b) assumes men are faster. Option (c) is vague and not a conclusion.
Tip: before calculating, check whether every rate is given. If one key comparison is missing, "data inadequate" is often right.
(a) assumes a man and a woman work equally fast. The question never says so.
Answer as per the official UPSC answer key.
What is the value of X in the sequence 20, 10, 10, 15, 30, 75, X?
Answer (d) & explanation
X is 225 (d). Step 1: divide each term by the one before it. 10 ÷ 20 = 0.5; 10 ÷ 10 = 1; 15 ÷ 10 = 1.5; 30 ÷ 15 = 2; 75 ÷ 30 = 2.5. Step 2: the multiplier rises by 0.5 each step. The next one is 3. Step 3: X = 75 × 3 = 225. Option (c), 150, uses × 2 again. Options (a) and (b) come from adding instead of multiplying.
Tip: when a sequence falls and then rises sharply, look at the ratios between terms. A steadily growing multiplier is a common UPSC pattern.
Answer as per the official UPSC answer key.
P, Q, R, S, T and U are six members of a family. R is the spouse of Q. U is the mother of T and S is the daughter of U. P's daughter is T and R's son is P. There are two couples in the family. Which one of the following is correct?
No official answer (question dropped) & notes
UPSC dropped this question, so it has no official answer. Step 1: R is married to Q, and R's son is P. So P is the child of the couple Q and R. Step 2: P's daughter is T. So T is the granddaughter of Q (and of R). That matches option (d). Step 3: the genders of Q and R are never given. So "grandfather" (a), "grandmother" (b) and "R is the mother" (c) cannot be fixed. The wording about "two couples" adds more doubt, which is a likely reason UPSC dropped it.
Tip: in family puzzles, mark genders only when the question states them. Practise it, but don't overthink dropped items.
UPSC dropped this question from evaluation, so it has no official answer. It is printed here for practice only.
UPSC dropped this question from evaluation; there is no official answer.
Consider the following statements :
- 1. Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide.
- 2. Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide.
Which of the above statements is/are correct?
Answer (c) & explanation
Both statements are correct (c). Step 1: after 3 o'clock, the hands meet at (60 ÷ 11) × 3 = 16 4/11 minutes. That is about 3:16:22, between 3:16 and 3:17 (1 is true). Step 2: at 4:58:00, the minute hand is at the 58-minute mark and the second hand at 0. The second hand moves about 59 marks per minute faster. Step 3: it catches up in 58/59 minute, about 59 seconds, near 4:58:59. That is between 4:58 and 4:59 (2 is true). So options (a), (b) and (d) fail.
Tip: the hour and minute hands meet every 65 5/11 minutes. After H o'clock, they meet at (60/11) × H minutes.
Answer as per the official UPSC answer key.
X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
Answer (b) & explanation
X passes Y 3 times (b). Step 1: the race is 3 km = 3000 m on a 300 m track. So X runs 10 rounds. Step 2: the speeds are 3 : 2, so in the same time Y runs 2/3 × 10 = 6⅔ rounds. Step 3: X gains 10 − 6⅔ = 3⅓ rounds over Y. Each full round gained is one pass. So X passes Y 3 times. Options (a), (c) and (d) miscount; the extra ⅓ round is not a full pass.
Tip: on a circular track, the number of passes = the number of full laps the faster runner gains. The start is not counted.
Answer as per the official UPSC answer key.
A person X wants to distribute some pens among six children A, B, C, D, E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?
Answer (c) & explanation
The minimum is 294 pens (c). Step 1: A gets 2, 3, 4, 5 and 6 times the others. So A must be divisible by all of them: a multiple of 60. Step 2: every share must also be even. With A = 60, B = 30, C = 20, D = 15 (odd). So A must be a multiple of 120. Step 3: with A = 120: B = 60, C = 40, D = 30, E = 24, F = 20. Total = 120 + 60 + 40 + 30 + 24 + 20 = 294. Option (a), 147, is the total for A = 60, which gives odd shares.
Tip: after finding the LCM, check the extra condition (even shares). Doubling the base often fixes it.
147 (with A = 60) is the answer if you ignore "even". Then D gets 15.
Answer as per the official UPSC answer key.
What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits?
Answer (a) & explanation
There are 72 such numbers (a). Step 1: X can be any non-zero digit: 9 choices (1 to 9). Step 2: Y must be non-zero and different from X: 8 choices. Step 3: 9 × 8 = 72. Option (b), 81, allows X and Y to be the same. Options (c) and (d) include zero, which the question rules out. Note that X and Y are only the two decimal places, so 0.XY always has exactly two digits after the point.
Tip: "distinct" removes one choice for the second place. "Non-zero" removes 0 from both places.
Answer as per the official UPSC answer key.
On one side of a 1·01 km long road, 101 plants are planted at equal distance from each other. What is the total distance between 5 consecutive plants?
Answer (b) & explanation
The distance is 40.4 m (b). Step 1: 101 plants in a line leave 100 gaps between them. The road is 1.01 km = 1010 m. Step 2: so each gap = 1010 ÷ 100 = 10.1 m. Step 3: 5 plants in a row have 4 gaps between them. 4 × 10.1 = 40.4 m. Option (d), 50.5 m, counts 5 gaps. Options (a) and (c) use 10 m per gap.
Tip: n posts in a line have n − 1 gaps. This "fence-post" rule is a common UPSC trap.
5 plants have 4 gaps, not 5.
Answer as per the official UPSC answer key.
What is the remainder when 91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99 is divided by 1261?
Answer (d) & explanation
The remainder is 0 (d). Step 1: break the divisor into factors: 1261 = 13 × 97. Step 2: look for these factors in the product. 91 = 7 × 13, so 13 is there. 97 itself is one of the numbers. Step 3: so the product is divisible by 13 × 97 = 1261, and the remainder is 0. Options (a), (b) and (c) assume some remainder is left.
Tip: when dividing a long product, first factorise the divisor. If all its factors appear in the product, the remainder is zero.
Answer as per the official UPSC answer key.
An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?
Answer (a) & explanation
1. Work from the left. The first 2 digits are divisible by 2, so the 2nd digit is even. The first 5 are divisible by 5, so the 5th digit is 5.
2. The first 4 digits must be divisible by 4 and the first 3 by 3. The first 6 must be divisible by 6, so the 6th digit is even. The digit sum 36 makes the whole number divisible by 9 automatically. Only two numbers pass every test: 7412589 and 1472589.
3. The middle three digits (3rd, 4th, 5th) add up to 1 + 2 + 5 = 8 in 7412589. (In the other number they give 14, which is not an option.)
"the first digit from the right" is the units digit. Read the deletions from the right carefully.
Traps like this come back in new clothes. The PYQ Book collects all of them, topic by topic, so none catch you twice. Try the free sample
Answer as per the official UPSC answer key.
Consider the Question and two Statements given below in respect of three cities P, Q and R in a State :
Question : How far is city P from city Q?
Statement-1 : City Q is 18 km from city R.
Statement-2 : City P is 43 km from city R.
Which one of the following is correct in respect of the Question and the Statements?
Answer (d) & explanation
Even both statements are not enough (d). Step 1: together we know Q is 18 km from R and P is 43 km from R. Step 2: we are not told the directions. If P and Q are on the same side of R, PQ could be 43 − 18 = 25 km. On opposite sides in a line, PQ could be 43 + 18 = 61 km. In other directions, anything in between. Step 3: so PQ cannot be fixed. Options (a), (b) and (c) fail.
Tip: two distances from a common point fix only a range for the third distance (between their difference and their sum).
Answer as per the official UPSC answer key.
There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?
Answer (a) & explanation
m equals n (a). Step 1: both containers end with 100 ml. Whatever water ends up in X must equal the milk left in Y, because they swapped places. Step 2: check: Y has 100 ml water + 20 ml milk. 20 ml of this mix holds 16⅔ ml water and 3⅓ ml milk. Step 3: X now has 80 + 3⅓ = 83⅓ ml milk, and Y keeps 100 − 16⅔ = 83⅓ ml water. So m = n. Options (b), (c) and (d) fail.
Tip: in back-and-forth mixing with equal final volumes, the amount of each "foreign" liquid is always equal. No calculation is needed.
Answer as per the official UPSC answer key.