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.
If 'ZERO' is written as 'CHUR', then how is 'PLAYER' written ?
Answer (d) & explanation
PLAYER is written SODBHU (d). Step 1: compare ZERO with CHUR. Z → C, E → H, R → U, O → R. Each letter moves 3 places forward, wrapping from Z back to A. Step 2: apply this to PLAYER: P → S, L → O, A → D, Y → B, E → H, R → U. Step 3: the code is SODBHU. Option (a) gets A and Y wrong. Options (b) and (c) go wrong on the last letters.
Tip: when a letter near Z changes to one near A, the code wraps around. Count forward: Y, Z, A, B is 3 steps.
Answer as per the official UPSC answer key.
There are large number of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements :
- 1. To buy 78 gm of coins one must buy at least 7 coins.
- 2. To weigh 78 gm using these coins one can use less than 7 coins.
Which of the statements given above is/are correct ?
Answer (c) & explanation
Both statements are correct (c). Step 1: buying 78 g: 50 + 10 + 10 + 2 + 2 + 2 + 2 = 78 with 7 coins. 50 + 25 leaves 3 g, which no coin can make. Other mixes need more coins. So at least 7 are needed (1 true). Step 2: weighing allows coins on both pans. Put 50 + 25 + 5 on one pan and 2 on the other. That measures 80 − 2 = 78 g with only 4 coins (2 true). Step 3: so options (a), (b) and (d) fail.
Tip: "buy" means adding coins only; "weigh" lets you subtract by using the other pan. The wording changes the answer.
'buy' and 'weigh' are different. On a balance, a coin can also subtract.
Answer as per the official UPSC answer key.
A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A + B + C?
Answer (a) & explanation
A + B + C is 18 (a). Step 1: 37DD = 3700 + 11D. Since ABC × D = 37DD, D must divide 3700. So D is 1, 2, 4 or 5. Step 2: D = 1 or 2 makes ABC a 4-digit number. D = 5 gives 3755 ÷ 5 = 751, which repeats the digit 5. Step 3: D = 4: 3744 ÷ 4 = 936. All digits differ. A + B + C = 9 + 3 + 6 = 18. Option (d) is wrong: the data fix the answer.
Tip: split a coded number into a fixed part and a part with the unknown. Divisibility then narrows the choices quickly.
Answer as per the official UPSC answer key.
What is the number of selections of 10 consecutive things out of 12 things in a circle taken in the clockwise direction ?
Answer (c) & explanation
There are 12 selections (c). Step 1: in a circle, a run of consecutive things is fixed by where it starts. Step 2: any of the 12 things can be the starting point. Going clockwise, each start gives a different run of 10. Step 3: so there are 12 selections. Option (a), 3, applies to a straight line of 12 (12 − 10 + 1). Option (d), 66, counts any 10 things, not consecutive ones.
Tip: in a line, runs of k from n = n − k + 1. In a circle (with k less than n), runs of k = n.
66 = 12C10 counts all selections, consecutive or not.
Answer as per the official UPSC answer key.
The letters of the word "INCOMPREHENSIBILITIES" are arranged alphabetically in reverse order. How many positions of the letter/letters will remain unchanged ?
Answer (c) & explanation
Two positions stay the same (c). Step 1: the 21 letters in reverse alphabetical order are: T S S R P O N N M L I I I I I H E E E C B. Step 2: the original word is I N C O M P R E H E N S I B I L I T I E S. Step 3: compare place by place. Only places 13 and 15 match, both with the letter I. So two positions stay unchanged. Options (a), (b) and (d) miscount.
Tip: write both orders in two rows, one under the other. Count the letters carefully first; repeated letters like I (5 times) decide the answer.
write both rows one above the other and compare letter by letter.
Fell for this one? Most aspirants do. The PYQ Book puts every UPSC trap side by side, so the pattern finally clicks. Try the free sample
Answer as per the official UPSC answer key.
A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13 ?
Answer (a) & explanation
The remainder is 11 (a). Step 1: 999999 = 13 × 76923. So every block of six 9s is a multiple of 13. Step 2: 99 = 6 × 16 + 3. After 16 blocks, only 999 is left over. Step 3: 999 = 13 × 76 + 11. So the remainder is 11. Options (b), (c) and (d) do not match.
Tip: 999999 (six 9s) is divisible by 7, 11, 13 and 37. Use it to cut long strings of 9s into simple blocks.
Answer as per the official UPSC answer key.
Consider a 3-digit number.
Question : What is the number ?
Statement-1: The sum of the digits of the number is equal to the product of the digits.
Statement-2: The number is divisible by the sum of the digits of the number.
Which one of the following is correct in respect of the above Question and the Statements ?
Answer (d) & explanation
Even both statements are not enough (d). Step 1: Statement-1: the digit sum equals the digit product. For three digits this works for 1, 2 and 3 (1 + 2 + 3 = 1 × 2 × 3 = 6), in any order: six numbers. Step 2: Statement-2: the number must be divisible by the digit sum, 6. So it must be even. Step 3: both 132 and 312 survive. Two answers remain, so the number is not fixed. Options (a), (b) and (c) fail.
Tip: in "what is the number" questions, keep testing until only one number is left. Two survivors mean insufficient data.
Answer as per the official UPSC answer key.
There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements :
- 1. It is possible that exactly one letter goes into an incorrect envelope.
- 2. There are only six ways in which only two letters can go into the correct envelopes.
Which of the statements given above is/are correct?
Answer (b) & explanation
Only statement 2 is correct (b). Step 1: if three letters are in the right envelopes, only one envelope is left, and it is the right one for the fourth letter. So exactly one wrong letter is impossible. Statement 1 is false. Step 2: for exactly two right letters, choose which two are right: AB, AC, AD, BC, BD, CD = 6 ways. Step 3: the other two must both be wrong, so they swap, in only 1 way. Total = 6 × 1 = 6. Statement 2 is true. Options (a), (c) and (d) fail.
Tip: in matching problems, "exactly one wrong" can never happen. A wrong letter always pushes at least one other letter out of place.
Answer as per the official UPSC answer key.
Consider the following statements :
- 1. A is older than B.
- 2. C and D are of the same age.
- 3. E is the youngest.
- 4. F is younger than D.
- 5. F is older than A.
How many statements given above are required to determine the oldest person/persons ?
Answer (d) & explanation
All five statements are needed (d). Step 1: put them in a chain: C = D (2), D > F (4), F > A (5), A > B (1), and E is the youngest (3). So C = D > F > A > B, and E is last. Step 2: to call C and D the oldest, we must show they beat everyone. B is beaten only through statement 1. E is placed only by statement 3. Step 3: C is linked to D only through statement 2. Drop any one and someone's position is unknown. So all five are needed. Options (a), (b) and (c) fail.
Tip: to name the oldest, every other person must be placed below. Check each person is covered by at least one statement.
Answer as per the official UPSC answer key.
Consider the following :
- I. A + B means A is neither smaller nor equal to B.
- II. A − B means A is not greater than B.
- III. A × B means A is not smaller than B.
- IV. A ÷ B means A is neither greater nor equal to B.
- V. A ± B means A is neither smaller nor greater than B.
Statement : P × Q, P − T, T ÷ R, R ± S
Conclusion-1 : Q ± T
Conclusion-2 : S + Q
Which one of the following is correct in respect of the above Statement and the Conclusions ?
Answer (b) & explanation
Only Conclusion-2 follows (b). Step 1: decode the symbols: + means >, − means ≤, × means ≥, ÷ means < and ± means =. Step 2: the statement becomes P ≥ Q, P ≤ T, T < R, R = S. So S = R > T ≥ P ≥ Q. Step 3: Conclusion-1 (Q = T) need not be true; T could be bigger. Conclusion-2 (S > Q) is true, since S > T ≥ Q. So options (a), (c) and (d) fail.
Tip: decode every symbol first, then write one chain. A single strict ">" in the chain makes the end-to-end link strict.
Answer as per the official UPSC answer key.
For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by :
Answer (d) & explanation
XYZXYZ is always divisible by 7, 11 and 13 (d). Step 1: write it out: XYZXYZ = XYZ × 1000 + XYZ = XYZ × 1001. Step 2: 1001 = 7 × 11 × 13. Step 3: so every such number is divisible by all three. Options (a), (b) and (c) each leave one out. For example, 123123 = 123 × 7 × 11 × 13.
Tip: 1001 = 7 × 11 × 13 is worth remembering. Any 3-digit block written twice is a multiple of 1001.
Answer as per the official UPSC answer key.
If today is Sunday, then which day is it exactly on 1010 th day ?
Answer (a) & explanation
The 10¹⁰th day is a Wednesday (a). Step 1: today (Sunday) is day 1. So the 10¹⁰th day is 10¹⁰ − 1 days later. Step 2: 10 leaves remainder 3 when divided by 7. So 10¹⁰ leaves the same remainder as 3¹⁰. Since 3⁶ leaves 1, 3¹⁰ leaves the same as 3⁴ = 81, which is 4. Step 3: so 10¹⁰ − 1 leaves 3. Sunday + 3 days = Wednesday. Option (b), Thursday, forgets that today is day 1.
Tip: "the nth day" counting today as day 1 means n − 1 days ahead. This off-by-one trap is common.
today is day 1, not day 0. Counting it as day 0 gives Thursday, which is an option.
UPSC repeats traps like this year after year. The PYQ Book gathers every trap in one place, so you see them coming. Try the free sample
Answer as per the official UPSC answer key.
Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number ?
Answer (c) & explanation
The digit sum is 81 (c). Step 1: 111111111 × 111111111 = 12345678987654321. Step 2: add the digits: 2 × (1 + 2 + ... + 8) + 9 = 2 × 36 + 9 = 81. Step 3: so the answer is (c). Option (a), 64, is 8², the result for eight ones. Options (b) and (d) are guesses.
Tip: for a number made of n ones (n up to 9), the square reads 1, 2, ..., n, ..., 2, 1. Its digit sum is simply n². Here 9² = 81.
Answer as per the official UPSC answer key.
For five children with ages a < b < c < d < e; any two successive ages differ by 2 years.
Question: What is the age of the youngest child ?
Statement-1: The age of the eldest is 3 times the youngest.
Statement-2: The average age of the children is 8 years.
Which one of the following is correct in respect of the above Question and the Statements ?
Answer (b) & explanation
Either statement alone is enough (b). Step 1: the ages go up by 2 each time: a, a + 2, a + 4, a + 6, a + 8. Step 2: Statement-1: the eldest is 3 times the youngest. So a + 8 = 3a, giving a = 4. Step 3: Statement-2: the average is 8. The average of five equally spaced ages is the middle one, a + 4 = 8, so a = 4. Each works alone. Options (a), (c) and (d) fail.
Tip: for equally spaced numbers, the average is the middle term. This saves time in many sequence questions.
Answer as per the official UPSC answer key.
What is the remainder when 85 × 87 × 89 × 91 × 95 × 96 is divided by 100 ?
Answer (a) & explanation
The remainder is 0 (a). Step 1: 100 = 4 × 25. Step 2: 85 = 5 × 17 and 95 = 5 × 19 give two 5s, so the product has 5 × 5 = 25. 96 = 32 × 3 gives plenty of 2s, so 4 also divides it. Step 3: so the product is a multiple of 4 × 25 = 100. The remainder is 0. Options (b), (c) and (d) assume something is left over.
Tip: to divide by 100, check for two 5s and two 2s among the factors. If both are there, the remainder is zero.
Answer as per the official UPSC answer key.
Consider the following including the Question and the Statements :
There are 5 members A, B, C, D, E in a family.
Question : What is the relation of E to B?
Statement-1 : A and B are a married couple.
Statement-2 : D is the father of C.
Statement-3 : E is D's son.
Statement-4 : A and C are sisters.
Which one of the following is correct in respect of the above Question and Statements?
Answer (c) & explanation
All four statements together are sufficient (c). Step 1: statements 2 and 4: D is C's father, and A is C's sister. So D is A's father too. Step 2: statement 3: E is D's son, so E is A's brother. Step 3: statement 1: B is married to A. So E is B's brother-in-law. Each statement is needed: without 2 or 4 we cannot link A to D; without 3 we know nothing of E; without 1 we know nothing of B. Options (a), (b) and (d) fail.
Tip: build a small family tree as you read each statement. Then test each option by removing one statement.
Option (b) leaves out D being C's father, so A cannot be tied to D and E.
Answer as per the official UPSC answer key.
Read the passage
In India, while the unemployment rate is a frequently used measure of poor performance of the economy, under conditions of rising school and college enrolment, it paints an inaccurate picture. The reported unemployment rate is dominated by the experience of younger Indians who face higher employment challenges and exhibit greater willingness to wait for the right job than their older peers. The unemployment challenge is greater for people with secondary or higher education, and rising education levels inflate unemployment challenges.
Which one of the following statements most likely reflects as to what the author of the passage intends to say ?
Answer (b) & explanation
The author says unemployment should be seen in light of rising education and aspirations of young Indians (b). Step 1: the passage says the unemployment rate paints an inaccurate picture when school and college enrolment are rising. Step 2: young, educated Indians are more willing to "wait for the right job", and rising education "inflates" unemployment. So it reflects education and aspirations. That is (b). Step 3: option (a), quality of education, and option (c), labour-intensive industry, are not discussed. Option (d), self-employment, is not suggested.
Tip: this is "aspirational unemployment". Educated youth may wait for a suitable job rather than take any job.
Answer as per the official UPSC answer key.
125 identical cubes are arranged in the form of a cubical block. How many cubes are surrounded by other cubes from each side?
Answer (a) & explanation
27 cubes are surrounded on every side (a). Step 1: 125 = 5 × 5 × 5, so the block is 5 cubes on each side. Step 2: a cube with neighbours on all six sides cannot be on the outer surface. Remove one layer from each face. Step 3: the inside block is (5 − 2) × (5 − 2) × (5 − 2) = 3 × 3 × 3 = 27. Options (b), (c) and (d) miscount.
Tip: for an n × n × n cube, the hidden inner cubes are (n − 2)³. The cubes with paint on just one face are 6(n − 2)².
Answer as per the official UPSC answer key.
There are three traffic signals. Each signal changes colour from green to red and then from red to green. The first signal takes 25 seconds, the second signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colours are same. At 2:00 p.m., they together turn green. At what time will they change to green next, simultaneously ?
Answer (b) & explanation
They turn green together again at 4:10 p.m. (b). Step 1: green and red last the same time. So each full cycle is double: 50 s, 78 s and 120 s. Step 2: LCM of 50, 78 and 120 = 2³ × 3 × 5² × 13 = 7800 s = 130 minutes. Step 3: 2:00 p.m. + 2 hours 10 minutes = 4:10 p.m. Option (a), 4:00 p.m., uses wrong cycles. Options (c) and (d) miscalculate.
Tip: always use the full cycle (green + red) for "turn green again". Using only the green time is the common trap.
LCM of 25, 39 and 60 gives the next time they all change, not the next time they all turn green.
Answer as per the official UPSC answer key.
What is the sum of all digits which appear in all the integers from 10 to 100?
Answer (b) & explanation
The sum is 856 (b). Step 1: from 10 to 99, the tens place shows each digit 1 to 9 exactly 10 times. That gives 45 × 10 = 450. Step 2: the units place shows each digit 0 to 9 exactly 9 times (once per ten). That gives 45 × 9 = 405. Step 3: add the digits of 100, which is 1. Total = 450 + 405 + 1 = 856. Option (a), 855, forgets 100. Options (c) and (d) miscount.
Tip: count digit sums place by place. Each place cycles through the digits evenly.
don't drop the 100 at the end. 855 is the trap option.
Answer as per the official UPSC answer key.