Arrangements, ranking, ordering and puzzles: previous-year questions
141 real UPSC Prelims questions (2011–2026) with the official answer and a clear explanation. 35 of them came in the last five papers.
How often UPSC asks this
Questions per year, counted from the official papers.
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(Same information as the question above.)
The football is in the box of which colour ?
Answer (c) & explanation
The colour of the football box cannot be determined (c). Step 1: from the earlier steps, the football is in box D. Step 2: F is indigo, so D and B share blue and yellow. Step 3: no clue tells us whether D is blue or yellow. The hockey rule fixes only F. So option (a) yellow and option (d) blue are both possible but not certain. Option (b), indigo, is wrong because F is indigo.
Tip: when two items can swap places with no rule broken, the answer is "cannot be determined". Before you choose it, check that you have used every clue. Here no clue links D or B to blue or yellow.
Answer as per the official UPSC answer key.
In a question paper there are five questions to be attempted and answer to each question has two choices — True (T) or False (F). It is given that no two candidates have given the answers to the five questions in an identical sequence. For this to happen, the maximum number of candidates is :
Answer (d) & explanation
At most 32 candidates (d). Step 1: each question has 2 possible answers, True or False. Step 2: for five questions, the number of different answer patterns is 2 × 2 × 2 × 2 × 2 = 32. Step 3: if no two candidates may have the same pattern, there can be at most 32 candidates. Option (a), 10, is 2 × 5, a common mistake of multiplying instead of raising to the power. Options (b) 18 and (c) 26 do not fit.
Tip: when each of n choices has k options, the number of combinations is k multiplied by itself n times. For yes/no questions that is 2, 4, 8, 16, 32 and so on.
Answer as per the official UPSC answer key.
When three friends A, B and C met, it was found that each of them wore an outer garment of a different colour. In random order, the garments are: jacket, sweater and tie; and the colours are: blue, white and black. Their surnames in random order are: Ribeiro, Kumar and Singh. Further, we know that :
- 1. neither B nor Ribeiro wore a white sweater
- 2. C wore a tie
- 3. Singh's garment was not white
- 4. Kumar does not wear a jacket
- 5. Ribeiro does not like to wear the black colour
- 6. Each of the friends wore only one outer garment of only one colour
What is C's surname ?
Answer (a) & explanation
C's surname is Ribeiro (a). Step 1: someone wore the white sweater. It was not B (clue 1) and not C, who wore the tie (clue 2). So A wore the white sweater. Step 2: A is not Ribeiro (clue 1) and not Singh, whose garment was not white (clue 3). So A is Kumar. Step 3: clue 1 names B and Ribeiro as two different people. So B is not Ribeiro, which makes C Ribeiro and B Singh. Options (b) Kumar and (c) Singh belong to A and B. Option (d) fails because the clues settle it.
Tip: clues like "neither B nor Ribeiro" quietly tell you B and Ribeiro are different people. Use such hidden facts.
Answer as per the official UPSC answer key.
(Same information as the question above.)
What is the colour of the tie ?
Answer (b) & explanation
The tie is blue (b). Step 1: C wears the tie, and C is Ribeiro. Step 2: white is already A's colour, because A wore the white sweater. Step 3: Ribeiro does not wear black (clue 5). So the only colour left for the tie is blue. B, Singh, then wears the black jacket. Option (a), black, is ruled out by clue 5. Option (c), white, belongs to A. Option (d) fails because the colour is fixed.
Tip: once names and garments are fixed, colours fall into place quickly. Build a small table with rows for A, B and C and columns for surname, garment and colour. Fill it in as each clue settles a box.
Answer as per the official UPSC answer key.
(Same information as the question above.)
Who wore the sweater ?
Answer (a) & explanation
A wore the sweater (a). Step 1: someone wore a white sweater. Clue 1 says B did not wear it. Clue 2 says C wore a tie. So the white sweater belongs to A. Step 2: this also fixes the rest. A is Kumar, C (Ribeiro) wears the blue tie, and B (Singh) wears the black jacket. Kumar does not wear a jacket, which fits A wearing the sweater. Step 3: so option (b) B wears the jacket, and option (c) C wears the tie. Option (d) fails because the answer is clear.
Tip: in linked puzzles, the first fact you work out often answers a later question directly. Write down each solved fact as you go.
Answer as per the official UPSC answer key.
Four-digit numbers are to be formed using the digits 1, 2, 3 and 4; and none of these four digits are repeated in any manner. Further,
- 1. 2 and 3 are not to immediately follow each other
- 2. 1 is not to be immediately followed by 3
- 3. 4 is not to appear at the last place
- 4. 1 is not to appear at the first place
How many different numbers can be formed ?
Answer (a) & explanation
Six numbers can be formed (a). Step 1: the rules are: 2 and 3 are not next to each other, 1 is not directly before 3, 4 is not last, and 1 is not first. So each number starts with 2, 3 or 4. Step 2: test each arrangement. Numbers starting with 2: 2143, 2431. Starting with 3: 3142, 3412, 3421. Starting with 4: 4312. Step 3: every other order breaks a rule, for example 2134 ends in 4, and 4213 has 1 before 3. That is 6 numbers. Options (b), (c) and (d) do not fit.
Tip: when there are only 24 orders, list them in a fixed order by first digit. A neat list stops you missing or repeating any.
Answer as per the official UPSC answer key.
In a class of 60 students, where the number of girls is twice that of boys, Kamal, a boy, ranked seventeenth from the top. If there are 9 girls ahead of Kamal, the number of boys in rank after him is :
Answer (b) & explanation
12 boys rank after Kamal (b). Step 1: girls are twice the boys, and there are 60 students. So boys = 60 ÷ 3 = 20, girls = 40. Step 2: Kamal is 17th, so 16 students are ahead of him. Nine of them are girls, so 16 − 9 = 7 are boys. Step 3: boys after Kamal = 20 − 7 − 1 (Kamal himself) = 12. Option (a), 13, forgets to remove Kamal. Option (c), 7, is the boys ahead of him. Option (d), 3, does not fit.
Tip: in rank questions, always remember to count or remove the person himself. That is the most common mistake.
Answer as per the official UPSC answer key.
Five people A, B, C, D and E are seated about a round table. Every chair is spaced equidistant from adjacent chairs.
- (i) C is seated next to A
- (ii) A is seated two seats from D
- (iii) B is not seated next to A
On the basis of above information, which of the following must be true ?
- 1. D is seated next to B
- 2. E is seated next to A
- 3. D and C are separated by two seats
Select the correct answer using the code given below :
Answer (b) & explanation
Statements 1 and 2 must be true (b). Step 1: with five seats, A has two neighbours. B cannot sit next to A, and D sits two seats away, so not next to A either. So A's neighbours are C and E. Statement 2 is true. Step 2: the two seats that are not next to A are next to each other. B and D take them. So D sits next to B, and statement 1 is true. Step 3: the order could be A, C, D, B, E or A, C, B, D, E. In the second case D and C are not two seats apart. So statement 3 need not be true.
Tip: in seating puzzles, place the person with the most rules first. Then try every arrangement left before saying something "must" be true.
Answer as per the official UPSC answer key.
A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white. The radius of the red band is 0.20 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability that the arrows fall in the red region of the archery target ?
Answer (c) & explanation
The probability of hitting red is 0.16 (c). Step 1: the target's diameter is 1 m, so its radius is 0.5 m. The red circle's radius is 0.2 m. Step 2: probability = red area ÷ whole area = π × 0.2² ÷ π × 0.5². The π cancels. Step 3: = (0.2 ÷ 0.5)² = 0.4² = 0.16. Option (a), 0.40, compares radii instead of areas. Option (b), 0.20, compares the red radius with the diameter. Option (d), 0.04, is just 0.2².
Tip: area grows with the square of the radius. When comparing circles, square the ratio of their radii. The widths of the other bands do not matter here.
the areas go with the square of the radius, so 0.2/0.5 = 0.4 is the trap.
Answer as per the official UPSC answer key.
Four friends A, B, C and D need to cross a bridge. A maximum of two persons can cross it at a time. It is night and they just have one lamp. Persons that cross the bridge must carry the lamp to find the way. A pair must walk together at the speed of slower person. After crossing the bridge, the person having faster speed in the pair will return with the lamp each time to accompany another person in the group. Finally, the lamp has to be returned at the original place and the person who returns the lamp has to cross the bridge again without lamp. To cross the bridge, the time taken by them is as follows : A: 1 minute, B: 2 minutes, C: 7 minutes and D: 10 minutes. What is the total minimum time required by all the friends to cross the bridge ?
Answer (a) & explanation
The minimum time is 23 minutes (a). Step 1: the rule says the faster person of each pair brings the lamp back. So A, the fastest (1 minute), should walk with everyone. Step 2: A + D cross (10), A returns (1), A + C cross (7), A returns (1), A + B cross (2). That is 21 minutes, and all four are across. Step 3: the puzzle adds that the lamp must be returned to the start, and the person who returns it must cross again without the lamp. A returns (1) and crosses back (1): 21 + 2 = 23 minutes. Option (c), 21, forgets this last rule. Options (b) and (d) do not follow the rules.
Tip: read every rule to the end; the last line often changes the answer.
the usual 17-minute trick (C and D crossing together) is not allowed here, because the faster person must return each time.
Answer as per the official UPSC answer key.
Six boxes A, B, C, D, E and F have been painted with six different colours viz., violet, indigo, blue, green, yellow and orange and arranged from left to right (not necessarily either kept or painted with the colours in the same order). Each box contains a ball of any one of the following six games: cricket, hockey, tennis, golf, football and volleyball (not necessarily in the same order). The golf ball is in violet box and is not in the box D. The box A which contains tennis ball is orange in colour and is at the extreme right. The hockey ball is neither in box D nor in box E. The box C having cricket ball is painted green. The hockey ball is neither in the box painted blue nor in the box painted yellow. The box C is fifth from right and next to box B. The box B contains volleyball. The box containing the hockey ball is between the boxes containing golf ball and volleyball.
Which one of the following boxes contains the golf ball ?
Answer (b) & explanation
The golf ball is in box E (b). Step 1: box A has tennis and is orange, at the far right. Box C has cricket and is green, fifth from the right. Box B, next to C, has volleyball. Step 2: that leaves golf, hockey and football for D, E and F. Golf is not in D. Hockey is in neither D nor E, so hockey is in F. Step 3: golf cannot go in D, so golf is in E, and football is in D. The violet box is E. Option (a) F has hockey. Option (c) D has football. Option (d) fails because E works.
Tip: in box puzzles, place the fixed facts first. Then use "not" clues to fill the last few gaps.
Answer as per the official UPSC answer key.
A selection is to be made for one post of Principal and two posts of Vice-Principal. Amongst the six candidates called for the interview, only two are eligible for the post of Principal while they all are eligible for the post of Vice-Principal. The number of possible combinations of selectees is
Answer (d) & explanation
The answer is 20, which is none of the given numbers (d). Step 1: choose the Principal. Only 2 candidates are eligible, so 2 ways. Step 2: choose two Vice-Principals from the remaining 5 people (everyone is eligible). Pairs from 5 = 5 × 4 ÷ 2 = 10 ways. We divide by 2 because the two posts are equal and order does not matter. Step 3: total = 2 × 10 = 20. 20 is not among (a), (b) or (c), so the answer is (d).
Tip: once a person is picked for one post, remove them before choosing the next. For choosing 2 from n without order, use n × (n − 1) ÷ 2.
Answer as per the official UPSC answer key.
A student has to opt for 2 subjects out of 5 subjects for a course, namely, Commerce, Economics, Statistics, Mathematics I and Mathematics II. Mathematics II can be offered only if Mathematics I is also opted. The number of different combinations of two subjects which can be opted is
Answer (c) & explanation
There are 7 combinations (c). Step 1: count all possible pairs of 2 subjects from 5. That is 5 × 4 ÷ 2 = 10 pairs. Step 2: remove pairs that break the rule. Maths II can be taken only with Maths I. So pairs with Maths II but not Maths I are not allowed: Maths II with Commerce, with Economics, and with Statistics. That is 3 pairs. Step 3: allowed pairs = 10 − 3 = 7. Options (a), (b) and (d) do not match.
Tip: when there is a restriction, count everything first, then subtract the forbidden cases. This is often faster than counting the allowed cases one by one.
Answer as per the official UPSC answer key.
Usha runs faster than Kamala, Priti runs slower than Swati, Swati runs slower than Kamala. Who is the slowest runner ?
Answer (b) & explanation
Priti is the slowest (b). Step 1: write each clue as a comparison. Usha > Kamala. Swati > Priti. Kamala > Swati. Step 2: link them into one line, fastest to slowest: Usha > Kamala > Swati > Priti. Step 3: the slowest is Priti. Options (a), (c) and (d) are faster than Priti.
Tip: change "runs slower than" into ">" pointing the right way. "Priti runs slower than Swati" means Swati > Priti. Turning every clue into the same symbol avoids mistakes. Then join the chains at the shared name.
Answer as per the official UPSC answer key.
There are 5 tasks and 5 persons. Task-1 cannot be assigned to either person-1 or person-2. Task-2 must be assigned to either person-3 or person-4. Every person is to be assigned one task. In how many ways can the assignment be done ?
Answer (c) & explanation
There are 24 ways (c). Step 1: Task-2 must go to person-3 or person-4: 2 ways. Step 2: Task-1 cannot go to person-1 or person-2, so it must go to one of persons 3, 4 or 5. One of 3 or 4 is already used by Task-2, so 2 choices are left. Step 3: the remaining 3 tasks go to the remaining 3 persons in 3 × 2 × 1 = 6 ways. Step 4: total = 2 × 2 × 6 = 24. Options (a), (b) and (d) miss or double a step.
Tip: in assignment problems, place the most restricted items first (here Task-2, then Task-1). Then the rest can be arranged freely: n items in n! ways.
Answer as per the official UPSC answer key.
A, B, C, D, E and F are cousins. No two cousins are of the same age, but all have birthdays on the same day of the same month. The youngest is 17 years old and the oldest E is 22 years old. F is somewhere between B and D in age. A is older than B. C is older than D. A is one year older than C.
Which one of the following is possible ?
Answer (b) & explanation
F can be 18 years old (b). Step 1: all six have the same birthday and different ages from 17 to 22. So their ages are exactly 17, 18, 19, 20, 21, 22. E is the oldest, 22. Step 2: A is one year older than C. A is older than B, and C is older than D. A and C must be high to have people below them, so A = 21 and C = 20. Step 3: B, D and F share 17, 18, 19, with F between B and D. So F = 18. Options (a), (c) and (d) fail: D is 17 or 19, and F cannot be 19 or 20.
Tip: when ages are whole numbers in a fixed range with no repeats, list them all first.
Answer as per the official UPSC answer key.
(Same information as the question above.)
What is the number of logically possible orders of all six cousins in terms of increasing age ?
Answer (b) & explanation
There are 2 possible orders (b). Step 1: from the question above, E = 22, A = 21, C = 20 and F = 18. Step 2: B and D take the ages 17 and 19, with F in between. Either B is 17 and D is 19, or D is 17 and B is 19. Both fit all the clues: A is older than B, and C is older than D, in both cases. Step 3: so there are 2 orders. Options (a), (c) and (d) do not match.
Tip: in follow-up questions, reuse the fixed results and look only at the people who are still free to move. Count their possible arrangements.
Answer as per the official UPSC answer key.
In a society it is customary for friends of the same sex to hug and for friends of opposite sex to shake hands when they meet. A group of friends met in a party and there were 24 handshakes.
Which one among the following numbers indicates the possible number of hugs ?
Answer (c) & explanation
1. Handshakes happen only between a man and a woman, so men × women = 24.
2. Hugs happen between each pair of the same sex. Among 4 people there are 3 + 2 + 1 = 6 pairs; among 6 people there are 5 + 4 + 3 + 2 + 1 = 15 pairs.
3. 4 men and 6 women (4 × 6 = 24 handshakes) give 6 + 15 = 21 hugs.
4. The other splits (3 and 8, 2 and 12, 1 and 24) give 31, 67 and 276 hugs, which are not options.
Answer as per the official UPSC answer key.
Two men, Anil and David, and two women, Shabnam and Rekha are in a sales group. Only two speak Tamil. The other two speak Marathi. Only one man and one woman can drive a car. Shabnam speaks Marathi. Anil speaks Tamil. Both Rekha and David can drive.
Which of the following statements is true ?
Answer (d) & explanation
One of the drivers speaks Tamil (d). Step 1: list what we know. Anil speaks Tamil. Shabnam speaks Marathi. Rekha and David are the drivers (one man, one woman). Step 2: exactly two speak Tamil and two speak Marathi. Anil has one Tamil and Shabnam one Marathi, so Rekha and David share the other Tamil and the other Marathi between them. Step 3: so one driver speaks Tamil and one speaks Marathi. That is option (d). Options (a), (b) and (c) need both drivers to speak the same language, which is impossible here.
Tip: in grouping puzzles, place the known people first. Then the remaining slots must be split among the unknown people.
Answer as per the official UPSC answer key.
Twelve people form a club. By picking lots, one of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is
Answer (d) & explanation
It cannot be predicted (d). Step 1: understand the rule. Every month, a lot is drawn from all twelve members to choose the host. Step 2: lots are drawn fresh each month, so the same person can be picked again, and someone may never be picked. Step 3: in one year (12 draws), a member might host zero, one, two or more dinners. No single number is certain. Option (a) is the trap: "one" would be true only if each member took a turn, which the question does not say. Options (b) and (c) are also only possibilities.
Tip: "picking lots" means chance. With chance, an exact count cannot be fixed; only an average could be estimated (here one a year on average).
12 dinners for 12 people does not mean one each. Lots are drawn at random every time.
Answer as per the official UPSC answer key.