CSAT 2026: every question, solved
80 questions from the official UPSC Prelims 2026 paper, in paper order. Tap an option; the answer and the reason appear instantly.
Question : X receives three coins of different denominations : 1, 2, 5, 10 and 20. If the total amount received by X is m, does X receive a coin of denomination 5?
Statement I : m is not a prime number.
Statement II : The sum of the digits of m is greater than 5.
Answer (a) & explanation
Statement II alone is enough; Statement I alone is not (a). Step 1: three different coins from 1, 2, 5, 10, 20 give ten totals. With a 5: 8, 16, 17, 26, 27, 35. Without a 5: 13, 23, 31, 32. Step 2: Statement I (m not prime): 8, 16, 26, 27, 35 have a 5, but 32 (2 + 10 + 20) does not. Mixed answers, so I fails. Step 3: Statement II (digit sum above 5): 8, 16, 17, 26, 27, 35 qualify, and every one has a 5. (13, 23, 31, 32 have digit sums 4, 5, 4, 5.) So II answers "yes". Options (b), (c) and (d) fail.
Tip: when cases are few, list them all. Then check each statement against the full list.
don't assume both statements are needed. Listing all ten cases takes thirty seconds and settles it.
Answer as per the official UPSC answer key.
Question : For two distinct real numbers x and y, which of them is bigger?
Statement I : x2 < y < 1
Statement II : y < √x < 1
Answer (d) & explanation
Even both statements together are not enough (d). Step 1: together they give x² < y < √x, with √x < 1, so x is between 0 and 1. Step 2: test x = 1/4. Then x² = 1/16 and √x = 1/2, so y can be anywhere between 0.0625 and 0.5. Step 3: y = 0.1 is smaller than x (0.25); y = 0.4 is bigger than x. Both fit, so we cannot say which is bigger. Options (a), (b) and (c) fail.
Tip: for numbers between 0 and 1, x² < x < √x. So x itself sits inside the range for y, and y can fall on either side. Test with x = 1/4; it gives clean numbers.
Answer as per the official UPSC answer key.
Question : If x and y are integers, then is x even?
Statement I : x2y2 is even.
Statement II : 1 + x2 + y2 is odd.
Answer (c) & explanation
Both statements together are needed (c). Step 1: Statement I: x²y² is even, so xy is even. That means at least one of x and y is even. x might be odd if y is even. Not enough. Step 2: Statement II: 1 + x² + y² is odd, so x² + y² is even. That means x and y have the same parity (both odd or both even). Not enough. Step 3: together: same parity, and at least one even, so both are even. Hence x is even. Options (a), (b) and (d) fail.
Tip: remember odd + odd = even, even + even = even, odd + even = odd. A square keeps the parity of its number.
Answer as per the official UPSC answer key.
Question : X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the numbers all of which are either from X or from Y. Is every number of T from Y?
Statement I : The sum of any two numbers belonging to T is even.
Statement II : If both p and q are picked from T, then (p – 1)q is even.
Answer (d) & explanation
Even both statements together are not enough (d). Step 1: Statement I: any two numbers in T add to an even number. That happens only if T is all odd or all even. Step 2: Statement II: (p − 1)q is even for any p, q in T. If T is all odd, p − 1 is even, so it holds. If T is all even, q is even, so it holds. Both cases still allowed. Step 3: an all-odd T (from X) fits both statements, and so does an all-even T (from Y). So we cannot say every number is from Y. Options (a), (b) and (c) fail.
Tip: test each statement on both possible cases. If a case survives every statement, the data is not enough.
Answer as per the official UPSC answer key.
Question : If x, y and z are integers, each greater than 1, then is x a prime number?
Statement I : xy2 = 116
Statement II : xz = 261
Answer (a) & explanation
Statement I alone is enough; Statement II alone is not (a). Step 1: Statement I: xy² = 116 = 2² × 29. y is above 1 and y² must divide 116, so y² = 4, y = 2, and x = 29, a prime. So I answers "yes". Step 2: Statement II: xz = 261 = 3² × 29. With x, z above 1, x could be 3, 9, 29 or 87. Some are prime (3, 29), some are not (9, 87). So II fails. Step 3: options (b), (c) and (d) fail.
Tip: break numbers into primes first. A squared variable can only take square factors, which often leaves just one choice.
Answer as per the official UPSC answer key.
Read the passage
‘Kalagram’, the cultural village set up at the Maha Kumbh Mela, unfolded as a mosaic of India’s diverse regions, each represented by seven meticulously crafted ‘Sanskriti Angans’—stepping through the grand portal was like entering another world. These thematic zones, inspired by iconic temples like the Dakshineshwar Kali Temple and the Brahma Mandir, were treasure troves of regional artistry. Bengal’s Pattachitra paintings, Assam’s bamboo crafts, Tamil Nadu’s Thanjavur paintings, and Madhya Pradesh’s tribal sculpture—all were showcased in these living galleries where 230 master artisans breathed life into them using age-old techniques, their hands shaping India’s ancient history into creations to behold.
Which of the following conclusions are valid?
- 1. Seven Sanskriti Angans, representing different regions of India, had been showcased in Kalagram.
- 2. Regional artistry was recognised via the inspiration drawn from iconic temples.
- 3. India’s ancient history had been crafted by the contemporary craftsmanship of 230 artisans into creations to behold.
- 4. Art forms from all regions of India had been showcased in these living galleries.
Select the answer using the code given below.
Answer (a) & explanation
Conclusions 1 and 2 are valid (a). Step 1: the passage says Kalagram had seven "Sanskriti Angans" representing India's diverse regions (1 is valid). Step 2: it says these thematic zones were inspired by iconic temples like Dakshineshwar Kali Temple and Brahma Mandir, and were treasure troves of regional artistry (2 is valid). Step 3: conclusion 3 calls the craft "contemporary", but the artisans used "age-old techniques". Conclusion 4 says art from "all regions"; only some are named. So options (b), (c) and (d) fail.
Tip: watch for single-word changes: "age-old" became "contemporary", and "diverse" became "all". Kalagram was set up by the Ministry of Culture at the Maha Kumbh in Prayagraj (13 January–26 February 2025).
Answer as per the official UPSC answer key.
Read the passage
‘Kalagram’, the cultural village set up at the Maha Kumbh Mela, unfolded as a mosaic of India’s diverse regions, each represented by seven meticulously crafted ‘Sanskriti Angans’—stepping through the grand portal was like entering another world. These thematic zones, inspired by iconic temples like the Dakshineshwar Kali Temple and the Brahma Mandir, were treasure troves of regional artistry. Bengal’s Pattachitra paintings, Assam’s bamboo crafts, Tamil Nadu’s Thanjavur paintings, and Madhya Pradesh’s tribal sculpture—all were showcased in these living galleries where 230 master artisans breathed life into them using age-old techniques, their hands shaping India’s ancient history into creations to behold.
Which one of the following statements is not correct?
Answer (a) & explanation
The incorrect statement is (a): paintings from four States are not mentioned. Step 1: the passage names only two paintings: Pattachitra of Bengal and Thanjavur paintings of Tamil Nadu. Step 2: Assam is mentioned for bamboo crafts and Madhya Pradesh for tribal sculpture, not paintings. So four States appear, but only two for paintings: (a) is wrong. Step 3: (b) matches "like entering another world"; (c) matches "living galleries"; (d) matches thematic zones "inspired by iconic temples". These are correct, so they are not the answer.
Tip: in "not correct" questions, check each detail against the text. Count carefully when an option gives a number.
Answer as per the official UPSC answer key.
The weight of X, in kg, is denoted by X. The weights of A, B, C, D, P, Q, R and S are measured. Given :
A + B + C + D = 17
A + C = 6
P + Q + S + D = 15
P + Q + R + B = 17
P = R and Q = S
Which one of the following statements is correct?
Answer (b) & explanation
1. From the first two equations: B + D = 11.
2. Put R = P and S = Q, then add the last two equations: 3P + 3Q + B + D = 32, so 3(P + Q) = 21 and P + Q = 7.
3. 7 > 6 = A + C, so (b) is true. (a) fails because 11 > 7. P and Q separately cannot be fixed, so (c) and (d) cannot be claimed.
Answer as per the official UPSC answer key.
How many words can one form by shuffling the letters of the word QUEUE, if Q is always followed by U? The words thus formed need not necessarily have any meaning.
Answer (d) & explanation
12 words can be formed (d). Step 1: Q must always be followed by U, so tie them together as one block, QU. Step 2: the letters of QUEUE are Q, U, E, U, E. After making the block, we have QU, U, E, E: four items. Step 3: four items can be arranged in 4 × 3 × 2 × 1 = 24 ways. But the two Es are identical, so swapping them gives the same word: 24 ÷ 2 = 12. Options (a), (b) and (c) miss arrangements or divide wrongly.
Tip: "always together" means treat them as one block. Then divide by the factorial of each repeated letter's count.
don't halve again for the Us. One U is inside the block, so the two Us are no longer interchangeable items.
Answer as per the official UPSC answer key.
X, Y and Z jump forward 4', 6' and 5', respectively. At 8 AM, they all land on mark 199'. How many times will they all land on the same mark (need not be at the same moment) between mark 195' and 1000', if all of them cross mark 1000' by 9 AM?
Answer (d) & explanation
They land on a common mark 14 times (d). Step 1: all three are at 199' together. After that, they share a mark every LCM(4, 6, 5) = 60'. So common marks are 199, 259, 319, … Step 2: the largest common mark up to 1000' is 199 + 60k ≤ 1000, so k ≤ 13 (199 + 780 = 979). Step 3: k = 0 to 13 gives 14 marks. The mark before 199 would be 139', which is below 195', so it does not count. Options (a), (b) and (c) miss the starting mark or the end.
Tip: common points repeat at the LCM. Count from the first shared point, and include both ends when they fall inside the range.
199' itself counts. It lies between 195' and 1000'.
Answer as per the official UPSC answer key.
Read the passage
Sport is not just about winning medals or getting jobs through a sports quota. Today’s generation is struggling with issues like depression and anxiety. Parents often say that their children are inactive and rarely leave the house. Sport can help tackle these problems. From sport you can learn time management, fitness, teamwork, coordination, and so much more. We need to develop a culture in which sport is seen as a way of life—a path to building a healthier, happier society.
Which of the following conclusions are valid?
- 1. Sport is more than just games; it is a way of life.
- 2. Sport can help mitigate the problems of seclusion among the young.
- 3. Earning laurels in sport can help one secure a job on the basis of an assigned quota.
- 4. Standard corporate sector skills cannot be learnt through sport.
Select the answer using the code given below.
Answer (d) & explanation
Conclusions 1, 2 and 3 are valid (d). Step 1: conclusion 1 matches the last line: sport should be seen as "a way of life". Step 2: conclusion 2 follows from parents saying children are inactive and "rarely leave the house", which sport can help fix. Conclusion 3 follows from the mention of "getting jobs through a sports quota". Step 3: conclusion 4 says corporate skills cannot be learnt through sport. But the passage says sport teaches time management and teamwork, so 4 contradicts it. Options (a), (b) and (c) fail.
Tip: a conclusion that contradicts the passage fails at once. The Khelo India and Fit India movements promote sport as a way of life.
Answer as per the official UPSC answer key.
Read the passage
Sport is not just about winning medals or getting jobs through a sports quota. Today’s generation is struggling with issues like depression and anxiety. Parents often say that their children are inactive and rarely leave the house. Sport can help tackle these problems. From sport you can learn time management, fitness, teamwork, coordination, and so much more. We need to develop a culture in which sport is seen as a way of life—a path to building a healthier, happier society.
Which of the following statements is/are correct?
- 1. Parents are not encouraging enough when it comes to children playing sport.
- 2. Participation in sporting activities can help develop life skills.
- 3. Sport as a way of life can help evolve the very nature of society itself.
Select the answer using the code given below.
Answer (b) & explanation
Statements 2 and 3 are correct (b). Step 1: statement 2 matches the line that sport teaches "time management, fitness, teamwork, coordination". These are life skills. Step 2: statement 3 matches the closing line: sport as a way of life is "a path to building a healthier, happier society". Step 3: statement 1 blames parents for not encouraging sport. The passage only says parents report that children are inactive; it never blames them. So options (a), (c) and (d) fail.
Tip: do not turn a reporter into a culprit. When the passage quotes someone's complaint, it does not mean that person caused the problem.
Answer as per the official UPSC answer key.
A toy T jumps forward or backward. In each forward jump, it moves 5' forward whereas in each backward jump, it moves 2' backward. If in 31 jumps, T moves exactly 15' forward, then what is the difference of the number of forward and backward jumps?
Answer (d) & explanation
The difference is 9 jumps (d). Step 1: let f be forward jumps and b backward jumps. Total jumps: f + b = 31. Net movement: 5f − 2b = 15. Step 2: put b = 31 − f: 5f − 2(31 − f) = 15, so 5f − 62 + 2f = 15, giving 7f = 77 and f = 11. Then b = 20. Step 3: difference = 20 − 11 = 9. Check: 5 × 11 − 2 × 20 = 55 − 40 = 15 ✓. Options (a), (b) and (c) fail.
Tip: two unknowns need two equations: one for the count and one for the total effect. Always check your answer in both.
Answer as per the official UPSC answer key.
Eight persons P, Q, R, S, T, U, V and W sit around a round table in eight different seats placed with equal distance between any two consecutive seats. Both P and R are adjacent to Q. Both T and R are adjacent to S. Both U and W are adjacent to V. S and W are on opposite chairs. If while going in the clockwise direction around the table from P, one meets R before T, then how many persons shall Q cross while moving in the clockwise direction around the table before meeting W?
Answer (a) & explanation
1. P–Q–R and R–S–T join into one run P, Q, R, S, T. Clockwise from P, R comes before T, so number the seats 1 to 8 clockwise: P 1, Q 2, R 3, S 4, T 5.
2. U, V, W take seats 6, 7, 8 with V in the middle (seat 7). W must face S (seat 4), so W is at seat 8 and U at 6.
3. Clockwise from Q: R, S, T, U, V, then W. Q crosses 5 persons.
Answer as per the official UPSC answer key.
The top of a table is rectangular and its dimensions are 6′ × 10′. Two rectangular portions of the table top are painted in blue colour; both these portions have dimensions 2.5′ × 8′ and each of them has exactly two sides common with two edges of the table top. If the table is fixed to the ground and the remaining portion of the table top is painted in white, how many different patterns are possible when observed from above?
Answer (b) & explanation
Four patterns are possible (b). Step 1: each blue strip is 2.5′ × 8′. Its 8′ side cannot lie along the 6′ edge, so it lies along a 10′ edge, and it touches two edges, so it sits in a corner. Step 2: two strips on the same 10′ edge would need 8 + 8 = 16′, more than 10′, so they would overlap and merge into one shape. So one strip goes along each 10′ edge. Step 3: each strip can sit at the left or right end of its edge: 2 × 2 = 4 patterns. The table is fixed, so mirror images count as different. Options (a), (c) and (d) miscount.
Tip: in arrangement puzzles, first use the sizes to rule out positions. Then count the free choices and multiply.
Answer as per the official UPSC answer key.
Read the passage
How is deflation done? Most countries use a method called ‘double deflation’, where input and output prices are deflated separately. Consider a manufacturer importing oil for use in production. If oil prices fall, output prices do not and quantities remain the same, real value added should not change. But if the same deflator is used for inputs and outputs, as in India, it would look as if the manufacturer had become more productive.
Which of the following statements is/are correct?
- 1. Real value should not change in the instance of static output cost and unchanged quantities against falling oil prices.
- 2. Deflators are to be used separately for inputs and outputs, and this is a practice universally adopted by all economies.
Select the answer using the code given below.
Answer (d) & explanation
Neither statement is correct (d). Step 1: the passage says if oil prices fall while output prices and quantities stay the same, real value added should not change. Statement 1 changes this to "real value" and "static output cost", which distorts the idea. So 1 is not correct as worded. Step 2: statement 2 says separate deflators are used "universally" by all economies. But the passage says India uses the same deflator for both. So 2 is false. Step 3: options (a), (b) and (c) fail.
Tip: in economic passages, exact terms matter: "value added" is not "value", and "price" is not "cost". "Universally" is disproved by a single exception, here India.
Answer as per the official UPSC answer key.
Read the passage
How is deflation done? Most countries use a method called ‘double deflation’, where input and output prices are deflated separately. Consider a manufacturer importing oil for use in production. If oil prices fall, output prices do not and quantities remain the same, real value added should not change. But if the same deflator is used for inputs and outputs, as in India, it would look as if the manufacturer had become more productive.
Which of the following assumptions is/are valid?
- 1. Deflation strategies can be used to make manufacturers appear to be doing better than they actually are.
- 2. When input and output prices are both deflated against a single input price, it is referred to as ‘double deflation’.
Select the answer using the code given below.
Answer (a) & explanation
Only assumption 1 is valid (a). Step 1: the passage says that using one deflator for inputs and outputs, as in India, makes it "look as if the manufacturer had become more productive". So deflation methods can make firms appear better than they are (1). Step 2: assumption 2 says double deflation means deflating both against a single price. But the passage defines double deflation as deflating inputs and outputs separately. So 2 reverses the definition. Step 3: options (b), (c) and (d) fail.
Tip: check definitions word for word against the passage. Deflating means removing the effect of price changes to find real growth, as in real GDP.
Answer as per the official UPSC answer key.
A pattern formed by two characters a and b is repeated more than once in the following string :
× b × a × a × × a × a × bab
What is × × in the 7th and 8th positions from the left in the above string?
Answer (d) & explanation
Positions 7 and 8 are bb (d). Step 1: the string has 15 places, so try a block of 5 letters repeated three times: (× b × a ×)(a × × a ×)(a × b a b). Step 2: read each column across the three blocks. Position 1: ×, a, a → a. Position 2: b, ×, × → b. Position 3: ×, ×, b → b. Position 4: a, a, a → a. Position 5: ×, ×, b → b. Every known letter fits, so the block is abbab. Step 3: places 7 and 8 are the 2nd and 3rd letters of the second block: b, b. Options (a), (b) and (c) fail.
Tip: for repeating patterns, try block sizes that divide the total length. Stack the blocks and fill each column from the known letters.
a block of 3 fails: the 2nd column would need both b and a.
Answer as per the official UPSC answer key.
If 10m × 1000 × n = 7525 × 2532 × 3275, where n is not divisible by 10, then the value of m is
Answer (b) & explanation
m is 111 (b). Step 1: each 10 needs one 2 and one 5. Count the 5s: 75²⁵ = (3 × 5²)²⁵ = 3²⁵ × 5⁵⁰, and 25³² = 5⁶⁴. Total 5s = 50 + 64 = 114. Step 2: count the 2s: 32⁷⁵ = (2⁵)⁷⁵ = 2³⁷⁵. Far more than 114. Step 3: so the right side has exactly 114 factors of 10 (n has no more, since n is not divisible by 10). The left side has 10ᵐ × 1000 = 10^(m + 3). So m + 3 = 114 and m = 111. Options (a), (c) and (d) fail.
Tip: the number of 10s equals the smaller count of 2s and 5s. Do not forget the extra 10s hidden in 1000.
remember the 1000 on the left: it already holds 103.
Answer as per the official UPSC answer key.
The speed of a train T is 100 km per hour and the speed of a person P is 4 km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T. If P travels along the opposite direction of T, then in how much time does T cross P, in seconds, approximately?
Answer (c) & explanation
The train crosses him in about 13.85 seconds (c). Step 1: same direction: relative speed = 100 − 4 = 96 km/h. The train takes 15 seconds to pass him. Step 2: opposite direction: relative speed = 100 + 4 = 104 km/h. The train's length stays the same, so time falls in proportion. Step 3: time = 15 × 96 ÷ 104 = 1440 ÷ 104 ≈ 13.85 seconds. Options (a), (b) and (d) are close numbers from rounding or arithmetic slips.
Tip: when the distance (train length) is the same, time is inversely proportional to relative speed. No need to find the length itself.
Answer as per the official UPSC answer key.
For 1/3 < x < y < 2, which of the following statements is/are always correct?
- I. x + 1/x < y + 1/y
- II. √(1 + y2)/y < √(1 + x2)/x
Select the answer using the code given below.
Answer (b) & explanation
Only statement II is always correct (b). Step 1: statement I: t + 1/t falls until t = 1, then rises. So it is not always increasing in this range. Test x = 1/2, y = 1: x + 1/x = 2.5, y + 1/y = 2. Here 2.5 is not less than 2, so I fails. Step 2: statement II: √(1 + y²)/y = √(1/y² + 1). As y grows, 1/y² shrinks, so this value gets smaller. Since x < y, the y-value is always smaller than the x-value. II always holds. Step 3: options (a), (c) and (d) fail.
Tip: "always correct" needs to hold for every case; one counter-example kills it. Rewrite expressions to see if they rise or fall.
the range crosses 1, where t + 1/t turns around. "Always" fails with one counter-example.
Answer as per the official UPSC answer key.
What is the minimum number of times one needs to measure to get 298 litres of water from a tank, if the measuring cylinders have capacities 1 litre, 6 litres, 25 litres and 100 litres?
Answer (b) & explanation
The minimum is 5 measures (b). Step 1: adding only, the best is 2 × 100 + 2 × 25 + 8 × 6 = 298, which needs 12 measures. That is not an option, so think about taking water out too. Step 2: 298 = 3 × 100 − 2 × 1. Pour in 100 litres three times, then remove 1 litre twice: 5 measures. Step 3: could 4 work? 3 × 100 leaves 2 litres to remove, and no single cylinder holds 2 litres, so 4 is impossible. Options (a), (c) and (d) fail.
Tip: when adding gives too many steps, try overshooting and subtracting. Measuring questions often allow both pouring in and taking out.
Answer as per the official UPSC answer key.
There are four types of weights, namely 1 kg, 2 kg, 5 kg and 10 kg. What is the maximum number of different ways one can measure 20 kg, if at least eight but not more than eleven weights of 1 kg are to be used while measuring?
Answer (b) & explanation
There are 8 ways (b). Step 1: with eight 1 kg weights, we need 12 kg from 2, 5 and 10 kg weights (no more 1s): 10 + 2, 5 + 5 + 2, and six 2s: 3 ways. Step 2: with nine 1 kg, we need 11 kg: only 5 + 2 + 2 + 2: 1 way. Step 3: with ten 1 kg, we need 10 kg: 10, 5 + 5, five 2s: 3 ways. With eleven 1 kg, we need 9 kg: 5 + 2 + 2: 1 way. Total = 3 + 1 + 3 + 1 = 8. Options (a), (c) and (d) miscount.
Tip: fix one variable at a time and count the rest. Here, fixing the number of 1 kg weights keeps the cases clean.
an odd remainder needs exactly one 5 (two or more would be too much or leave an odd gap).
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 cut on a solid object divides the object into two parts where the new surfaces thus produced are plane. On the other hand, one single cut can be used to cut more than one object at a time. In an experiment, the total number of pieces produced by applying n cuts is denoted by xₙ. The experiment is performed on a solid cube where pieces remain unmoved after each cut. In this experiment, if after the third cut, the pieces are identical, then which of the following is not a possible value for x₄?
Answer (a) & explanation
16 is not possible (a). Step 1: three plane cuts that leave identical pieces can give 4 slabs (all parallel), 6 equal pieces (two parallel plus one across), or 8 small cubes (one in each direction). Step 2: a fourth cut can add at most one piece for each piece it passes through. From 4 slabs: 5 to 8 pieces. From 6 pieces: up to 12. From 8 cubes: a single plane can pass through at most 7 of the 8 small cubes, so at most 15. Step 3: so 5, 8 and 12 are possible, but 16 would need the cut to split all 8 cubes, which no plane can do. Options (b), (c) and (d) are possible values.
Tip: a plane can never cut all 8 octants of a cube at once; it misses at least one.
Answer as per the official UPSC answer key.
The class average x in a test increases by 4 when the score of a student is rectified, whose corrected score is 100 instead of 0. Later, the score of another student was found to have been recorded as 81 in place of 56. If there are no other corrections and the final corrected average is y, then y − x is
Answer (b) & explanation
y − x is 3 (b). Step 1: one student's score rose by 100 (from 0 to 100), and the average rose by 4. So the class has 100 ÷ 4 = 25 students. Step 2: the second correction changes 81 to 56: the total falls by 25 marks. Shared by 25 students, the average falls by 1. Step 3: overall, the average went up by 4 and then down by 1: y − x = 3. Options (a), (c) and (d) fail.
Tip: change in average = change in total ÷ number of people. Use the first correction to find the class size, then reuse it.
x is the average before both corrections, so both changes count.
Answer as per the official UPSC answer key.
Read the passage
When SARS-CoV-2 was first detected in 2019, it was a truly novel virus for the world. At that time, no one in the world had been exposed to SARS-CoV-2 or had specific immunity against it. In contrast, people across the world have been exposed to HMPV for decades and the virus is well-studied. HMPV and SARS-CoV-2 belong to two very different virus families with fundamentally different characteristics and epidemiology, with strong seasonality seen in HMPV, unlike SARS-CoV-2. Both viruses cause different severity of symptoms, particularly over the long term, and the affected population segments do not fully overlap. In general, HMPV causes milder illness with deaths being very rare and with no long-term post-viral symptoms.
Which of the following conclusions is/are valid?
- 1. Though SARS-CoV-2 and HMPV are similar viruses with somewhat different epidemiology, the former became a pandemic because it was novel and people had not been exposed to it in the past.
- 2. The two viruses have fundamentally different impacts on human populations and should not therefore be dealt with in a similar manner.
Select the answer using the code given below.
Answer (b) & explanation
Only conclusion 2 is valid (b). Step 1: the passage stresses that SARS-CoV-2 and HMPV belong to "two very different virus families" with different seasonality, severity and affected groups. So they affect people differently and should not be handled the same way (2). Step 2: conclusion 1 calls them "similar viruses", which contradicts the passage. Step 3: so options (a), (c) and (d) fail.
Tip: one wrong word ("similar") can sink a long statement. HMPV was first identified in 2001 in the Netherlands; India reported cases in January 2025, and the Health Ministry said there was no unusual rise in illness.
Answer as per the official UPSC answer key.
Read the passage
When SARS-CoV-2 was first detected in 2019, it was a truly novel virus for the world. At that time, no one in the world had been exposed to SARS-CoV-2 or had specific immunity against it. In contrast, people across the world have been exposed to HMPV for decades and the virus is well-studied. HMPV and SARS-CoV-2 belong to two very different virus families with fundamentally different characteristics and epidemiology, with strong seasonality seen in HMPV, unlike SARS-CoV-2. Both viruses cause different severity of symptoms, particularly over the long term, and the affected population segments do not fully overlap. In general, HMPV causes milder illness with deaths being very rare and with no long-term post-viral symptoms.
Which of the following reflect the intent of the writer in the above passage?
- 1. To evolve methodologies for objective analysis of the two viruses
- 2. To establish the epidemiological similarities and differences between the two viruses
- 3. To offer a better understanding of the remedies of HMPV when analysed in conjunction with SARS-CoV-2
Select the answer using the code given below.
Answer (d) & explanation
None of the three reflects the writer's intent (d). Step 1: the writer only contrasts the two viruses: HMPV is old and well-studied, seasonal and usually mild; SARS-CoV-2 was new. The aim is to show they are different, easing fear about HMPV. Step 2: statement 1, evolving methods of analysis, is not the aim. Statement 2 speaks of similarities and differences, but the passage stresses only differences. Step 3: statement 3, remedies for HMPV, is never discussed. So options (a), (b) and (c) fail.
Tip: intent questions ask "why did the writer write this?" Here, the answer is reassurance through contrast, which none of the statements captures.
Answer as per the official UPSC answer key.
Read the passage
When SARS-CoV-2 was first detected in 2019, it was a truly novel virus for the world. At that time, no one in the world had been exposed to SARS-CoV-2 or had specific immunity against it. In contrast, people across the world have been exposed to HMPV for decades and the virus is well-studied. HMPV and SARS-CoV-2 belong to two very different virus families with fundamentally different characteristics and epidemiology, with strong seasonality seen in HMPV, unlike SARS-CoV-2. Both viruses cause different severity of symptoms, particularly over the long term, and the affected population segments do not fully overlap. In general, HMPV causes milder illness with deaths being very rare and with no long-term post-viral symptoms.
Which of the following statements reflect the logical and rational inferences that can be drawn from the passage?
- 1. HMPV has, historically, had longer documentation of studies when compared with SARS-CoV-2.
- 2. The two viruses are different from each other and this results in markedly different outcomes amongst those affected.
- 3. Long-term impacts of the two viruses are dissimilar and this is an important differentiator between them.
- 4. One of the common factors between the two viruses is seasonal specificity.
Select the answer using the code given below.
Answer (b) & explanation
Inferences 1, 2 and 3 follow (b). Step 1: HMPV has been around "for decades" and is "well-studied", while SARS-CoV-2 was new in 2019. So HMPV has a longer record of study (1). Step 2: the viruses are "fundamentally different" and cause different severity, so outcomes differ (2). Step 3: severity differs "particularly over the long term"; HMPV has no long-term after-effects. So long-term impact is a key difference (3). Statement 4 fails: seasonality is seen in HMPV "unlike SARS-CoV-2", so it is a difference, not a common factor. Options (a), (c) and (d) fail.
Tip: "unlike" signals a difference. Do not turn it into a similarity.
Answer as per the official UPSC answer key.
Three variables x, y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression {(x × y) + z}; then M – N is
Answer (c) & explanation
M − N is 13 (c). Step 1: to make (x × y) + z largest, multiply the two biggest numbers and add the next one: M = 5 × 4 + 3 = 23. (Check: 5 × 3 + 4 = 19 and 4 × 3 + 5 = 17 are smaller.) Step 2: to make it smallest, multiply the two smallest and add the next smallest: N = 2 × 3 + 4 = 10. (Check: 2 × 4 + 3 = 11 is bigger.) Step 3: M − N = 23 − 10 = 13. Options (a), (b) and (d) come from other pairings.
Tip: multiplication has a bigger effect than addition, so give the product the biggest (or smallest) numbers. Quickly check one or two other pairings to be safe.
Answer as per the official UPSC answer key.
Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x2 and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?
Answer (b) & explanation
z equals 1/5 (b). Step 1: y is directly proportional to x², so y = k × x². With x = 5 and y = 50: 50 = k × 25, so k = 2. Step 2: y = 98 means 2x² = 98, so x² = 49 and x = 7. Step 3: x is inversely proportional to z, so x × z stays the same. At the start: 5 × 7/25 = 7/5. Now 7 × z = 7/5, so z = 1/5. Options (a), (c) and (d) fail.
Tip: "directly proportional" means the ratio stays fixed; "inversely proportional" means the product stays fixed. Find the constant first, then use it.
Answer as per the official UPSC answer key.
Read the passage
India is starting to deploy AI for critical use cases such as weather forecasting, pest detection and control, and crop yield optimisation. However, penetration is limited to a small subset of tech-savvy farmers. In the US and in Europe, generative AI tools have started offering precision farming at scale, integrating large datasets to provide real-time agronomic insights. For at-scale integration and accessibility of AI tools in India, it would be helpful to develop Indian languages-based AI tools for smallholder farmers, partner with AgTechs to create affordable AI solutions, and disseminate AI-based advisory services through government programmes.
Which of the following assumptions is/are valid?
- 1. Agricultural productivity has marched ahead in the West because of the economies of scale facilitated by the adoption of AI tools.
- 2. Affordable AI tools rendered available in local languages can help AI-based solutions reach more and more small farmers.
- 3. Though penetration is as yet low, critical application areas deploying AI tools are already in use in India.
Select the answer using the code given below.
Answer (d) & explanation
Assumptions 2 and 3 are valid (d). Step 1: the passage suggests Indian-language AI tools, affordable solutions with AgTechs, and government advisory services to reach smallholders. This rests on assumption 2: affordable, local-language tools can reach more small farmers. Step 2: it opens by saying India is already using AI for weather forecasting, pest control and crop yields, though only among tech-savvy farmers. That is assumption 3. Step 3: assumption 1 says Western farm productivity rose because of AI and economies of scale. The passage only says AI tools "have started" offering precision farming there. So options (a), (b) and (c) fail.
Tip: reject cause-and-effect claims the passage does not make. "Started offering" is not "caused growth".
Answer as per the official UPSC answer key.
Read the passage
India is starting to deploy AI for critical use cases such as weather forecasting, pest detection and control, and crop yield optimisation. However, penetration is limited to a small subset of tech-savvy farmers. In the US and in Europe, generative AI tools have started offering precision farming at scale, integrating large datasets to provide real-time agronomic insights. For at-scale integration and accessibility of AI tools in India, it would be helpful to develop Indian languages-based AI tools for smallholder farmers, partner with AgTechs to create affordable AI solutions, and disseminate AI-based advisory services through government programmes.
Which of the following statements is/are not correct?
- 1. Tech-savvy farmers will drive the AgTech companies of the future.
- 2. The development of advisory services by the government programmes for the use of AI tools in agriculture would be helpful.
- 3. In the US and Europe, AI tools have replaced traditional agricultural practices.
- 4. The integration of large datasets for use in real-time agronomic analysis is already a reality.
Select the answer using the code given below.
Answer (a) & explanation
Statements 1 and 3 are not correct (a). Step 1: statement 1 says tech-savvy farmers will drive AgTech companies. The passage only says AI use is limited to such farmers; it never says they will drive companies. Not correct. Step 2: statement 3 says AI has replaced traditional farming in the US and Europe. The passage says AI tools have "started offering" precision farming, not replaced old methods. Not correct. Step 3: statement 2 matches the suggestion of government advisory services, and statement 4 matches "integrating large datasets to provide real-time agronomic insights" already happening in the West. So both are correct, and options (b), (c) and (d) fail.
Tip: in "not correct" questions, mark each statement true or false, then pick the false ones.
Answer as per the official UPSC answer key.
P, Q, R, S and T are ranked 1 to 5 (not necessarily in that order). The rank of P is 4, the rank of Q is not 5, the rank of R is 1, the rank of S is not 2, the rank of T is not 3. Then which of the following is/are correct?
- I. If the rank of S is 3, then that of T is 2.
- II. If the rank of Q is 3, then that of T is 5.
Select the answer using the code given below.
Answer (d) & explanation
Neither statement is correct (d). Step 1: P = 4 and R = 1 are fixed. Ranks 2, 3 and 5 remain for Q, S and T, with rules: Q is not 5, S is not 2, T is not 3. Step 2: statement I: if S = 3, then Q and T share 2 and 5. Q cannot be 5, so Q = 2 and T = 5, not 2. I is wrong. Step 3: statement II: if Q = 3, then S and T share 2 and 5. S cannot be 2, so S = 5 and T = 2, not 5. II is wrong. Options (a), (b) and (c) fail.
Tip: fix the known ranks first, then apply each "if" condition and let the "not" rules decide the rest. Write the small table on paper.
Answer as per the official UPSC answer key.
Two identical straight rods are painted in five distinct colours so that each of them gets divided into five equal parts along the length. In one of them, the portions are marked P1, P2, P3, P4 and P5 (not necessarily in that order) whereas in the other, they are marked Q1, Q2, Q3, Q4 and Q5 (not necessarily in that order). When the rods are kept parallel to each other side by side, P1 and Q3 match, P4 matches Q1 or Q2, and Q4 matches P3 or P5. If Q3 and Q5 are adjacent, which of the following is/are possible?
- I. Q3 is marked at the middle portion of the straight rod.
- II. P2 is marked at one of the extreme portions of the straight rod.
Select the answer using the code given below.
Answer (c) & explanation
Both statements are possible (c). Step 1: "possible" needs just one arrangement that fits all rules. Number the portions 1 to 5 on each rod. Step 2: try rod Q: Q1, Q2, Q3, Q5, Q4 and rod P: P2, P4, P1, P5, P3. Step 3: check the rules: P1 and Q3 both sit at position 3 ✓; P4 is at 2, beside Q2 ✓; Q4 is at 5, beside P3 ✓; Q3 and Q5 are adjacent ✓. In this arrangement, Q3 is in the middle (I) and P2 is at an end (II). So both are possible, and options (a), (b) and (d) fail.
Tip: for "possible" questions, build one valid example. For "must be true", you would need to check every case.
'possible' asks for one example, not for something that is always true.
Answer as per the official UPSC answer key.
Seven persons A, B, C, D, E, F and G travel by three cars X, Y, Z. A and another two of them travel by X. Only E travels with G. C travels by Z, but B does not travel by Y. Besides, A and B do not travel by the same car. Then which of the following are correct?
- I. No one travels alone.
- II. Only D travels with F.
- III. Only C travels with B.
Select the answer using the code given below.
Answer (b) & explanation
1. B is not in Y and not with A (in X), so B is in Z with C.
2. E and G form a car of their own; X already has A and Z has B and C, so E and G are in Y. D and F join A in X.
3. Cars: X = A, D, F; Y = E, G; Z = B, C. I and III are true. II is false, because A also travels with F.
Answer as per the official UPSC answer key.
There are four statements X, Y, Z and W. Their relations are as follows :
If X is incorrect, then so is Z; if Y is incorrect, then W is correct; if W is correct, then X is incorrect.
Which of the following is/are correct?
- I. If X is correct, then so is Y.
- II. If Z is correct, then it is not necessary that Y is correct.
Select the answer using the code given below.
Answer (a) & explanation
Only statement I is correct (a). Step 1: turn each rule around (the contrapositive, which is always equally true): "X incorrect → Z incorrect" becomes Z correct → X correct. "Y incorrect → W correct" becomes W incorrect → Y correct. "W correct → X incorrect" becomes X correct → W incorrect. Step 2: statement I: X correct → W incorrect → Y correct. So I is true. Step 3: statement II: Z correct → X correct → W incorrect → Y correct. So Y must be correct; II says it is not necessary, which is false. Options (b), (c) and (d) fail.
Tip: "If A then B" also means "if not B then not A". Chaining contrapositives solves most such puzzles.
only the contrapositive of an 'if … then' is safe. Here it links all four statements into one chain.
Answer as per the official UPSC answer key.
X and Y are two runners who run for the same duration of time on the same circular track. They started running at the same time in the same direction with uniform speeds. When X completed 7 rounds, Y did exactly 5. After completing 5 rounds, Y changed his direction and started running in the opposite direction with speed which is double of his earlier speed. On the other hand, X continued to run with the same speed. They stopped running when X completed exactly 21 rounds. How many times did X and Y meet after they had started and before they finally stopped?
Answer (a) & explanation
1. Phase 1, same direction, speeds 7 : 5. X gains 2 rounds, so they meet 2 times. The second meeting is at the start point, when Y turns.
2. Phase 2, opposite directions, speeds 7 and 10. X runs 14 more rounds, which takes 2 units of time. Together they cover 17 × 2 = 34 rounds, so they meet 34 times.
3. The 34th meeting is at the moment they stop, and that one is excluded. Total = 2 + 33 = 35.
read "before they finally stopped". The meeting at the stopping moment does not count.
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.
In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all the questions and got a score of 69. Had he been awarded 4 marks for a correct answer and 1 mark deducted for a wrong answer, he would have scored 84. How many questions were there in the question paper?
Answer (b) & explanation
There were 81 questions (b). Step 1: let c be correct and w wrong answers. First scheme: 5c − 2w = 69. Second scheme: 4c − w = 84. Step 2: from the second, w = 4c − 84. Put it in the first: 5c − 2(4c − 84) = 69, so 5c − 8c + 168 = 69, giving 3c = 99 and c = 33. Then w = 132 − 84 = 48. Step 3: he attempted all questions, so total = 33 + 48 = 81. Check: 165 − 96 = 69 ✓; 132 − 48 = 84 ✓. Options (a), (c) and (d) fail.
Tip: two marking schemes give two equations. Solve, then check both before answering.
Answer as per the official UPSC answer key.
Read the passage
The Juvenile Justice (Care and Protection of Children) Act, or the JJ Act, 2015 allows for the possibility for trying adolescents above 16 as adults if they are accused of committing a heinous offence. A heinous offence is one with a minimum punishment of seven years. Offences such as culpable homicide and causing death by negligence, which are common in drunken driving cases, are not heinous offences because they do not have a prescribed minimum punishment. The JJ Act, amended in 2021, now categorises an offence that has no minimum sentence, but has a maximum sentence of seven years or more as a serious offence which nonetheless, in the opinion of activists, does not merit the transfer of a case to the adult criminal justice system.
Which of the following conclusions is/are valid?
- 1. Only a ‘serious’ offence as categorised by the revised JJ Act, justifies the transfer of a case to the adult judicial system.
- 2. The JJ Act, 2021, categorises an offence as a serious offence based on the maximum sentence it carries, rather than on the minimum sentence.
Select the answer using the code given below.
Answer (b) & explanation
Only conclusion 2 is valid (b). Step 1: the passage says the 2021 amendment treats an offence with no minimum sentence but a maximum of seven years or more as a "serious offence". So the label depends on the maximum, not the minimum (2). Step 2: conclusion 1 says only a serious offence justifies transfer to the adult system. But the passage links transfer to heinous offences (minimum seven years), and activists say a serious offence "does not merit" transfer. So 1 fails. Step 3: options (a), (c) and (d) fail.
Tip: keep legal categories apart: heinous (minimum 7 years) versus serious (no minimum, maximum 7+ years). The JJ Act, 2015, allows children aged 16–18 accused of heinous offences to be tried as adults after assessment.
Answer as per the official UPSC answer key.
Read the passage
The Juvenile Justice (Care and Protection of Children) Act, or the JJ Act, 2015 allows for the possibility for trying adolescents above 16 as adults if they are accused of committing a heinous offence. A heinous offence is one with a minimum punishment of seven years. Offences such as culpable homicide and causing death by negligence, which are common in drunken driving cases, are not heinous offences because they do not have a prescribed minimum punishment. The JJ Act, amended in 2021, now categorises an offence that has no minimum sentence, but has a maximum sentence of seven years or more as a serious offence which nonetheless, in the opinion of activists, does not merit the transfer of a case to the adult criminal justice system.
Which of the following statements is/are correct?
- 1. If an offence has no minimum prescribed punishment, it cannot be considered heinous as per the JJ Act, 2015.
- 2. As per the JJ Act, 2021, an offence for which there is a provision for a maximum sentence of seven years or more, but no minimum sentence, is to be considered a serious offence.
Select the answer using the code given below.
Answer (c) & explanation
Both statements are correct (c). Step 1: statement 1: the passage says a heinous offence has a minimum punishment of seven years, and gives culpable homicide as an example that is not heinous "because they do not have a prescribed minimum punishment". So an offence with no minimum cannot be heinous: correct. Step 2: statement 2 repeats the 2021 amendment: no minimum sentence plus a maximum of seven years or more = serious offence. Correct. Step 3: so options (a), (b) and (d) fail.
Tip: when a passage gives a definition plus an example, use both to test statements. The example (culpable homicide) confirms the rule in statement 1.
Answer as per the official UPSC answer key.
An explosion takes place at a certain distance from an army camp. As soon as the sensor in the camp receives the sound of the explosion, a drone starts flying towards the spot of explosion. The drone clicks a picture from the spot and the camp receives it at the same time. Immediately another drone starts flying to the spot and it also sends a picture as soon as it reaches the spot. The two pictures were received at 5:02 PM and 5:05 PM, respectively. If the speed of the drones is 30 m/s, at what time did the explosion take place? Assume that the speed of sound is 300 m/s.
Answer (c) & explanation
The explosion happened at 4:58:42 PM (c). Step 1: drone 2 left at 5:02 (when picture 1 arrived) and reached the spot at 5:05. So one flight takes 180 seconds, and the distance = 30 × 180 = 5400 m. Step 2: drone 1 also flew 180 seconds and reached at 5:02, so it left at 4:59:00, the moment the sound reached the camp. Step 3: sound took 5400 ÷ 300 = 18 seconds. So the explosion was at 4:59:00 − 18 s = 4:58:42 PM. Option (a) forgets the sound delay. Options (b) and (d) miscalculate.
Tip: work backwards one step at a time. Pictures arrive instantly, so only flight time and sound travel time matter.
don't stop at 4:59:00. That is when the sound reached the camp, not when the blast happened.
Answer as per the official UPSC answer key.
The digit in the unit place of the number 6129 × 7307 is
Answer (c) & explanation
The unit digit is 8 (c). Step 1: every power of 6 ends in 6 (6, 36, 216, …). Step 2: powers of 7 end in a cycle of four: 7, 9, 3, 1. Divide 307 by 4: remainder 3. So 7³⁰⁷ ends in the third digit of the cycle: 3. Step 3: 6 × 3 = 18, so the unit digit is 8. Options (a), (b) and (d) use the wrong place in the cycle.
Tip: digits 0, 1, 5 and 6 keep the same unit digit for every power. For others, find the cycle of four and use the remainder of the power divided by 4.
Answer as per the official UPSC answer key.
A person saves 10% of his salary every month. If his salary increases by 12% and the expenditure increases by 10%, then what will be the change in his saving per month?
Answer (b) & explanation
His saving rises by 30% (b). Step 1: take salary = 100. He saves 10%, so saving = 10 and expenditure = 90. Step 2: new salary = 112 (12% more). New expenditure = 99 (10% more than 90). Step 3: new saving = 112 − 99 = 13. Saving goes from 10 to 13, a rise of 3 on 10 = 30%. Options (a), (c) and (d) fail.
Tip: take 100 for the salary and split it into saving and spending. Small percentage changes in big amounts can cause large changes in the small leftover.
the saving is a small base. A 2% gap between the two growth rates becomes a 30% change in saving.
Answer as per the official UPSC answer key.
P has a son and a daughter. S is the mother of T. S is R's spouse. Q and R are children of P. Then how is Q related to S?
Answer (d) & explanation
Q is the sister of S's husband (d). Step 1: S is T's mother, so S is a woman. S is R's spouse, so R is a man. Step 2: Q and R are P's children, and P has one son and one daughter. R is the son, so Q is the daughter. Step 3: Q is R's sister, and R is S's husband. So Q is the sister of the husband of S (her sister-in-law). Options (a), (b) and (c) give wrong relations.
Tip: in blood-relation puzzles, first fix genders from clues like "mother" and "spouse". Then draw a small family tree.
Answer as per the official UPSC answer key.
How many three-digit numbers can be expressed as an integral power of 2?
Answer (c) & explanation
Three three-digit numbers are powers of 2 (c). Step 1: keep doubling from 1: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Step 2: only 128 (2⁷), 256 (2⁸) and 512 (2⁹) have three digits. 1024 (2¹⁰) has four. Step 3: so the count is 3. Options (a), (b) and (d) miscount.
Tip: learn powers of 2 up to 2¹⁰ = 1024. Between any two powers of 10 there are always three or four powers of 2, since 2¹⁰ is about 10³.
Answer as per the official UPSC answer key.
Read the passage
The key source of the battle for clean skies and clear lungs is the fuel we burn—from household Chulhas to the thermal power plants. In most cases, it is biomass or coal. The Supreme Court banned the use of pet coke—the dirtiest of such fuels. The Delhi Government banned the use of coal, which was later extended to the entire National Capital Region. It was also agreed that the thermal power plants would clean up or shut down. Action on this has been patchy to say the least. The lesson from the transition to CNG is that people need alternatives for a ban to be effective. When diesel buses were stopped, CNG supply had to be assured. It also had to be feasible in terms of cost. The Supreme Court agreed that fiscal measures were needed to keep clean fuel cheaper than dirty fuel. Now even as coal is banned, the price of natural gas makes industry uncompetitive.
Which of the following inferences is/are correct?
- 1. The source of the energy we consume is the key to the battle for cleaner air.
- 2. Bans are effective where the will is strong and the people are convinced that such bans are for the greater good of society.
- 3. There is judicial approval for a policy that intervenes fiscally to facilitate benevolent pricing for cleaner fuel.
Select the answer using the code given below.
Answer (c) & explanation
Inferences 1 and 3 are correct (c). Step 1: the passage opens: the key to clean skies is "the fuel we burn". So the source of energy is central (1). Step 2: it says "the Supreme Court agreed that fiscal measures were needed to keep clean fuel cheaper than dirty fuel". That is judicial approval for pricing help (3). Step 3: inference 2 says bans work when people are convinced they are for the greater good. But the passage says bans work when people have alternatives at a feasible cost, like CNG. So options (a), (b) and (d) fail.
Tip: find the passage's own reason; do not accept a different reason that sounds good. Delhi's switch of buses to CNG followed Supreme Court orders around 2001–02.
Answer as per the official UPSC answer key.
Read the passage
The key source of the battle for clean skies and clear lungs is the fuel we burn—from household Chulhas to the thermal power plants. In most cases, it is biomass or coal. The Supreme Court banned the use of pet coke—the dirtiest of such fuels. The Delhi Government banned the use of coal, which was later extended to the entire National Capital Region. It was also agreed that the thermal power plants would clean up or shut down. Action on this has been patchy to say the least. The lesson from the transition to CNG is that people need alternatives for a ban to be effective. When diesel buses were stopped, CNG supply had to be assured. It also had to be feasible in terms of cost. The Supreme Court agreed that fiscal measures were needed to keep clean fuel cheaper than dirty fuel. Now even as coal is banned, the price of natural gas makes industry uncompetitive.
Which of the following statements is/are correct?
- 1. Thermal power stations in Delhi were required to summarily shut down.
- 2. CNG supplies had to be assured once diesel vehicles were prohibited from plying.
- 3. The Supreme Court banned the use of coal across the National Capital Region.
Select the answer using the code given below.
Answer (c) & explanation
Only statement 2 is correct (c). Step 1: statement 2 matches: "When diesel buses were stopped, CNG supply had to be assured." Correct. Step 2: statement 1 says thermal plants had to summarily shut down. The passage says they would "clean up or shut down", a choice, not an immediate closure. Wrong. Step 3: statement 3 says the Supreme Court banned coal across NCR. The passage says the Delhi Government banned coal, later extended to NCR; the Court banned pet coke. Wrong. Options (a), (b) and (d) fail.
Tip: check who did what. Swapping the actor (Court versus Government) is a common trap in fact-based passages.
Answer as per the official UPSC answer key.
Consider the following statements :
Every red is blue. Every blue is green. Every green is yellow.
Which of the following statements denoted by P, Q and R are correct?
P. Every blue is yellow.
Q. Every red is green.
R. Every red is yellow.
Select the answer using the code given below.
Answer (d) & explanation
All three, P, Q and R, are correct (d). Step 1: "Every red is blue" means red is inside blue. Likewise blue is inside green, and green is inside yellow. So red ⊂ blue ⊂ green ⊂ yellow, like circles nested one inside another. Step 2: P: blue sits inside green, which sits inside yellow, so every blue is yellow ✓. Q: red ⊂ blue ⊂ green, so every red is green ✓. Step 3: R: red sits inside all the larger circles, so every red is yellow ✓. Options (a), (b) and (c) leave one out.
Tip: "every A is B" chains pass along: if A is inside B and B inside C, then A is inside C. Draw nested circles to check.
Answer as per the official UPSC answer key.
How many times does 5 appear in all two-digit positive integers?
Answer (b) & explanation
The digit 5 appears 19 times (b). Step 1: 5 in the tens place: 50, 51, …, 59 = 10 times. Step 2: 5 in the units place: 15, 25, 35, 45, 55, 65, 75, 85, 95 = 9 times (05 is not a two-digit number). Step 3: total = 10 + 9 = 19. The number 55 has two 5s, and both are counted. Option (a), 18, counts 55 once. Options (c) and (d) wrongly add 05 or 5.
Tip: count place by place. The question asks how many times the digit appears, not how many numbers contain it (that would be 18).
Answer as per the official UPSC answer key.
X travels 6 km on a bicycle with average speeds of 5 km per hour, 10 km per hour and 4 km per hour during the first 1 km, the next 2 km and the remaining 3 km, respectively. Y travels the same distances with average speeds of 4 km per hour, 10 km per hour and 5 km per hour, respectively. How many minutes early will Y complete the journey if both X and Y start at the same time?
Answer (d) & explanation
Y finishes 6 minutes earlier (d). Step 1: time = distance ÷ speed. X: 1 km at 5 km/h = 12 min; 2 km at 10 km/h = 12 min; 3 km at 4 km/h = 45 min. Total 69 min. Step 2: Y: 1 km at 4 km/h = 15 min; 2 km at 10 km/h = 12 min; 3 km at 5 km/h = 36 min. Total 63 min. Step 3: 69 − 63 = 6 minutes. Options (a), (b) and (c) fail.
Tip: work in minutes: time (min) = distance ÷ speed × 60. Y wins because Y is faster over the longer last stretch.
Answer as per the official UPSC answer key.
Seven cubes are identical in shape. Out of these, the weight of each of the six cubes is equal and the weight of the remaining cube is less than the weight of any other cube. A balance is used to identify the lightest cube. What is the minimum number of attempts required to distinguish the odd cube with certainty?
Answer (a) & explanation
Two weighings are enough (a). Step 1: put 3 cubes against 3, keeping one aside. If they balance, the cube kept aside is the light one: done in one weighing. Step 2: if one side is lighter, the odd cube is among those three. Weigh 1 against 1 of them. Step 3: the lighter pan holds the odd cube; if they balance, it is the third cube. So 2 weighings always work. One weighing (d) cannot cover all cases. Options (b) and (c) use more than needed.
Tip: each weighing has three outcomes (left, right, balance), so split into three groups. With n weighings you can find a light coin among up to 3ⁿ coins.
one weighing can only split the cubes into three groups (left, right, aside), so 7 cubes need at least two.
Answer as per the official UPSC answer key.
Read the passage
Previous waves of customer-service technology, including email and those pesky voice menus, stoked concerns of job losses, only for them to fail to materialise. AI could yet prove different. And if it does, its effects may be salutary. Human agents could be freed up to spend more time on creative and rewarding tasks, like using feedback to make products and services better—and thereby spend less time listening to irate customers!
Which one among the following statements most appropriately reflects the point of view of the given passage?
Answer (c) & explanation
The view is that AI might raise the value of human work by moving people to more fulfilling tasks (c). Step 1: the writer's own view is in the last lines: AI's effects "may be salutary" (good). Step 2: human agents "could be freed up" for "creative and rewarding tasks", like using feedback to improve products. That is (c). Step 3: option (a), no work left for humans, is extreme. Options (b) and (d) only describe the background about earlier technology, not the writer's point of view.
Tip: separate background from the author's view. Words like "may be salutary" usually mark the author's own opinion.
Answer as per the official UPSC answer key.
Read the passage
Previous waves of customer-service technology, including email and those pesky voice menus, stoked concerns of job losses, only for them to fail to materialise. AI could yet prove different. And if it does, its effects may be salutary. Human agents could be freed up to spend more time on creative and rewarding tasks, like using feedback to make products and services better—and thereby spend less time listening to irate customers!
Which of the following conclusions, made on the basis of the given passage, is/are correct?
- 1. The advent of new customer-service technology had invariably sparked fears about job losses.
- 2. Often it is found that instead of job losses, alternative channels for employee engagement are discovered while certain tasks are replaced by technology.
- 3. The advent of technology inevitably leads to stressful outcomes.
Select the answer using the code given below.
Answer (d) & explanation
Conclusions 1 and 2 are correct (d). Step 1: the passage says earlier waves like email and voice menus "stoked concerns of job losses". So new customer-service technology has sparked such fears (1). Step 2: those losses "failed to materialise", and AI may free humans for creative, rewarding work. So technology often redirects people rather than replacing them (2). Step 3: conclusion 3 says technology inevitably leads to stress. The passage expects salutary effects and less time with irate customers, the opposite. So options (a), (b) and (c) fail.
Tip: "inevitably" is a strong word; check that the passage supports it fully. Here it says the reverse.
Answer as per the official UPSC answer key.
Read the passage
Cattle from the nearby villages came to the common ground to graze, and there was still a cool freshness in the air. Hori took several deep breaths and thought of sitting down for a while, since he’d be dying of heat in the scorching ‘loo’ wind the rest of the day. A number of farmers were eager to lease this bit of land and had offered a good price, but Rai Sahib—God bless him—had plainly told them it was reserved for grazing and would not be relinquished for any price. If he’d been one of those selfish Zamindars, he’d have said the cattle could go to hell, that there was no reason for him to miss the chance to make a little money. But the Rai Sahib still held to the old values, feeling that any landlord who didn’t look after his tenants was less than human.
Which of the following conclusions is/are correct?
- 1. All landlords essentially have some goodness trapped within them.
- 2. The common grazing grounds of a village are intended for use by the cattle of that village.
- 3. Landlords who believe in tradition tend to be more concerned about their tenants.
- 4. Winds later in the day tend to be cooler post the hot winds of the morning.
Select the answer using the code given below.
Answer (c) & explanation
Only conclusion 3 is correct (c). Step 1: Rai Sahib "held to the old values", believing a landlord who did not look after his tenants was "less than human". So tradition-minded landlords care more for tenants (3). Step 2: conclusion 1 says all landlords have goodness; but the passage mentions "selfish Zamindars". Conclusion 2 says the grazing land is for the cattle of that village; but cattle came "from the nearby villages". Step 3: conclusion 4 says winds get cooler later; but Hori expects the scorching "loo" for the rest of the day. So options (a), (b) and (d) fail.
Tip: check small details like "nearby villages" and time of day. This passage is from Premchand's novel Godaan (1936).
Answer as per the official UPSC answer key.
Read the passage
Cattle from the nearby villages came to the common ground to graze, and there was still a cool freshness in the air. Hori took several deep breaths and thought of sitting down for a while, since he’d be dying of heat in the scorching ‘loo’ wind the rest of the day. A number of farmers were eager to lease this bit of land and had offered a good price, but Rai Sahib—God bless him—had plainly told them it was reserved for grazing and would not be relinquished for any price. If he’d been one of those selfish Zamindars, he’d have said the cattle could go to hell, that there was no reason for him to miss the chance to make a little money. But the Rai Sahib still held to the old values, feeling that any landlord who didn’t look after his tenants was less than human.
Which of the following statements are not correct?
- 1. The landholdings of Rai Sahib were currently not being used for farming.
- 2. Temperamentally, Rai Sahib was as greedy as other landlords.
- 3. It cannot be ascertained that Rai Sahib could have made some money by leasing out the grazing land.
- 4. It may be asserted that Rai Sahib valued his tenants and wanted to protect their livelihood.
Select the answer using the code given below.
Answer (d) & explanation
Statements 1, 2 and 3 are not correct (d). Step 1: statement 1 says his land was not used for farming. The passage says only "this bit of land" was kept for grazing; nothing about the rest. So 1 overreaches. Step 2: statement 2 calls him greedy like others. But he refused a good price, unlike "selfish Zamindars". So 2 is wrong. Step 3: statement 3 says his possible earnings cannot be ascertained. But farmers "had offered a good price", so he clearly could have earned. So 3 is wrong. Statement 4, that he valued his tenants, is correct. Options (a), (b) and (c) fail.
Tip: in "not correct" questions, find the one true statement first; the rest are your answer.
Answer as per the official UPSC answer key.
A person facing the East travels 4 km straight and then turns right and travels 3 km, then further turns left and travels 2 km and finally turns left and travels 3 km. The minimum distance between the final point and the initial point, and the direction in which the person is facing at the final point are, respectively
Answer (d) & explanation
He ends 6 km away, facing North (d). Step 1: trace the path. Facing East, he walks 4 km East. A right turn faces South: 3 km. A left turn faces East: 2 km. A left turn faces North: 3 km. Step 2: South 3 and North 3 cancel out. East total = 4 + 2 = 6 km. So he is 6 km east of the start. Step 3: his last walk was northward, so he is facing North. Option (b) has the right distance but the wrong direction. Options (a) and (c) add the distances wrongly.
Tip: track north-south and east-west separately; opposite moves cancel. The final facing direction is simply the direction of the last walk.
Answer as per the official UPSC answer key.
In a sequence of numbers, each number other than the first two is the sum of the two immediately preceding numbers from it. If the first two numbers in the sequence are 4 and 7, then the sixth number is
Answer (d) & explanation
The sixth number is 47 (d). Step 1: the rule: each number after the first two is the sum of the two before it. Step 2: start with 4 and 7. Third: 4 + 7 = 11. Fourth: 7 + 11 = 18. Fifth: 11 + 18 = 29. Step 3: sixth: 18 + 29 = 47. Option (a), 29, is the fifth number, a common slip from miscounting positions. Options (b) and (c) are wrong sums.
Tip: this is a Fibonacci-style sequence. Write out every term and number its position so you do not stop one step early. The classic Fibonacci series starts 1, 1, 2, 3, 5, 8.
Answer as per the official UPSC answer key.
The ratio of male to female workers in two companies A and B is 13 : 10 and 7 : 5, respectively. If both the companies have the same number of female workers, then what is the ratio of the total number of workers in A to those in B?
Answer (b) & explanation
The ratio of total workers is 23 : 24 (b). Step 1: the female numbers must be equal. In A, males : females = 13 : 10. In B, it is 7 : 5, which equals 14 : 10 (doubling both). Step 2: now both have 10 parts of females. A's total = 13 + 10 = 23 parts. B's total = 14 + 10 = 24 parts. Step 3: so A : B = 23 : 24. Option (a) reverses the order. Options (c) and (d) do not equalise the females first.
Tip: when one group is the same in two ratios, scale the ratios so that group has the same number of parts. Then compare totals directly.
don't add 13 + 10 and 7 + 5 directly. Equalise the common term first.
Answer as per the official UPSC answer key.
If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct?
- I. The difference of the numbers is an even number.
- II. One of the numbers is a perfect square.
Select the answer using the code given below.
Answer (c) & explanation
Both statements are correct (c). Step 1: for any two numbers, HCF × LCM = product of the numbers. So a × b = a³ (the cube of one of them), giving b = a². Step 2: statement II: b = a² is a perfect square. True. Step 3: statement I: the difference is a² − a = a(a − 1), the product of two consecutive numbers. One of any two consecutive numbers is even, so the product is always even. True. Example: 3 and 9: HCF 3 × LCM 9 = 27 = 3³; difference 6 is even, and 9 is a square. Options (a), (b) and (d) fail.
Tip: remember HCF × LCM = a × b for two numbers. It turns many HCF-LCM puzzles into simple algebra.
Answer as per the official UPSC answer key.
If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x + y is divided by 11?
Answer (d) & explanation
1. Test for 11: add every second digit, add the others, and the two totals must differ by 0 or 11.
2. Digits 4, x, 5, y, 7, 9, 0. First group: 4 + 5 + 7 + 0 = 16. Second group: x + y + 9.
3. So 16 − (x + y + 9) = 7 − (x + y) must be 0 or −11. That gives x + y = 7 or x + y = 18.
4. 7 ÷ 11 leaves 7, and 18 ÷ 11 also leaves 7. Either way the remainder is 7.
Answer as per the official UPSC answer key.
Read the passage
Was it the sun-dappled ambience, the strawberries and cream, the frustration of Flavio Cobolli’s unforced errors against Serbian Novak Djokovic on Centre Court or simply the crushing weight of being a 64-year-old man in the third act of a very public life? Whatever the reason, Hugh Grant, the actor, deserves empathy. There he was, in the Royal Box at Wimbledon, flanked by Britain’s well-dressed and well-rested spectators, watching the men’s singles quarterfinals, when the actor did something quietly radical : head at a tilt, eyes closed, utterly unbothered, he took a nap. So praise be to Grant for serving up an unexpected ace. In that small, delicious moment, he didn’t merely catch forty winks, he made an elegant case for surrender. Not to laziness, but to limits. To the body’s quiet wisdom over society’s relentless performance metrics. Wimbledon had its tennis. The perpetually sleep-deprived discovered a leading man, not of action, but of rest.
Which of the following statements is/are correct?
- 1. Radical action can also be attributed to mild surrender where one acts against societal expectations.
- 2. Submitting to one’s limitations, given the effect of age and other factors, ought not to be conflated with laziness.
- 3. ‘Leading man’ usually refers to one who plays the lead role in a movie; in this instance the implication is that Hugh Grant is performing the role of not an action hero, but that of a resting one!
Select the answer using the code given below.
Answer (c) & explanation
All three statements are correct (c). Step 1: statement 1: the writer calls Hugh Grant's nap "quietly radical" and "an elegant case for surrender". Napping in the formal Royal Box goes against social expectation, so mild surrender becomes radical action. Correct. Step 2: statement 2 matches "Not to laziness, but to limits": giving in to age and tiredness is not laziness. Correct. Step 3: statement 3 explains the pun in the last line: "a leading man, not of action, but of rest". A leading man is a film's lead actor; here Grant leads in resting. Correct. So options (a), (b) and (d) fail.
Tip: in light, witty passages, look for wordplay. The nap happened at Wimbledon in July 2025, during the Djokovic–Cobolli quarterfinal.
Answer as per the official UPSC answer key.
Read the passage
Was it the sun-dappled ambience, the strawberries and cream, the frustration of Flavio Cobolli’s unforced errors against Serbian Novak Djokovic on Centre Court or simply the crushing weight of being a 64-year-old man in the third act of a very public life? Whatever the reason, Hugh Grant, the actor, deserves empathy. There he was, in the Royal Box at Wimbledon, flanked by Britain’s well-dressed and well-rested spectators, watching the men’s singles quarterfinals, when the actor did something quietly radical : head at a tilt, eyes closed, utterly unbothered, he took a nap. So praise be to Grant for serving up an unexpected ace. In that small, delicious moment, he didn’t merely catch forty winks, he made an elegant case for surrender. Not to laziness, but to limits. To the body’s quiet wisdom over society’s relentless performance metrics. Wimbledon had its tennis. The perpetually sleep-deprived discovered a leading man, not of action, but of rest.
Which of the following statements is/are correct?
- 1. Hugh Grant was watching, from the Royal Box, the men’s semifinal match on Centre Court between Flavio Cobolli and Novak Djokovic.
- 2. The phrase ‘unexpected ace’ in the context uses a term from the game of tennis to highlight Hugh Grant’s somewhat uncharacteristic act of catching ‘forty winks’; an act that is viewed with opprobrium.
- 3. Grant subjects the demands of society to the wisdom of his body.
Select the answer using the code given below.
Answer (b) & explanation
Only statement 3 is correct (b). Step 1: statement 3 matches "the body's quiet wisdom over society's relentless performance metrics". Grant let his body's need win over social demands. Correct. Step 2: statement 1 says it was the semifinal. The passage says "men's singles quarterfinals". Wrong. Step 3: statement 2 rightly explains "ace" as a tennis term, but adds that the nap is viewed with "opprobrium" (disgrace). The writer praises it: "praise be to Grant". So 2 is wrong. Options (a), (c) and (d) fail.
Tip: a statement that is half right is still wrong. Check every part, especially the tone words like "opprobrium". The match was played on 9 July 2025.
Answer as per the official UPSC answer key.
Read the passage
The process by which countries close their labour-productivity gap with the technology leader is based on convergence theory. The convergence model divides economic eras into three phases : the breakaway, the catch-up, and the fine-tuning phase. It also divides economic entities into two categories : the technology leaders and the technology followers. The process begins with the development of a new technology, such as scavenging three million years ago (MYA), hunting—one MYA, farming—12 thousand years ago, and industrial technology—a little more than 200 years ago. During the breakaway phase, the per capita income of the technology leaders (e.g., Western Europe and North America in the industrial era) rises, but is unchanged for the technology followers. In the catch-up phase, the followers adopt the new technology and close their per capita income gap with the technology leaders. In the fine-tuning phase, where participants try to extract the remaining benefits from an increasingly exhausted technology, leaders and followers have similar per capita incomes.
Which of the following conclusions are correct?
- 1. In the breakaway phase, economic progress is slow for the technology followers.
- 2. In the catch-up phase, leaders stagnate and followers, therefore, close the gap between them and the leaders.
- 3. In the fine-tuning phase, technology is exhausted, as it were, and both leaders and followers attempt to extract leftover benefits, leading to more or less similar per capita income levels.
- 4. Industrial technology followed scavenging, which preceded hunting, which itself was followed by farming.
Select the answer using the code given below.
Answer (a) & explanation
Conclusions 3 and 4 are correct (a). Step 1: conclusion 3 restates the fine-tuning phase: participants extract the remaining benefits from an "increasingly exhausted" technology, and leaders and followers have similar incomes. Correct. Step 2: conclusion 4 follows the timeline: scavenging (3 million years ago), hunting (1 million), farming (12,000 years) and industry (200 years). Correct. Step 3: conclusion 1 says followers' progress is "slow" in the breakaway phase; the passage says their income is "unchanged". Conclusion 2 says leaders stagnate in catch-up; the passage only says followers close the gap. So options (b), (c) and (d) fail.
Tip: "unchanged" is not "slow"; "followers catch up" does not mean "leaders stagnate". Match the exact word.
Answer as per the official UPSC answer key.
Read the passage
The process by which countries close their labour-productivity gap with the technology leader is based on convergence theory. The convergence model divides economic eras into three phases : the breakaway, the catch-up, and the fine-tuning phase. It also divides economic entities into two categories : the technology leaders and the technology followers. The process begins with the development of a new technology, such as scavenging three million years ago (MYA), hunting—one MYA, farming—12 thousand years ago, and industrial technology—a little more than 200 years ago. During the breakaway phase, the per capita income of the technology leaders (e.g., Western Europe and North America in the industrial era) rises, but is unchanged for the technology followers. In the catch-up phase, the followers adopt the new technology and close their per capita income gap with the technology leaders. In the fine-tuning phase, where participants try to extract the remaining benefits from an increasingly exhausted technology, leaders and followers have similar per capita incomes.
Which of the following statements is/are correct?
- 1. The convergence model divides nations into three phases of economic progress.
- 2. At the heart of the convergence theory is the closing of the gap between labour and productivity.
- 3. Technology leaders typically have arrived earlier at different economic eras.
- 4. The time period covered by the convergence theory presented herein encompasses, as mentioned, 4012200 years.
Select the answer using the code given below.
Answer (b) & explanation
Statements 2 and 3 are correct (b), as per UPSC's key. Step 1: statement 2: the opening line says convergence is how countries close their labour-productivity gap with the leader. UPSC reads this as the heart of the theory. Step 2: statement 3: in the breakaway phase, leaders (such as Western Europe and North America) gain first, so leaders arrive earlier at new eras. Correct. Step 3: statement 1 says the model divides nations into three phases; it divides economic eras into phases and entities into two categories. Statement 4 gives a wrong total period; the process begins about 3 million years ago. So options (a), (c) and (d) fail.
Tip: check what is being divided: eras into phases, entities into leaders and followers. Mixing them is the trap.
Answer as per the official UPSC answer key.
An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio, amounts of P and Q be mixed in order to get R?
Answer (a) & explanation
P and Q must be mixed in the ratio 1 : 3 (a). Step 1: "equal copper and zinc" means R is 50% copper. Step 2: use alligation on copper: P has 20%, Q has 60%, and the mix needs 50%. P : Q = (60 − 50) : (50 − 20) = 10 : 30. Step 3: simplify to 1 : 3. Check: 1 kg P gives 0.2 kg copper; 3 kg Q gives 1.8 kg; total 2 kg copper in 4 kg = 50% ✓. Option (b) reverses the ratio. Options (c) and (d) fail.
Tip: in alligation, the amount of each item is the distance of the other item from the mean. Always check with a quick calculation.
Answer as per the official UPSC answer key.
A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If A – B is a multiple of 27, where A > B, how many such different A's are possible?
Answer (b) & explanation
Nine such numbers are possible (b). Step 1: let A = 10a + b and B = 10b + a, with a > b. Then A − B = 9(a − b). Step 2: for this to be a multiple of 27, a − b must be a multiple of 3: 3, 6 or 9. Step 3: a − b = 3: b = 1 to 6 (A = 41, 52, 63, 74, 85, 96): 6 numbers. a − b = 6: b = 1 to 3 (A = 71, 82, 93): 3. a − b = 9 needs b = 0, making B a one-digit number (09), so it is not allowed. Total = 9. Options (a), (c) and (d) fail.
Tip: A number minus its reverse is always 9 × (digit difference). B must also be two-digit, so the units digit of A cannot be 0.
B must also be a 2-digit number, so 90 is out.
Answer as per the official UPSC answer key.
If ZERO is encoded as ADSN, then how do you encode STOP?
Answer (b) & explanation
STOP is encoded as TSPO (b). Step 1: compare ZERO and ADSN letter by letter: Z → A (+1, wrapping round), E → D (−1), R → S (+1), O → N (−1). The moves alternate +1, −1. Step 2: apply to STOP: S + 1 = T, T − 1 = S, O + 1 = P, P − 1 = O. Step 3: so STOP becomes TSPO. Options (a) SPOT, (c) TSOP and (d) POST are rearrangements that do not follow the rule.
Tip: in letter codes, write the shift for each position. Remember that after Z comes A again. Options that are real words are often traps.
Answer as per the official UPSC answer key.
There are three types of rectangular tiles : 3' × 3', 3' × 7' and 3' × 11'. An area of rectangular shape of dimensions 3' × 100' is to be covered using these tiles without breaking them. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x – y is
Answer (a) & explanation
x − y is 20 (a). Step 1: every tile is 3' wide, like the strip, so only lengths matter: 3a + 7b + 11c = 100, where a, b, c are the numbers of each tile. Step 2: maximum tiles: use as many short 3' tiles as possible. 100 is not a multiple of 3, but 31 × 3 + 7 = 100. So x = 32 tiles. Step 3: minimum tiles: use as many long 11' tiles as possible. 9 × 11 = 99 leaves 1 (impossible); trying downwards, 8 × 11 + 4 × 3 = 88 + 12 = 100 works with 12 tiles, and no combination with 11 or fewer tiles works. So y = 12. x − y = 20.
Tip: for maximum count, use the smallest pieces; for minimum, the largest. Then adjust to hit the exact total.
Answer as per the official UPSC answer key.
A train has to complete a journey of 800 km. If it meets a minor accident, its speed becomes half of the existing speed. If there is a mechanical defect, the speed becomes one-fourth of the existing speed. On its way, the train meets with a minor accident after 200 km; and 400 km thereafter, it develops a mechanical defect. Had the train developed the mechanical defect after 200 km and met the minor accident 400 km thereafter, it would have taken 4 more hours to reach its destination. What was the original speed of the train in km per hour?
Answer (a) & explanation
The original speed was 200 km/h (a). Step 1: actual journey: 200 km at v; then a minor accident halves speed: 400 km at v/2; then a defect quarters it: 200 km at v/8. Time = 200/v + 800/v + 1600/v = 2600/v. Step 2: other order: 200 km at v; defect: 400 km at v/4; accident halves again: 200 km at v/8. Time = 200/v + 1600/v + 1600/v = 3400/v. Step 3: the difference is 4 hours: 800/v = 4, so v = 200 km/h. Options (b), (c) and (d) fail.
Tip: speed changes multiply: half then a quarter gives one-eighth, in either order. Only the middle stretch differs between the two cases.
the cuts apply to the existing speed. After both events the speed is v/8 in either order. Only the middle 400 km differs.
Answer as per the official UPSC answer key.
| Candidate | Score in component 1 | Score in component 2 | Score in component 3 |
|---|---|---|---|
| 1 | 5 | 4 | 6 |
| 2 | 4 | 6 | 5 |
| 3 | 3 | 2 | 8 |
| 4 | 9 | 4 | 3 |
| 5 | 8 | 8 | 2 |
In a recruitment process, the selection of candidates is based on their performance in three components. The weightages of the components 1, 2 and 3 are 0·2, 0·3 and 0·5, respectively. Use the data given below and find the cutoff score if exactly three candidates are to be selected :
Answer (a) & explanation
The cutoff score is 5.1 (a). Step 1: weighted score = 0.2 × (component 1) + 0.3 × (component 2) + 0.5 × (component 3). Candidate 1: 1.0 + 1.2 + 3.0 = 5.2. Candidate 2: 0.8 + 1.8 + 2.5 = 5.1. Candidate 3: 0.6 + 0.6 + 4.0 = 5.2. Step 2: candidate 4: 1.8 + 1.2 + 1.5 = 4.5. Candidate 5: 1.6 + 2.4 + 1.0 = 5.0. Step 3: the top three are 5.2, 5.2 and 5.1. The cutoff is the third score, 5.1. Options (b), (c) and (d) would select too few.
Tip: the cutoff is the lowest score that still gets selected. Calculate every weighted score carefully before ranking.
Answer as per the official UPSC answer key.
Consider the following three statements, namely S1, S2 and S3:
S1. Protecting the environment is an existential exigency for humans, given the impact of environmental degradation on climate change.
S2. Scientific consensus has not been achieved with regard to the extent of the contribution of human intervention to climate change.
S3. Environmental activism includes climate alarmism and other extremist points of view that often become the focus of climate change deniers.
Which of the following relationships based on the statements given above is/are correct?
- 1. S3 is a counterpoint to S1
- 2. S3 is unconnected to S1 and S2
- 3. S2 could be the reason for S3
Select the answer using the code given below.
Answer (d) & explanation
Only relationship 3 is correct (d). Step 1: relationship 1: S3 says some environmental activism is extreme and gets targeted by deniers. That does not argue against S1 (protecting the environment is vital). So S3 is not a counterpoint to S1. Step 2: relationship 2 says S3 is unconnected to S1 and S2. But S3 is linked to S2. Step 3: relationship 3: since scientists have not agreed on how much humans cause climate change (S2), there is room for both alarmism and denial (S3). So S2 could be a reason for S3. Options (a), (b) and (c) fail.
Tip: a counterpoint must oppose the main claim. A statement about how a debate is conducted is not opposition to the cause itself.
Answer as per the official UPSC answer key.
| List-I (Relationship category) | List-II (Communication type) |
|---|---|
| A. Between cricket captain and team members | 1. Informal and firm |
| B. Between judge and lawyers in court | 2. Informal and open-ended |
| C. Between Vice Chancellor and Deputy Registrar | 3. Formal and open-ended |
| D. Between peers and coworkers | 4. Formal and firm |
Match List-I with List-II and select the answer using the code given below the Lists :
Answer (b) & explanation
The match is A-1, B-4, C-3, D-2 (b). Step 1: a court is the most formal and binding setting, so judge and lawyers = formal and firm (B-4). Peers and coworkers talk freely and loosely = informal and open-ended (D-2). Step 2: a cricket captain is friendly with players, but his decision is final = informal and firm (A-1). Step 3: a Vice Chancellor and Deputy Registrar work through official channels but discuss matters = formal and open-ended (C-3). Options (a), (c) and (d) mismatch these.
Tip: in matching questions, fix the clearest pairs first (here court and peers). The rest often fall into place.
Answer as per the official UPSC answer key.
| List-I (Tool of communication) | List-II (Purpose) |
|---|---|
| A. Memorandum | 1. To record decisions |
| B. Flyer | 2. To inform confidentially |
| C. Bcc | 3. To intimate a directive |
| D. Minutes | 4. To disseminate non-targeted information |
Match List-I with List-II and select the answer using the code given below the Lists :
Answer (c) & explanation
The match is A-3, B-4, C-2, D-1 (c). Step 1: Minutes are the written record of a meeting, so they record decisions (D-1). Step 2: a memorandum (memo) is an internal office note that conveys an instruction, so it intimates a directive (A-3). Step 3: a flyer is handed out to anyone, so it spreads non-targeted information (B-4). Bcc (blind carbon copy) hides recipients from each other, so it informs confidentially (C-2). Options (a), (b) and (d) mismatch.
Tip: know basic office communication terms: memo, circular, minutes, notice and agenda. "Cc" shows all recipients; "Bcc" hides them.
Answer as per the official UPSC answer key.
Which among the following actions would constitute the most appropriate directive(s) in resolving interpersonal conflict in an office with culturally diverse personnel?
- 1. Direct personnel to practise activities that are the cultural markers of diverse groups
- 2. Allow conflicts to resolve naturally over time to set an appropriate precedent of leadership
- 3. Encourage personnel to seek each other's perspectives
Select the answer using the code given below.
Answer (c) & explanation
Only action 3 is appropriate (c). Step 1: action 1, forcing staff to practise other groups' cultural customs, can make people uncomfortable or offended. Respect cannot be imposed. Step 2: action 2, letting conflicts resolve on their own, is not leadership. Unresolved conflict usually grows and hurts teamwork. Step 3: action 3, encouraging staff to seek each other's perspectives, builds understanding and respect, the root of resolving cultural conflict. So options (a), (b) and (d) fail.
Tip: in workplace-ethics questions, prefer options that build dialogue and empathy. Avoid options that force behaviour or ignore problems.
in decision items, an option that forces people or does nothing is rarely the best one.
Answer as per the official UPSC answer key.
| List-I (Barrier to communication) | List-II (Example) |
|---|---|
| A. Semantic | 1. Lack of feedback |
| B. Cognitive | 2. Misunderstanding the meaning of a word |
| C. Organisational | 3. Fear of social stigma |
| D. Affective | 4. Information overload |
Match List-I with List-II and select the answer using the code given below the Lists :
Answer (d) & explanation
The match is A-2, B-4, C-1, D-3 (d). Step 1: semantic barriers concern the meaning of words, so misunderstanding a word (A-2). Step 2: cognitive barriers concern the mind's ability to process, so information overload (B-4). Step 3: organisational barriers come from the system, like lack of feedback channels (C-1). Affective barriers come from feelings, such as fear of social stigma (D-3). Options (a), (b) and (c) mismatch.
Tip: link each word to its root: semantic = meaning, cognitive = thinking, affective = emotion, organisational = structure. This quickly solves communication-barrier matching.
Answer as per the official UPSC answer key.
You are required to design a 'questionnaire' to be filled on-location by visitors, based on the following objective while writing a report :
"To determine the feasibility of setting up a family-oriented vacation resort in the vicinity of a lake destination in the mountains"
Which of the following heads would you include in the questionnaire to make it most appropriate for your purpose?
- 1. Size of family
- 2. Budget
- 3. Number of earners in the family
- 4. Food allergies and dietary restrictions
Select the answer using the code given below.
Answer (c) & explanation
Heads 1 and 2 only should be included (c). Step 1: the goal is to test the feasibility of a family resort: will there be demand, and at what price? Step 2: family size (1) shows the kind of rooms needed. Budget (2) shows what visitors will spend, which sets pricing. Both bear directly on feasibility. Step 3: number of earners (3) is personal, and its effect already shows in the budget. Food allergies (4) matter for running the resort later, not for deciding whether to build it. So options (a), (b) and (d) fail.
Tip: include only questions that serve the stated objective. Extra personal questions also reduce response rates in surveys.
Answer as per the official UPSC answer key.
With reference to 'circular letters', which of the following statements is/are correct?
- 1. Circular letters are usually addressed to a group of people.
- 2. Non-standard and customized content is typical of circular letters.
- 3. Circular letters are used to intimate appraisals and increments of employees within organisations.
- 4. Circular letters are less cost-effective than personalised and specific recipient-directed letters.
Select the answer using the code given below.
Answer (d) & explanation
Only statement 1 is correct (d). Step 1: a circular letter sends the same message to many people, so it is addressed to a group (1 correct). Step 2: statement 2 is wrong: circular content is standard, not customised. Statement 3 is wrong: appraisals and increments are personal, so they go in individual letters. Step 3: statement 4 is wrong: circulars are more cost-effective, since one text serves everyone. So options (a), (b) and (c) fail.
Tip: think of a school circular about a holiday: one message, many readers, low cost. Anything personal or private does not go by circular.
Answer as per the official UPSC answer key.
Three partners A, B and C entered into a business. A invested one-third of the capital for one-third duration. B invested one-fourth of the capital for one-fourth duration. C invested the remaining capital for the whole duration. Out of a profit of ₹ 17,000, how much profit will C get?
Answer (a) & explanation
C gets ₹12,000 (a). Step 1: profit is shared in the ratio of capital × time. A: 1/3 of capital for 1/3 of the time = 1/9. B: 1/4 for 1/4 = 1/16. C put in the rest: 1 − 1/3 − 1/4 = 5/12, for the whole time = 5/12. Step 2: multiply by 144 to clear fractions: A : B : C = 16 : 9 : 60. Total = 85 parts. Step 3: C's share = 60/85 × 17,000 = ₹12,000. Options (b), (c) and (d) fail.
Tip: in partnerships, multiply capital by time for each partner. Clear fractions with the LCM of the denominators before sharing.
Answer as per the official UPSC answer key.
There are two chemicals which do not react with each other. A container contains 10 litres of the chemical A. One litre of this chemical is removed from it and one litre of the chemical B is poured. Then one litre of the mixture is removed from the container and one litre of B is poured. If this process of replacing one litre of the mixture by one litre of B is performed once more, then what is the volume of B that is present in the container approximately (in percentage)?
Answer (b) & explanation
B is about 27% of the container (b). Step 1: each time, 1 litre of the 10-litre mixture is removed, so 9/10 of chemical A stays. Step 2: after three rounds, A left = 10 × (9/10)³ = 10 × 0.729 = 7.29 litres, that is 72.9%. Step 3: the rest is B: 100 − 72.9 = 27.1%, about 27%. Option (a), 25, and the others come from subtracting 10% three times or similar slips.
Tip: for repeated replacement, use: original left = start × (1 − removed/total)ⁿ. Simple subtraction of 10% each time gives the wrong answer.
it is not 3 × 10% = 30%. Later rounds take out some B as well.
Answer as per the official UPSC answer key.
A shopkeeper employs a delivery boy and gives him a motorcycle for home delivery. For every delivery, the boy is given ₹ 5. At the end of the day, he also gets ₹ 2 for every kilometre of the distance covered in the day. The boy wants to earn more than ₹ 500 a day, but does not want to travel more than 100 km. Which of the following numbers of deliveries would definitely meet his target?
Answer (d) & explanation
The question cannot be answered due to insufficient data (d). Step 1: earnings = 5 × deliveries + 2 × km, and km can be anything from 0 to 100. Step 2: with 90 deliveries, he earns 450 + 2k. That crosses ₹500 only if he rides more than 25 km. With 80 or 85 deliveries he needs even more km. Step 3: we are not told how far he travels. So no option is definitely enough. Options (a), (b) and (c) would work only with enough kilometres.
Tip: "definitely" means it must work in the worst case. Here the worst case is very few kilometres, and then 101 or more deliveries would be needed.
the word "definitely" decides it. "Possibly" would give a different answer.
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Answer as per the official UPSC answer key.
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