UPSC 2024 Prelims Questions with Answers

Q − S = 2S gives Q = 3S. Among the numbers 4, 5, 10, 12 and 15, only S = 5 with Q = 15 satisfies this. Next, T = R + S + 3 = R + 8; trying the remaining numbers {4, 10, 12}, only R = 4 gives T = 12, which is valid. The leftover number is P = 10. Therefore P + R − T = 10 + 4 − 12 = 2.

The successive differences are 11, 25, 45, ..., and these differences grow by 14, 20, 26, 32. So the differences are 11, 25, 45, 71, 103 and the sequence is 3, 14, 39, 84, 155, 258. Hence * = 155.

The code writes the word in reverse and adds A at the beginning: POT reversed is TOP, giving ATOP; TRAP reversed is PART, giving APART. Hence ARENA reversed is ANERA, giving AANERA.

The code multiplies the positions of the letters: A(1) x B(2) x C(3) x D(4) = 24, and E x F x G x H = 5 x 6 x 7 x 8 = 1680. Hence IJKL = 9 x 10 x 11 x 12 = 11880.

2x >= 3y and 3x = 4z give 9y <= 8z, so 9y > 8z is false. But x < y and y <= z imply x < z, i.e. x is not greater than z (x R z) is true. Only statement 2 is correct.

-25. Replace the symbols as given: + becomes -, - becomes x, x becomes /, and / becomes +. Thus 10 + 30 - 100 x 50 / 25 becomes 10 - 30 x 100 / 50 + 25. Apply normal precedence: 30 x 100 / 50 = 60. So the value is 10 - 60 + 25 = -25.

The main statement says Pradeep becomes either a Director or a Producer. Statement S (not a Producer) forces him to be a Director, so SP is consistent. Statement R (not a Director) forces him to be a Producer, so RQ is consistent. Hence both SP and RQ.

Let P's age be 10a + b and Q's be 10b + a. Statement I (P > Q) gives a > b but not the difference, so it is not sufficient. Statement II: sum/difference = 11/6 gives 11(a + b) = (11/6) x 9(a - b), i.e., a + b = (3/2)(a - b), so a = 5b. With digits, b = 1 and a = 5, giving ages 51 and 15 and difference 36. Hence one of the statements alone (Statement II) is sufficient.

Assumption 1 is not valid: the passage says the flower flaunts its petals and perfume to attract insects for pollination, not as a luxury of Nature. Assumption 2 is not valid either: the flower's real usefulness is attracting pollinators - its beauty is called a by-product and a human invention. Hence neither is valid.

The passage says poetry abides by the plurality of life and existence, while those who claim absolute truths turn dictatorial and tyrannical. In a world marked by tyranny and bigotry, poetry - which does not expect belief in absolute truths - becomes a form of dynamic resistance.

Statement I: P + Q = R + S. Statement II: P + S > Q + R. From I and II we can only derive relationships among the four totals, not the individual comparison of P and Q; adding the inequalities does not isolate P > Q or Q > P. The question cannot be answered even with both statements.

The three articles cost Rs. 50, with q = Rs. 16, so p + r = 34. Statement I alone allows p <= 17; Statement II alone allows p >= 17. Together they force p = 17. Both statements are needed, and together they answer the question.

Checking distinct-prime triples whose sum is a prime less than 23: any triple containing 2 has an even sum greater than 2 (composite), and the only remaining candidate is (3, 5, 11) with sum 19, which is prime. So Statement I alone identifies the numbers. Statement II (one number is 5) is not unique. Hence one of the statements alone is sufficient.

Statement I gives only the highest and lowest marks, and Statement II says their removal does not change the average. This does not determine how many students there are, since the count of the remaining students is unknown. Hence the question cannot be answered even using both statements together.

Statement I: X = 4/5 (Y + Z). Statement II: Y = 2/7 (X + Z). Solving together: from I, Z = (5X - 4Y)/4; substituting into II gives 7Y = 2X + (5X - 4Y)/2, i.e. 18Y = 9X, so X = 2Y, and then Z = 1.5Y. So Y received the least. Both statements together are required.

From Statement II, the possible pairs are (1,12), (2,6) and (3,4). Statement I requires x/y to be an odd integer; only (6,2) satisfies this because 6/2 = 3 is odd. Hence both statements together determine x = 6 and y = 2.

The passage says growth strategies must be rethought for a resource-constrained world, with resource- and energy-intensive processes making way for efficient, resource-frugal ones that protect the environment available to the poor and vulnerable. The message is that maintaining high environmental standards is now a prerequisite for achieving steady, sufficient and inclusive growth.

The passage warns that connected home device manufacturers and service providers will gather more personal data, with or without consent, turning the home into a corporate storefront. The clear implication is that interconnected devices can be at security risk and home users may have privacy risk.

The passage says that in a robust democracy reality must find transparent expression through the media and deliberative articulation, with a normatively responsible media playing its role. The message is that responsible media should not distort the real in an ideal democracy.

Time = size / rate. The size (12 MB = 12 x 1024 = 12,288 KB) comes from Statement I and the transfer rate (2.4 KB/s) from Statement II. Time = 12,288 / 2.4 = 5,120 seconds. Both statements together are needed to compute the download time.

Statement I (m + n > mn with m > n) forces n = 1, because for m > n >= 2 the product mn is at least m + n. But it leaves m free. Statement II gives the pairs (1,24), (2,12), (3,8), (4,6). Together, only (m, n) = (24, 1) satisfies both. Hence both statements together are sufficient.

India being the largest producer of milk does not imply that it is the largest exporter of milk (I), nor that it does not import milk (II). Hence neither conclusion follows.

North-East. Starting westward, a left turn makes the person face south. From south, a 225 degree clockwise turn is the same as turning 180 degree to north and then 45 degree more to north-east. Therefore the final direction is North-East.

Working backwards from an office in the North-East, take the initial direction as South: 100 m South, turn left (East) 100 m, turn left (North) 300 m, turn right (East) 100 m gives a net 200 m North and 200 m East - exactly North-East of the house. Hence he initially walked South.

For k = 3, the pair is uniquely (1,2); for k = 4 it is uniquely (1,3). For k = 5, both (1,4) and (2,3) satisfy p < q and p + q = 5, so p and q are not uniquely determined. Hence the smallest such k is 5.

3^25 + 3^27 = 3^25(1 + 3^2) = 10 x 3^25, which is exactly divisible by 10.

The passage says caterpillar frass induces the plant to turn off its defence against pests, and that the find could throw light on compounds associated with plant response to pathogens. The practical implication is that this finding can help in the development of organic, ecologically sustainable pesticides.

The passage says giant icebergs store up to 20 percent of carbon in the Southern Ocean (1) and that their meltwater, rich in iron and nutrients, supports unexpectedly high phytoplankton productivity (2). Both statements are supported by the passage.

The experiment converted carbon dioxide into solid limestone inside basalt rocks - the carbon dioxide is literally converted into stone. The logical and practical suggestion is that this can be used as one of the methods of carbon sequestration.

Let orange, mango and apple cost o, m and a. 4o + 6m + 8a = 2(o + 2m + 5a) simplifies to 2o + 2m = 2a, i.e., o + m = a, so statement 2 is correct. Then 3o + 5m + 9a = 3o + 5m + 9(o + m) = 12o + 14m, and 4o + 6m + 8a = 4o + 6m + 8(o + m) = 12o + 14m, so statement 1 is also correct. Hence both statements are correct.

Four triplets. The first seven natural numbers are 1 to 7. Since x > 2y > 3z, z must be small. If z = 1, then 2y > 3, so y can be 2 or 3. For y = 2, x > 4 gives x = 5, 6 or 7. For y = 3, x > 6 gives x = 7. If z >= 2, then 3z >= 6 and 2y must be greater than 6, forcing y >= 4 and x > 8, impossible in 1 to 7. Thus four triplets are possible: (5,2,1), (6,2,1), (7,2,1), (7,3,1).

Both A = 9 (e.g. 91 + 86 = 177) and A = 8 (e.g. 81 + 96 = 177) work with distinct digits, so the value of A cannot be determined uniquely.

Let Q cost q. Then R costs 1.2q and P costs 1.25 x 1.2q = 1.5q. Total = q + 1.2q + 1.5q = 3.7q = 3330, so q = 900. Hence P costs 1.5 x 900 = Rs. 1,350.

The sequence consists of blocks 1; 1,2; 1,3,2; 1,4,3,2; ... where the k-th block sums to 1 + 2 + ... + k = k(k+1)/2. The first 28 terms are blocks 1 to 7, and their total is 1 + 3 + 6 + 10 + 15 + 21 + 28 = 84.

56. Count digit 5 in units and tens places from 1 to 260. Units place: 5, 15,., 255 gives 26 occurrences. Tens place: 50-59, 150-159 and 250-259 give 10 + 10 + 10 = 30 occurrences. Total = 26 + 30 = 56.

The passage says parents' solicitude is often a disguise for love of power, that they consider adolescent moral problems their province, and that they are so dogmatic the young seldom confide in them. The implication is that parents in general may not be of much help when children are on their way to becoming adults.

Assumption 1 is valid: parental solicitude is called a disguise for love of power, and parents are so dogmatic that the young seldom confide in them - the adolescent feels uncomfortable because parents tend to be dominating and assertive. Assumption 2 is not: the passage says nothing about the adolescent's respect for parents.

Assumption 1 contradicts the passage: the tyranny of the fixed-duration classroom leaving learners behind is precisely why change is needed. Assumption 2 contradicts it too: only about 10 percent employability in graduates shows the system does not produce enough skilled workers. Hence neither is valid.

The passage says the classroom model emphasizes fixed duration over learning effectiveness, subjecting every learner to the same lectures in the same way (1), and that this one-size-fits-all script leaves most learners behind (2). Both inferences are valid.

17.5. At 4:25, the minute hand is at 25 x 6 = 150 degrees. The hour hand is at 4 x 30 + 25 x 0.5 = 132.5 degrees. The angle between them is 150 - 132.5 = 17.5 degrees.

p and q are odd; r and s are even. Statement 1: (p - r)^2 is odd and qs is even, so their product is even - correct. Statement 2: (q - s) is odd, q^2 is odd and s is even, so the product is even - correct. Statement 3: (q + r)^2 is odd and (p + s) is odd, so their product is odd - correct. Hence all three statements are correct.

2025 is a non-leap year beginning on Wednesday. From 2025 to 2031 there are six years including one leap year (2028), an offset of 6 + 1 = 7 days, so 2031 also begins on Wednesday and is non-leap. Hence the calendar of 2025 matches that of 2031.

3 times. Clock hands coincide once every 720/11 minutes. Between 10:00 a.m. and 2:00 p.m., the overlaps occur roughly at 10:54, 12:00 and 1:05. Thus they coincide 3 times.

42. The source equality is: weight of 6 boys = weight of 7 girls = weight of 3 men = weight of 4 women. The average weight of a woman is 63 kg, so 4 women weigh 4 x 63 = 252 kg. Therefore 6 boys also weigh 252 kg. Average weight of a boy = 252/6 = 42 kg.

Let X = 10a + b and Y = 10b + a. X + Y = 11(a + b) = 99, the greatest two-digit number, so a + b = 9. The tens digit a can be 1 to 8 (b = 9 - a must be a non-zero digit), giving 8 possible values of X.

The passage says the merchant learns what is parochial and what is universal only through travel, and that learning fundamental common values is perhaps the greatest gain of travel. Assumptions 1 and 2 follow. Assumption 3 is not: the passage never claims travel experience enables resolving differences among people.

The passage says delicate goods such as justice, love and honour are valid everywhere but variously moulded, and that travel teaches what is parochial and what is universal. Hence when we meet other people while travelling, we learn to differentiate between local values and universal values.

Assumption 1 is wrong: the author asks whether the horrors are the inevitable result of science or whether the fault lies elsewhere - he does not assert inevitability. Assumption 2 is valid: the epigram's easily overlooked truth is the relation between science and mankind - science is what man has made it.

Statement 1 overstates: the passage says nothing about mankind not existing without science. Statement 2 also overstates: it never says science will ultimately determine the destiny of mankind. Hence neither is emphatically conveyed.

1 cubic metre = 1000 litres; 1 metric ton = 1000 kg; and 1 hectare = 10000 square metres. Hence all three statements are correct.