UPSC 2025 Prelims Questions with Answers

There can be more than one such number. Two natural numbers differing by 10 can have either one or two multiples of 5 strictly between them depending on their positions. For example, between 1 and 11, both 5 and 10 lie between them. Hence more than one such number can occur.

I only. For 0<x<1, multiplying by x makes a positive number smaller. Hence x^3 < x^2, so statement I is correct. But sqrt(x) is greater than x for 0<x<1, so x > sqrt(x) is false. Therefore only statement I is correct.

Let the average be k. Since p is as much more than the average as q is less than it, p - k = k - q, i.e., p + q = 2k. Then (p + q + r)/3 = k gives 2k + r = 3k, so r = k.

Value-I = Value-II. For 11 consecutive integers >= -5, the minimum average is obtained by -5,-4,...,5, whose average is 0. For 11 consecutive non-negative integers, the minimum product is obtained by 0,1,2,...,10, whose product is 0. Hence both values are equal.

Value-I = Value-II. If p+q=10 and p,q are positive integers, pq is maximised when p and q are as close as possible: p=q=5, so Value-I=25. Under p>=-6 and q>=-4, with q=10-p, the product p(10-p) is still maximised at p=5, q=5. Thus Value-II=25 as well.

Cannot be determined. Since X:Y = Y:Z, the scores form a geometric progression and X+Y+Z=37. Positive integer possibilities include 9,12,16 and 16,12,9. These give different orderings of Value-I, Value-II and Value-III. Therefore the relation cannot be uniquely determined.

(p + q)^2 - 4pq = p^2 - 2pq + q^2 = (p - q)^2. This is positive exactly when p is not equal to q. Statement I (p < q) and Statement II (p > q) each guarantee that p is not equal to q. Hence either statement alone answers the question.

P was behind by 3 goals with 10 minutes remaining. Statement I says P scored 4 goals in those minutes, but the result still depends on how many goals Q scored. Statement II only gives Q's total goals in the match, not how many came in the last 10 minutes. Even together, Q's late goals are unknown, so the question cannot be answered even using any of the statements.

The passage describes trust as involving vulnerability and exposure to betrayal, yet essential for entrepreneurship, globalization and economic activity; it holds others in good esteem while accepting risk. Hence the crux is that trust is important though it entails risk.

The passage explains that a single inflation number averages differently weighted items, while actual price rises differ across items and across income classes whose consumption baskets vary widely. Hence the present calculation of the inflation rate does not correctly measure the price rise of individual items/commodities.

Statement I tells us R and S are sisters of P, and Statement II says R's father is the brother of Q, making Q a sibling of P's father. But Q's gender is not given, so Q could be P's paternal uncle or aunt. Hence the relation cannot be determined even using both statements.

PP x PQ = (10P+P)(10P+Q) = 11P(10P+Q), and RRSS = 1100R + 11S = 11(100R+S), so P(10P+Q) = 100R + S. With P up to 3 and Q up to 4, the only fit is P = 3, Q = 4: 33 x 34 = 1122. Hence Q = 4 can be found without using any of the statements.

1-digit numbers with exactly 4 distinct factors are 6 (1, 2, 3, 6) and 8 (1, 2, 4, 8); the smallest is 6. This can be determined directly from the question itself, without using either statement.

0. For any positive power, 9^k leaves remainder 3 when divided by 6. From 9^3 to 9^100 there are 98 terms. Sum of remainders = 98 x 3 = 294, which is divisible by 6. Hence the remainder is 0.

The code maps each cube to the cube of a number 3 greater: 4^3 = 64 is written as 7^3 = 343, and 6^3 = 216 as 9^3 = 729. Hence 512 = 8^3 is written as 11^3 = 1331.

31 km. Assign coordinates: A=(0,0), B=(0,6), C=(10,0), D=(10,-6), E=(5,-6), F=(-9,6), G=(-9,-6). A route from D to F through the given roads can be D-C-A-B-F with length 6+10+6+9=31 km. The alternative D-E-G-F also gives 5+14+12=31 km. Hence the distance is 31 km.

Both I and II. Statement I is possible: n=2 has 2 factors, and increasing it by 50% gives 3, which also has 2 factors. Statement II is possible: n=2 increased by 150% gives 5, which also has 2 factors. Hence both statements are correct.

Voluntary associations act as a buffer between the individual and the State by drawing people out of isolation and enabling them to participate in a common collective endeavour, thereby strengthening them against State power.

The passage says corporate capitalism generates jobs and helps fix the unemployment challenge, so assumption I is valid. It also says the additional State revenues can be used for greater welfare of the marginalized, i.e., benefits trickling down, so assumption II is also valid. Hence both assumptions are valid.

The opening line states that no democracy has grown economically without corporate capitalism, and the passage shows how it modernizes the economy, generates jobs and raises revenues for welfare. Hence corporate capitalism is important for the economic growth of a State and also for democracy.

The successive differences are 2, 3, 5, 7, 11, 13 - the consecutive prime numbers. Hence X = 18 + 11 = 29, and 29 + 13 = 42 confirms the pattern.

4. Rates: X completes 1/3 in 6 days, so X's rate is 1/18 per day. Y's rate is 1/24 per day. Z completes 3/4 in 12 days, so Z's rate is 1/16 per day. Together their rate is 1/18+1/24+1/16 = 23/144. After n days, Y alone works for 8 2/3 days = 26/3 days, completing (1/24)(26/3)=13/36. So n(23/144)+13/36=1. This gives n=4.

4. T is non-zero and P=3T, so T can be 1, 2 or 3. Also Q=R+3 and S=Q+4=R+7. Testing digit values without repetition gives four valid numbers: 35291, 63072, 64182 and 94183. Hence 4 such numbers are possible.

From the two examples, each letter has a fixed digit: F = 6, R = 5, A = 4, N = 3, C = 2, E = 1, G = 9, M = 8, Y = 7. Hence YEMEN = 7 1 8 1 3, i.e., 71813.

The code multiplies the alphabet positions of the letters: N x O = 14 x 15 = 210; N x O x T = 210 x 20 = 4200; N x O x T x E = 4200 x 5 = 21000. Hence NOTES = 21000 x 19 (S) = 399000.

P is the brother of Q and R, so Q and R are siblings of P. T is P's father, so T is also the father of Q and R. S is R's mother, and since P and R share the same parents, S is also the mother of P and Q, making S and T a couple. Hence the definitely true statements are: I (S and T are a couple), III (T is Q's father), IV (S is P's mother) and VI (P is S's son). The genders of Q and R are unknown, so II and V are not definitely true. Thus only four statements are definitely true.

The passage says opponents keep a statesman on the path of reason and good sense, not that a strong opposition is required only if the Head of Government is indifferent; and it does not claim that the more aggressive the opposition, the better the governance. Hence neither assumption is valid.

The passage argues that opponents show a statesman where the dangers are, and that the balance of political power keeps the administration from being arbitrary and the opposition from being revolutionary. Hence the opposition is indispensable for the balance of political power and good governance.

The passage says climate change may make plant infections more common in all climatic zones, which supports the migration of plant diseases to new areas (assumption I). It also notes that useful genetic variations have been bred out of high-value crops, implying that understanding their wild relatives would strengthen food security (assumption II). Hence both assumptions are valid.

The passage warns that selectively bred, genetically honed crops have lost variations that help them cope with change, so a minor or unknown disease could suddenly rampage through them. Hence our total dependence on genetically honed crops entails possible food insecurity.

Both I and II. The three matches are P-Q, P-R and Q-R. Since each team scored exactly one goal in the tournament, each team's total goals across two matches must be 1. P has 3 points, so P must have one win and one draw. R has 1 point, so R must have one draw and one loss. The only score pattern satisfying the points and goal totals is: P-Q = 0-0, P-R = 1-0, and Q-R = 1-1. Therefore statement I is correct, and R scored 1 goal against Q, so statement II is also correct.

Cannot be concluded. The statements give what P, Q and R said, but the question does not specify how many statements are true or false. Without a truth-telling condition, several guilt assignments can be made consistent with parts of the responses. Therefore the thief cannot be concluded from the given information.

9. Digits 1 to 9 use 9 places. Two-digit numbers 10 to 99 use 90 x 2 = 180 places, so 189 places are used up to 99. Remaining position = 489 - 189 = 300. In the three-digit sequence, 300 digits cover exactly 100 numbers, from 100 to 199. The 300th digit is the last digit of 199, which is 9.

37. A three-digit number QQQ equals 111Q. Since 111 = 3 x 37 and 481 = 13 x 37, the common factor is 37. Thus the HCF is 37.

2. Since 1^n is always 1, consider 2^n modulo 4. For n=1, 2^n ≡ 2 mod 4, so 1^n+2^n ≡ 3 mod 4. For n>=2, 2^n is divisible by 4, so the remainder is 1. Thus there are exactly two distinct remainders: 3 and 1.

Rate of one pipe of set X = 70%/(20 x 14) = 0.25% of the tank per minute. Rate of one pipe of set Y = (3/8 x 100%)/(10 x 6) = 0.625% per minute. Rate of one pipe of set Z = 50%/(16 x 20) = 0.15625% per minute (emptying). With 10 pipes of X, 5 pipes of Y and 16 pipes of Z open, the net filling rate = 10 x 0.25 + 5 x 0.625 - 16 x 0.15625 = 2.5 + 3.125 - 2.5 = 3.125% per minute. Time to fill 50% = 50/3.125 = 16 minutes.

The passage discusses reusing battery materials, not automobile factories as examples of the circular economy, so assumption I is not valid. It shows that reusing materials makes sense and supports continued production, so economic growth is compatible with circular use of mineral resources, and assumption II is valid. Hence only assumption II is valid.

The passage shows that reusing scarce, pricey battery materials makes economic and environmental sense. Hence the circular economy can be beneficial for sustainable growth.

The passage says supply-side investments can make low-carbon options cheaper and more widely available, so assumption I is valid. It does not claim that people are incapable of low-carbon behaviour without Government and Companies, so assumption II is not valid. Hence only assumption I is valid.

The passage says behavioural change needs incentives through supply-side investments that make low-carbon options cheaper and more widely available. Hence low-carbon behaviour in people can be brought about by incentivising them.

9. The number 12345678987654321 is the square of 111111111. Therefore N has 9 digits.

20 m. Let the speed of the tram be v km/h and its length be L metres. While overtaking X, relative speed = v-3 km/h and time = 8 s, so L = (v-3) x 5/18 x 8. While overtaking Y, relative speed = v-4 km/h and time = 9 s, so L = (v-4) x 5/18 x 9. Equating these: 8(v-3)=9(v-4), giving v=12 km/h. Then L = 9 x 5/18 x 8 = 20 m.

QRPS. Substitute Q=-, R=x, P=+, S=/. The option QRPS gives 60 - 15 x 3 + 20 / 4. Applying normal order of operations: 15 x 3 = 45 and 20/4 = 5, so the value is 60 - 45 + 5 = 20.

13. Their relative speed in opposite directions is 5+3 = 8 rounds per hour, so they meet every 1/8 hour = 7.5 minutes. Between 5:20 a.m. and 7:00 a.m., excluding the endpoint at 7:00 as 'between', the meeting times are from 5:22:30 through 6:52:30. That gives 13 crossings.

The sequence multiplies successively by 0.5, 1.5, 2 and 2.5: 24 x 0.5 = 12 (X), 12 x 1.5 = 18, 18 x 2 = 36, 36 x 2.5 = 90. Hence X = 12.

4. Since 35 = 5 x 7, the power of 35 is limited by the smaller of the powers of 5 and 7 in the product. The factors provide four 5s: one from 385 and three from 1000. There are more than four 7s. Therefore the largest n is 4.

The passage does not prescribe that food industries everywhere align to society's changing needs, so assumption I is not valid. It shows that wealthier societies convert grains into animal feed at large calorie losses, so assumption II is valid. Hence only assumption II is valid.

The passage shows that converting plant food into animal food recovers only 16% of the calories in chickens and five to seven per cent in large animals. Hence animal-based food is far less efficient than grain/plant-based food in terms of production and utilization.

The passage calls for higher education to respond to the new demands of society and the future of work, so assumption I is valid. It does not discuss funding of higher education, so assumption II is not valid. Hence only assumption I is valid.

The passage says teaching has to be re-invented and the classroom reimagined for critical, independent thinking. Hence classroom needs to be reimagined and teaching needs to be re-invented.