UPSC 2022 Prelims Questions with Answers

41 kg. Average of A, B, C is 40, so A+B+C = 120. Average of B, D, E is 42, so B+D+E = 126. Since F = B, total A+B+C+D+E+F equals (A+B+C) + (B+D+E) = 120 + 126 = 246. Average of six persons = 246/6 = 41 kg.

72. X can be any of the 9 non-zero digits. Y must be non-zero and different from X, so it has 8 choices. Total numbers = 9 x 8 = 72.

Let the three consecutive integers be n-1, n, n+1. Then sum = 3n and product = n(n^2 - 1). Equating, 3n = n(n^2 - 1), i.e., n(n^2 - 4) = 0, giving n = 0, 2, -2. The corresponding triples are (-1, 0, 1), (1, 2, 3) and (-3, -2, -1). Hence there are only three possibilities.

81. Nine cups in equal rows and columns means a 3 x 3 arrangement. There are 6 coffee cups and 3 tea cups. The condition that every row has at least one coffee is automatically satisfied unless all three tea cups occupy the same row. Total placements of 3 tea cups among 9 positions = 9C3 = 84. Bad placements = choosing one full row for tea = 3. Valid arrangements = 84 - 3 = 81.

The password starts with a vowel (5 choices), ends with a consonant (21 choices) and has a non-zero digit in the middle (9 choices). Total passwords = 5 x 21 x 9 = 945.

252. Write the terms as n^2(n+1): 1^2 x 2 = 2, 2^2 x 3 = 12, 3^2 x 4 = 36, 4^2 x 5 = 80, and 5^2 x 6 = 150. The next term is 6^2 x 7 = 252.

6. The expression represents 15!. The maximum power of 3 in 15! is floor(15/3) + floor(15/9) = 5 + 1 = 6. Hence the maximum value of m is 6.

The passage notes that India receives most of its water in 120 days and far too little in the remaining 245, and that this skewed availability must be managed through the year. The practical, rational and lasting solution is buffer stocking of water through dams and recharging aquifers.

The author says that however silly, insignificant or mechanical the labours of researchers, there is always a chance that the results may be of value to an investigator of talent, who can use the facts as the basis of a fruitful generalization. Hence any research result can be of value to an intelligent investigator.

The author says scientific research is probably never completely valueless - however silly or mechanical, the results may serve a talented investigator. His assumption is that scientific research is never without some value.

250/9. In a pie chart, the full circle is 360 degrees. The given sectors B, C, D and E add up to 90 + 50 + 45 + 75 = 260 degrees. So A = 360 - 260 = 100 degrees. Percentage share of A = 100/360 x 100 = 250/9 per cent.

After 20 ml of milk moves to Y, Y has 120 ml with milk fraction 1/6. Transferring 20 ml of the mixture back moves 20/6 = 10/3 ml of milk to X, so X ends with 80 + 10/3 = 250/3 ml milk out of 100 ml: m = 5/6. Y retains 100 - 50/3 = 250/3 ml water out of 100 ml: n = 5/6. Hence m = n.

Both 1 and 2. For statement 1, at 3:00 the hour and minute hands are 90 degrees apart. The minute hand gains 5.5 degrees per minute, so overlap occurs after 90/5.5 = 16.36 minutes, i.e. between 3:16 and 3:17. For statement 2, at 4:58 the minute hand is at 348 degrees and the second hand is at 0 degrees, a 12-degree gap. The second hand gains on the minute hand at 354 degrees per minute, so it catches up just after 4:58. Both statements are correct.

1, 2 and 3. Statement 1: p x q can be odd, e.g. p=3 and q=9. Statement 2: q/p can be prime, e.g. q=6 and p=2 gives 3. Statement 3: p+q can be prime, e.g. p=2 and q=9 gives 11. Hence all three statements are correct.

9. Let p be a two-digit number and q its reverse. Testing factor pairs around 2430, the pair 45 and 54 satisfies 45 x 54 = 2430. The reverse pair also gives the same product. Difference = 54 - 45 = 9.

1083. If the number leaves remainder 3 when divided by 6, 9, 12, 15 and 18, then N-3 is divisible by their LCM. lcm(6,9,12,15,18)=180. The smallest number greater than 1000 of the form 180k+3 is 1083.

15000. X got 56% of votes cast and Y got 44%, so X's victory margin = 12% of votes cast. Given margin = 1440, votes cast = 1440/0.12 = 12000. Since 80% of voters cast votes, total voters = 12000/0.80 = 15000.

The passage says the social order is the basis of all other rights and is founded on conventions, not nature. Both statements follow: conventions are the sources of the rights of man (1), and rights can be exercised only when there is a social order (2).

The passage says people who fail to accumulate money are generally easily influenced by others' opinions - they let newspapers and gossiping neighbours think for them. The message is that people should not be influenced by the opinions of others.

The passage speaks of the majority of people who fail to accumulate money sufficient for their needs - it does not claim most people fail, only that there are people who fail to accumulate money for their needs.

The correct order is z < x < y. From 70% of x added to y becoming 165% of y: 0.70x + y = 1.65y, so 0.70x = 0.65y and y = 14x/13. From 60% of x added to z becoming 165% of z: 0.60x + z = 1.65z, so 0.60x = 0.65z and z = 12x/13. Therefore z < x < y.

Both 1 and 2. A 20 cm x 8 cm rectangle can be cut into two 8 cm x 8 cm squares and the remaining 4 cm x 8 cm strip can be cut into two 4 cm x 4 cm squares, giving exactly 4 square sheets. It can also be divided into 10 triangles of equal area by first dividing it into 10 equal-area rectangles and cutting each appropriately, or by using equal bases and common height. Hence both statements are possible.

0. Factor 1261 as 13 x 97. The product 91 x 92 x 93 x 94 x 95 x 96 x 97 x 98 x 99 contains 97 directly. It also contains 91 = 7 x 13, so it has a factor 13. Therefore the product is divisible by both 13 and 97, and hence by 1261. The remainder is 0.

Data is inadequate to draw any conclusion. Let one man's daily work rate be m and one woman's daily work rate be w. Given 24m + 12w completes the work in 30 days. The asked group has rate 12m + 24w. Without knowing the relation between m and w, this second rate may be greater, smaller or equal to the first. Therefore the number of days cannot be determined.

Eight equidistant points form 4 diameters. For each diameter, any of the remaining 6 points forms a right angle at the circumference (angle in a semicircle). Total right-angled triangles = 4 x 6 = 24.

10. Since digits are in decreasing order, each valid PIN corresponds to choosing 3 digits from 1 to 7 with gaps of at least 2. The valid triples are 531, 631, 731, 641, 741, 751, 642, 742, 752 and 753. Therefore maximum attempts needed = 10.

1 only. All six 3-digit numbers formed from A, B and C have digit sum contribution 222(A+B+C), because each digit appears twice in each place. Thus x = 222(A+B+C). The least distinct non-zero digit sum is 1+2+3=6, giving x=1332, so statement 1 is correct. A 3-digit value would need A+B+C <=4, impossible with three distinct non-zero digits. Therefore statement 2 is incorrect.

The passage contrasts children, whose joys are clear and complete because they do not look too far forward or backward, with grown-ups, whose thrill from presents has dimmed. The joy of receiving is dimmed by worrying too much about the past and future.

The author offers two tentative explanations - perhaps we have too much already, or perhaps we have lost the fullness of the joy of giving and with it the joy of receiving. The clear point is that there can be more than one reason why adults feel less thrilled by presents.

The passage says leisure is tedious except for those with intelligent activities, so a leisured population must be an educated one, educated for enjoyment as well as usefulness. The message is that only an educated population can best make use of the benefits of economic progress.

Both statements together are not sufficient. Statement 1 only says F is preceded by A and followed by C, so A-F-C must occur consecutively, but it can occupy several positions. Statement 2 only says B is the last lecture, which does not identify the third period. Even together, B is fixed in the sixth period, while A-F-C can be placed in periods 1-3, 2-4 or 3-5. The third period could therefore be C, F or A. Hence the question cannot be answered.

Both statements are sufficient. Statement 1 alone gives only an age difference, not Manisha's age. Statement 2 alone gives only a future ratio, not the absolute ages. Together, if Manisha is M, mother is M+24. Five years later, (M+5):(M+29)=3:5. Solving 5M+25 = 3M+87 gives M=31. Hence both statements together are sufficient.

The statements fix only the opposition pairs B-C and D-E and the pair F-B. This does not determine A's position relative to the others, so who sits on the immediate left of A cannot be answered even with both statements.

Let F receive f pens; then A, B, C, D, E receive 6f, 3f, 2f, 3f/2 and 6f/5. For D's share (3f/2) to be even, f must be a multiple of 4; for E's share (6f/5) to be even, f must be a multiple of 10. The smallest such f is 20, giving shares 120, 60, 40, 30, 24 and 20, whose total is 294.

5 minutes fast. Let onward travel time be t minutes. Return route is 1.25 times as long but speed is twice as fast, so return time = 1.25t/2 = 0.625t. Total actual time from 14:30 to 16:00 is 90 minutes, including 25 minutes' stay. Thus t + 25 + 0.625t = 90, so 1.625t = 65 and t = 40 minutes. Actual village arrival was 15:10, but village clock showed 15:15. It is 5 minutes fast.

Let X buy x notebooks. Z = x + 8; P = x + 5; Q = P - 5 = x. P + Q = 21 gives (x + 5) + x = 21, so x = 8. X + Y = 28 gives Y = 20. Total notebooks = 13 + 8 + 8 + 20 + 16 = 65. Total cost = 65 x 40 = Rs. 2,600.

The passage says the demographic dividend can be an engine of growth but its benefits depend on the quality of the working-age population - education, skills and human capital. It is not an essential condition of rapid growth (1), and higher education is not called essential (2) - the passage presents them as enhancers, not prerequisites. Hence neither inference can be drawn.

When the demographic dividend operates, the share of the working-age population rises, so the dependency ratio — the combined share of the very young and the very old — falls for a while (statement 2). Literacy does not fall automatically; it depends on schooling policy (statement 1 is not invariable). Population growth does not stabilise quickly either; demographic momentum keeps it rising for decades (statement 3 is incorrect). Hence only statement 2 is correct.

The passage says man does not want to think, or cannot even if he wants to; he seeks not self-improvement but entertainment that lets him be mentally idle and forget his usual activities. Hence man does not seek self-improvement because he loves amusement and is mentally idle.

The passage says excessive labour is the rule in every circle of society, so that man's spiritual element cannot thrive and he cannot use his little leisure seriously. The central idea is that the great evil of our age is overstrain.

B and D are neither adjacent to C nor opposite to C; A is between E and D; F is between B and H. Several valid circular arrangements satisfy these conditions in which B need not be between A and G, C need not be opposite G, and E need not be opposite F. Hence none of the given statements is definitely correct.

Some doctors are teachers, all teachers are engineers and all engineers are scientists, so those doctors are engineers and scientists: some scientists are doctors (I) and some engineers are doctors (III). All engineers being doctors (II) is not forced. Hence I and III follow.

All pens are books and no chair is a pen. Nothing forces chairs and books to be related in any particular way: chairs may or may not be books, and books may or may not be chairs. None of the four conclusions necessarily follows.

Knowing QR = 18 km and PR = 43 km gives two sides of a triangle but not the third side PQ, which can range between 25 km and 61 km depending on direction. The two statements together are not sufficient to answer how far P is from Q.

x weeks = 604800x seconds, x days = 86400x, x hours = 3600x, x minutes = 60x and x seconds = x. Total = x(604800 + 86400 + 3600 + 60 + 1) = 694861x seconds.

The passage links rising affluence to a shift toward protein-rich diets - milk products, fish and meat - that need significantly more water than cereal-based diets, and to higher energy consumption. The implication is that water management practices in India need to change dramatically in the coming years.

Assumption 1 is valid: the passage says species unable to overcome environmental adversity go extinct, so only species that can overcome catastrophes survive and perpetuate. Assumption 2 (90 per cent endangered) is not stated, and assumption 3 overreaches - the passage treats Darwinian laws as explaining natural phenomena, not all phenomena.

The author says the so-called theory of evolution is not a theory at all - evolution is a fact, and the mechanism of natural selection is amply supported by data: organisms go extinct as a function of environmental or biological assaults for which their inheritance leaves them ill-equipped. That observable, data-backed mechanism is why it is not merely a theory.

The passage says natural selection cannot anticipate future environments, so existing organisms are never fully prepared for environmental catastrophes (1); genomes unable to withstand environmental changes result in extinction (3); and extinction of species is presented as a common outcome (4). Statement 2 is wrong - the passage does not say all existing species would get extinct.

22. Let C's position be 12 because 11 persons are ahead of C. B must be 7 places away from C, so B can be at position 4 or 20. To minimise the queue while keeping 13 persons behind A, choose the arrangement that keeps A as far left as possible. If B is at 4, A can be 5 places away at position 9. Then total persons = A's position + 13 = 9 + 13 = 22. This satisfies both gaps, so the minimum is 22.