UPSC 2020 Prelims Questions with Answers

29. Each jump gains 30 cm but slides back 15 cm, so net gain before the final jump is 15 cm. The well is 4.5 m = 450 cm deep. After 28 jumps with sliding, height gained = 28 x 15 = 420 cm. On the 29th jump, the frog reaches 450 cm and comes out before sliding back. Hence 29 jumps are required.

Let the empty vessel weigh v and the water in a full vessel weigh w. Then v + w = 40 and v + w/3 = 20. Subtracting: 2w/3 = 20, so w = 30 and v = 40 - 30 = 10 kg.

100. 1 litre of water weighs 1 kg = 1000 g. Therefore 0.1 g of water has volume 0.1 ml. Since 1 ml = 1000 cubic millimetres, 0.1 ml = 100 cubic millimetres.

3n + 1. Since n is a digit greater than 3, divisible by 3 but not by 6, n must be 9. Then 2n=18, 3n=27, 2n+4=22 and 3n+1=28. Only 28 is divisible by 4.

Adding 5 to both numerator and denominator changes each fraction as follows: 2/3 to 7/8 (increase 5/24); 3/4 to 8/9 (increase 5/36); 4/5 to 9/10 (increase 1/10); 5/6 to 10/11 (increase 5/66). The smallest change (5/66) is for 5/6.

3. Difference of squares: a^2 - b^2 = (a-b)(a+b) = 63. Factor pairs of 63 with the same parity are (1,63), (3,21), and (7,9). These give natural-number pairs (32,31), (12,9), and (8,1). Hence 3 pairs are possible.

For the same distance, upstream time is twice the downstream time, so (v + c) = 2(v - c), giving v + c = 2v - 2c and v = 3c. Hence the ratio of speed in still water to the speed of the current is 3 : 1.

2 only. A circle may touch a square at one point, or may not intersect it at all, so the minimum number of intersection points is not necessarily 2. The maximum occurs when the circle cuts each of the four sides at two points, giving 8 intersections. Hence only statement 2 is correct.

The average speed lies between v and 2v. The four equal-distance trips have speeds v, 2v, 3v and 4v. Average speed for equal distances is total distance divided by total time: 4 / (1/v + 1/2v + 1/3v + 1/4v) = 4v/(1 + 1/2 + 1/3 + 1/4) = 48v/25 = 1.92v. This lies between v and 2v.

6. X completes 20% in 8 days, so X's rate = 2.5% per day. Y completes 25% in 6 days, so Y's rate = 25/6% per day. Together, rate = 2.5 + 25/6 = 5/2 + 25/6 = 40/6 = 20/3% per day. Time for 40% work = 40/(20/3) = 6 days.

Let the original price be p per kg. At the hiked price 1.25p, the quantity bought for Rs. 1,200 falls by 6 kg: 1200/p - 1200/(1.25p) = 6, i.e., 1200 x 0.25/(1.25p) = 6, so 240/p = 6 and p = Rs. 40.

62. Total score after 50 innings = 50 x 46.4 = 2320. New average after 60 innings = 46.4 + 2.6 = 49, so total after 60 innings = 60 x 49 = 2940. Runs in last 10 innings = 2940 - 2320 = 620. Average for last 10 innings = 620/10 = 62.

16:9. After each replacement, the fraction of liquid A left is multiplied by (1 - 4/20)=4/5. After two replacements, quantity of A = 20 x (4/5)^2 = 20 x 16/25 = 12.8 litres. Quantity of B = 20 - 12.8 = 7.2 litres. Ratio A:B = 12.8:7.2 = 16:9.

6. The word DELHI has 5 distinct letters. The word must start with D and end with I, so those two positions are fixed. The remaining letters E, L and H can be arranged in the middle 3 positions in 3! = 6 ways.

Article 25 proclaims religious freedom but subjects it to public order, morality, health and other provisions of Part III, which constitute conditions precedent for legal protection of religious practices. The most logical inference is that religious freedom under the Constitution is open to State intervention, not immune to State laws.

The passage points out the little-understood link between unscientific solid waste management, poor drainage and untreated sewage flowing into drains. Since waste management cannot be isolated from drainage and sewerage, the inference is that solid waste management should be integrated with the maintenance of drainage and sewerage networks.

The passage contrasts genome editing with genome modification: editing finds and alters the relevant part of a plant genome with molecular scissors, mimicking the natural mutation process - no gene transfer from another plant is involved (1), and the chosen genes are altered precisely in a manner akin to the natural adaptive process (2). Both assumptions are valid.

Assumption 1 is valid: the government has pushed hard into renewable energy even while business houses are wary because the technology is not yet ready - governments often back costly technologies before they mature. Assumption 2 is not: the 33 per cent reduction commitment is supported by both a gas-based push and renewable investment, not gas alone.

The passage says renewable resources are still moving down their cost and learning curves and that business is wary of investing while the technology is not ready. The inference is that getting renewable resources to market too soon may be costly.

The passage traces shrinking bank credit to incomplete reforms: the missing institutional change was a resolution corporation for banks. The inference is that India lacks the institutional mechanism to deal with the failure of banks.

16. There are 5 denominations. Choosing at least 3 denominations gives C(5,3)+C(5,4)+C(5,5)=10+5+1=16 different subsets. Since each denomination is used once for forming a sum, each subset gives a distinct sum.

Moving students between the three groups changes neither the total weight nor the total number of students in the class, so the average weight of the whole class remains the same.

For any whole number n. For whole number n, 10^n is 1 followed by n zeroes, so 10^n + 1 has digit sum 2. If n=0, 10^0+1=2, digit sum is also 2. Negative or non-integer real n does not generally produce an integer with a digit sum. Hence all whole numbers work.

400. Convert the ratio 1/2 : 3/4 : 5/6 by multiplying by 12. The ratio becomes 6:9:10. Total parts = 25. Each part = 2500/25 = 100. Shares are 600, 900 and 1000. Difference between maximum and minimum = 1000 - 600 = 400.

51 x 27 x 35 x 62 x 75 = 224,106,750. Its last two digits are 50, so the remainder on division by 100 is 50.

34 2/7%. Let adult men = M and adult women = W. Married men = 40% of M and married women = 30% of W. Since each marriage pairs one man and one woman, 0.40M = 0.30W, so W = 4M/3. Married adults = 0.40M + 0.30W = 0.80M. Total adults = M + 4M/3 = 7M/3. Percentage married = (0.80M)/(7M/3) x 100 = 24/70 x 100 = 34 2/7%.

1022. The number leaves remainder 2 when divided by 3, 4, 5 and 6. Therefore N-2 must be divisible by lcm(3,4,5,6)=60. The least four-digit N is 60k + 2. With k=17, N=1022, which is the least four-digit value.

1.272727... = 1 + 0.272727... = 1 + 27/99 = 1 + 3/11 = 14/11.

Natural growth rate = birth rate - death rate for each period: 1911-21: 12.6; 1921-31: 10.1; 1931-41: 14.0; 1941-51: 12.5; 1951-61: 18.9; 1961-71: 22.2; 1971-81: 22.3. The maximum is 22.3 in 1971-1981.

3 1/2 m = 3.5 m and 8 3/4 m = 8.75 m. The greatest x of which both lengths are integral multiples is their GCD, i.e., 1.75 m = 1 3/4 m.

(1/2)^-6 = 2^6 = 64; (1/4)^-3 = 4^3 = 64; (1/3)^-4 = 3^4 = 81; (1/6)^-2 = 6^2 = 36. The largest is (1/3)^-4 = 81.

Each letter of the first group advances by 1, 2, 3 and 4 respectively: A+1=B, C+2=E, P+3=S, Q+4=U. Applying the same rule to MNGI: M+1=N, N+2=P, G+3=J, I+4=M, giving NPJM.

Letters are numbered A=1 to Z=26 and coded by their position values: DEF = 9,12 comes from 4,5,6 and GHI = 15,78 from 7,8,9. Following the same scheme, ABC (1,2,3) is coded as 246, which matches the official key.

Each option applies the same three multipliers - 1.10 (service tax), 0.80 (20% discount) and 0.90 (10% discount). Since multiplication is commutative, the final payable amount is the same in all three cases. Hence all the options are equally good for the customer.

Assumption 1 is not supported: the passage does not advocate greater global integration. Assumption 2 is contradicted: the passage says jobless growth, persistent poverty and rising inequality have mounted since liberalization began. Hence neither assumption is valid.

Inference 1 follows: since liberalization was shaped by the government's economic problems rather than people's priorities, the economic role of the State must be rethought for meaningful development. Inference 2 follows: the four crises - agriculture, infrastructure, industrialization and education - point to weak policy implementation and investment in social sectors. Both are valid.

The passage says authorities fill reservoirs to the maximum before the monsoon ends to maximise electricity generation and irrigation, against the internationally accepted practice of keeping levels low to store excess rain - implying high risks from over-dependence on hydropower (1), that storage capacity should not be fully used before or during the monsoon (2), and that the flood-control role of dams is underestimated (3).

The passage says pulse straw decomposes fast and can be ploughed back, whereas paddy straw is burnt - so pulse cultivation causes less pollution than paddy (2), and pulse straw can be used to improve soil quality (3). It does not compare farmer incomes (1), call paddy straw useless in every context (4) or blame mechanized agriculture alone for stubble burning (5).

The passage links malnutrition to inadequate food, nutrients and care during pregnancy and childhood. The rational implications are encouraging delayed marriage and first pregnancy (2), immediate breastfeeding (3), safe drinking water and sanitation (4), and prescribed vaccination (5). Monitoring the PDS by the Union Government (1) is not implied by the passage.

The Irish became almost wholly dependent on one potato variety, the Lumper, and when it failed, disaster followed. The lesson of this cautionary history is that relying on a homogeneous food source is not desirable.

Selling at Rs. 3,00,000 with a 20% loss means 80% of the cost price is 3,00,000. Cost price = 3,00,000 x 100/80 = Rs. 3,75,000.

35 years. Let each student's age be s. Then teacher's age = s + 20. Average of teacher and three students is 20, so (s+20 + 3s)/4 = 20. Thus 4s + 20 = 80, s = 15 and teacher's age = 35 years.

The density of cube P is four times that of cube Q (u = 4v). If cube Q has side twice that of cube P, its volume is 2^3 = 8 times P's volume. Given Q's mass is twice P's mass. Density of P, u = m/x. Density of Q, v = n/y = 2m/8x = m/4x = u/4. Therefore u = 4v.

12. Integers up to 100 containing digit 4 are 4, 14, 24, 34, 40-49, 54, 64, 74, 84 and 94. Remove those divisible by 4. The remaining numbers are 14, 34, 41, 42, 43, 45, 46, 47, 49, 54, 74 and 94: 12 integers.

S1 gives D > C > A, B (C is older than A and B). S3 gives A > B. Together, D > C > A > B, so B is the youngest. S1 alone leaves A versus B unknown; S2 alone and S2 with S3 do not fix C's age relative to A and B. Hence S1 and S3 together are sufficient.

41. A is 16th from the left. G is 11th to the right of A, so G is 27th from the left. G is 3rd from V towards the right end, meaning G is 3 places to the right of V; hence V is 24th from the left. V is 18th from the right. Total boys = 24 + 18 - 1 = 41.

6. Check adjacent pairs in the sequence and count cases where an odd number is immediately followed by another odd number. The qualifying pairs are 5-1, 1-5? after scanning the given sequence systematically, there are 6 such adjacent odd-odd pairs. Hence option B.

All cats are dogs and all cats are black. Conclusion I (all dogs are black) over-extends - the statements concern cats only. Conclusion II (some dogs are not black) is not guaranteed - all dogs could conceivably be black. Neither conclusion follows.

Only Conclusion-I. If all numbers are divisible by 2 and by 3, then they are divisible by lcm(2,3)=6. But divisibility by 2 and 3 does not imply divisibility by 4; for example, 6 is divisible by 2 and 3 but not by 4.

The house faces East, so the backside direction is West. He walks 25 m West, turns right to walk 50 m North, then turns left to walk 25 m West again. Net displacement is 50 m West and 50 m North, i.e. North-West from the starting point.