CSAT Paper II of the 2020 Preliminary examination, held on 4 October 2020. 80 questions · 200 marks · qualifying at 33%. The questions broke down as Basic Numeracy 31, Comprehension 25, Mental Ability 11, Data Interpretation 7, Logical Reasoning 6.
The answer under each question is UPSC's official key. The note beside it is the first line of our explanation; the full reasoning, option by option, is one click away.
Which one of the following is best implied in the passage?
UPSC's answer: (d) — The passage states that India needs 24 million jobs over the next decade and that e-commerce can close only half of this gap.
On the basis of the above passage, the following assumptions have been made : 1. State should have some institutions to ensure its appropriate role in a digital society. 2. State should ensure that private parties do not violate the citizens' right to privacy. 3. Digital economy is not compatible with the idea of not violating the citizens' privacy. Which of the above assumptions is/are valid?
UPSC's answer: (a) — The passage states that the State's role is to actively ensure that private parties do not block rights, implying the need for mechanisms or institutions to enforce this in a digital society, validating Assumption 1.
Which one of the following is the most logical and rational inference that can be made from the above passage?
UPSC's answer: (c) — The passage highlights the irony that water is viewed as divorced from its natural sources, such as rivers and wetlands, despite originating from them. It argues that current public policy treats water merely as a resource, failing to recognize it as an integral part of the natural ecosystem.
Which one of the following statements best implies the suggestion given by the author of the passage?
UPSC's answer: (a) — The passage argues that while all assets carry some form of risk (job loss, home value drop, bank bankruptcy, bond default), these extreme risks do not manifest simultaneously. The author criticizes the tendency to keep money 'idle, unproductive but safe' because no asset is truly risk-free.
With reference to the above passage, the following assumptions have been made : 1. Biotechnology regulation is an evolving process. 2. Participation of people is needed in policy decisions regarding biotechnology regulation. 3. Biotechnology regulation should take into account socio-economic aspects in decision-making. 4. Wider involvement of political executive in biotechnology regulation improves its effectiveness in dealing with the country's trade policies and international obligations. Which of the above assumptions are valid?
UPSC's answer: (b) — Assumption 1 is valid because the passage states that current GM crops have single traits, but future crops will have multiple traits, implying that regulation must evolve to accommodate these changes.
Which one of the following statements best implies the crux of the passage?
UPSC's answer: (c) — The passage opens by stating that while current GM crops are engineered for single traits, future crops will be engineered for multiple traits, indicating that the technology's scope is expanding beyond current applications.
How many zeroes are there at the end of the following product? 1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60
UPSC's answer: (a) — The number of trailing zeroes in a product is determined by the number of pairs of prime factors 2 and 5, where the count of 5s is typically the limiting factor. The product consists of multiples of 5 from 5 to 60: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.
Let XYZ be a three-digit number, where (X + Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by
UPSC's answer: (b) — Expanding the three numbers: XYZ = 100X + 10Y + Z, YZX = 100Y + 10Z + X, ZXY = 100Z + 10X + Y. Adding them gives (100X + X + 10X) + (10Y + 100Y + Y) + (Z + 10Z + 100Z) = 111X + 111Y + 111Z = 111(X + Y + Z).
Let p, q, r and s be natural numbers such that p - 2016 = q + 2017 = r - 2018 = s + 2019 Which one of the following is the largest natural number?
UPSC's answer: (c) — Let the common value be k. Then p = k + 2016, q = k − 2017, r = k + 2018 and s = k − 2019. The largest amount added to k is 2018, so r is the largest. Hence option (c).
How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?
UPSC's answer: (a) — The sum of the digits 1, 2, 3, 4, and 5 is 1 + 2 + 3 + 4 + 5 = 15. A fundamental divisibility rule states that a number is divisible by 3 if and only if the sum of its digits is divisible by 3.
In the sum ⊗ + 1⊗ + 5⊗ + ⊗⊗ + ⊗1 = 1⊗⊗ for which digit does the symbol ⊗ stand?
UPSC's answer: (b) — Let ⊗ = x. Then ⊗ = x, 1⊗ = 10 + x, 5⊗ = 50 + x, ⊗⊗ = 11x, ⊗1 = 10x + 1 and 1⊗⊗ = 100 + 11x. Left side: x + (10 + x) + (50 + x) + 11x + (10x + 1) = 24x + 61. So 24x + 61 = 100 + 11x, giving 13x = 39 and x = 3. Check: 3 + 13 + 53 + 33 + 31 = 133 = 1⊗⊗. Hence option (b).
If you have two straight sticks of length 7·5 feet and 3·25 feet, what is the minimum length can you measure?
UPSC's answer: (b) — Using two sticks, the lengths we can measure are whole-number combinations of 7·5 ft and 3·25 ft, so the smallest length is their HCF. In quarter-feet: 7·5 ft = 30 quarters and 3·25 ft = 13 quarters. HCF(30, 13) = 1 quarter = 0·25 ft. For example, 7 × 3·25 − 3 × 7·5 = 22·75 − 22·5 = 0·25 ft.
A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence?
UPSC's answer: (c) — The given sequence is 14, 18, 20, 24, 30, 32, ... Subtracting 1 from each term yields: 13, 17, 19, 23, 29, 31, ... These resulting numbers (13, 17, 19, 23, 29, 31) are consecutive prime numbers. The next prime number after 31 is 37.
One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages is 195. The torn page contains which of the following numbers?
UPSC's answer: (b) — A torn leaf carries two consecutive page numbers, odd then even: (2k − 1, 2k), whose sum is 4k − 1. If the booklet has n pages, the total is n(n + 1)/2, so n(n + 1)/2 − (4k − 1) = 195. n = 20 gives a total of 210, so the torn pages add up to 210 − 195 = 15, i.e. pages 7 and 8.
Consider the following arrangement that has some missing letters : abab_b_bcb_dcdcded_d The missing letters which complete the arrangement are
UPSC's answer: (c) — Fill the blanks with a, c, c, e: abab(a)b(c)bcb(c)dcdcded(e)d. The completed series reads ababab cbcb cdcdcd eded. It is built from alternating pairs: ab three times, cb twice, cd three times and ed twice — the letters move forward one step at each change. Hence option (c).
Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D?
UPSC's answer: (c) — Units column: C + F must give 2, but since C and F are digits greater than 3, C + F = 12 with carry 1. Tens column: B + 2 + 1 = 0, so B + 3 = 10, giving B = 7 and carry 1. Hundreds column: 3 + E + 1 = 9, so E = 5 and there is no carry to the thousands column.
Two Statements S1 and S2 are given below followed by a Question : S1 : There are not more than two figures on any page of a 51-page book. S2 : There is at least one figure on every page. Question : Are there more than 100 figures in that book? Which one of the following is correct in respect of the above Statements and the Question?
UPSC's answer: (c) — S1 states that no page has more than 2 figures, so the maximum total is 51 pages × 2 figures = 102 figures. S2 states that every page has at least 1 figure, so the minimum total is 51 pages × 1 figure = 51 figures.
Consider the following data : | Average marks in English | Average marks in Hindi Girls | 9 | 8 Boys | 8 | 7 Overall average marks | 8·8 | x What is the value of x in the above table?
UPSC's answer: (a) — Let there be g girls and b boys. English: 9g + 8b = 8·8(g + b), so 0·2g = 0·8b and g = 4b. Hindi: x = (8g + 7b)/(g + b) = (32b + 7b)/5b = 39/5 = 7·8. Hence option (a).
A family of two generations consisting of six members P, Q, R, S, T and U has three males and three females. There are two married couples and two unmarried siblings. U is P's daughter and Q is R's mother-in-law. T is an unmarried male and S is a male. Which one of the following is correct?
UPSC's answer: (b) — U is P's daughter, so U is female. Q is R's mother-in-law, so Q is female. There are three males; T and S are two of them. U and Q are female, so the third male is P or R.
If in a particular year 12th January is a Sunday, then which one of the following is correct?
UPSC's answer: (c) — 12 January is Sunday; count the days from 12 January to 12 July. In a leap year, the interval is 31 + 29 + 31 + 30 + 31 + 30 = 182 days. 182 days is exactly 26 weeks, so 12 July is also Sunday in a leap year. In a non-leap year, the interval is 31 + 28 + 31 + 30 + 31 + 30 = 181 days, i.e.
With reference to the above passage, the following assumptions have been made : 1. Relying on foreign investment in the long run is not an economically sound policy. 2. Policies must be undertaken to reduce volatility in foreign private investment. 3. Policies must be undertaken to strengthen domestic private investment. 4. Public investment should be given priority over private investment. 5. Substantial public investment in education and health should be undertaken. Which of the above assumptions is/are valid?
UPSC's answer: (b) — The passage states that FDI inflows are volatile over time, sectors and regions, and that employment cannot be left to FDI, so assumption 1 is valid.
With reference to the above passage, which of the following could be the most rational and practical implications for India? 1. Inter-linking of rivers should be undertaken. 2. A network of dams and canals should be built across the country for proper distribution of water. 3. Farmers should be provided easy loans for digging borewells. 4. Usage of water for agriculture should be regulated by law. 5. Distribution of river water among regions should be regulated by the Union Government. Select the correct answer using the code given below.
UPSC's answer: (a) — The passage states that monsoon flows are highly skewed, seasonal and spatial, occurring in a four-month period from June to September annually.
With reference to the above passage, the following assumptions have been made : 1. Lower tax rates in a country invariably translate into greater investments in higher education. 2. Investment in the education of children ensures their economic freedom. 3. Economic freedom has a positive impact on building up human capital. Which of the above assumptions is/are valid?
UPSC's answer: (c) — Assumption 1 is invalid because the passage states that lower tax rates make it 'eminent sense' to invest, but does not claim this 'invariably' translates to greater investment, as other factors may influence decisions.
What is the most logical and crucial message conveyed by the passage?
UPSC's answer: (a) — The passage explicitly states that sustainable water delivery is impossible 'unless financing mechanisms are put in place.' It details the heavy investment required for collection, treatment, distribution, and sewage infrastructure.
With reference to the above passage, the following assumptions have been made : 1. Rich cities only can ensure sustainable delivery of water. 2. Sustainable delivery of water in cities means much more than supplying water to households. Which of the above assumptions is/are valid?
UPSC's answer: (b) — The passage states that sustainable water delivery requires 'heavy investment' in collection, treatment, distribution, sewerage, and sewage treatment plants.
With reference to the above passage, the following assumptions have been made : 1. Structural and rural transformation is impossible when farms are mainly small and marginal. 2. A good price incentive can trigger investments in agriculture. 3. India needs to build value chains for high-value agri-products like livestock and horticulture. 4. Higher global prices of agricultural commodities are essential for India's poverty reduction. Which of the above assumptions are valid?
UPSC's answer: (c) — Assumption 1 is invalid because the passage states India has slow transformation due to small farms but does not claim it is 'impossible'; China and Vietnam also had small farms yet transformed fast.
Which one of the following statements best reflects the critical message of the passage?
UPSC's answer: (d) — The passage highlights that India's poverty reduction accelerated dramatically between 2005 and 2012, a period distinct from the slower pace seen in 1988–2005.
Two Statements S1 and S2 are given below with regard to four numbers P, Q, R and S followed by a Question : S1 : R is greater than P as well as Q. S2 : S is not the largest one. Question : Among four numbers P, Q, R and S, which one is the largest? Which one of the following is correct in respect of the above Statements and the Question?
UPSC's answer: (c) — Statement S1 states that R is greater than both P and Q, establishing the relationship R > P and R > Q, but it provides no information about S relative to R, P, or Q.
Two Statements S1 and S2 are given below followed by a Question : S1 : n is a prime number. S2 : n leaves a remainder of 1 when divided by 4. Question : If n is a unique natural number between 10 and 20, then what is n? Which one of the following is correct in respect of the above Statements and the Question?
UPSC's answer: (d) — The range of natural numbers between 10 and 20 is {11, 12, 13, 14, 15, 16, 17, 18, 19}. Statement S1 states n is prime; the primes in this range are 11, 13, 17, and 19, so S1 alone is insufficient.
Two Statements S1 and S2 are given below with regard to two numbers followed by a Question : S1 : Their product is 21. S2 : Their sum is 10. Question : What are the two numbers? Which one of the following is correct in respect of the above Statements and the Question?
UPSC's answer: (c) — Let the two numbers be x and y. Statement S1 states that xy = 21, which has multiple integer solutions such as (1, 21), (3, 7), and their negatives, so it is not sufficient alone.
A man walks down the backside of his house straight 25 metres, then turns to the right and walks 50 metres again; then he turns towards left and again walks 25 metres. If his house faces to the East, what is his direction from the starting point?
UPSC's answer: (d) — The house faces East, so the backside of the house faces West. Walking straight 25 metres from the backside means moving 25 metres West. Turning right from a Westward direction results in facing North; walking 50 metres moves him 50 metres North.
Two Statements are given followed by two Conclusions : Statements : All numbers are divisible by 2. All numbers are divisible by 3. Conclusion-I : All numbers are divisible by 6. Conclusion-II : All numbers are divisible by 4. Which of the above Conclusions logically follows/follow from the two given Statements?
UPSC's answer: (a) — The first statement establishes that every number in the set is divisible by 2. The second statement establishes that every number in the set is also divisible by 3. Since 2 and 3 are co-prime integers, any number divisible by both must be divisible by their least common multiple, which is 6.
Two Statements are given followed by two Conclusions : Statements : All cats are dogs. All cats are black. Conclusion-I : All dogs are black. Conclusion-II : Some dogs are not black. Which of the above Conclusions logically follows/follow from the two given Statements, disregarding commonly known facts?
UPSC's answer: (c) — The first statement 'All cats are dogs' establishes that the set of cats is a subset of the set of dogs, but it does not imply that all dogs are cats or that all dogs share the properties of cats.
Consider the following sequence of numbers : 5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6 How many odd numbers are followed by the odd number in the above sequence?
UPSC's answer: (b) — First, identify all odd numbers in the sequence: 5, 1, 7, 3, 9, 5, 7, 3, 1, 5, 3, 5, 3, 9. Check the number immediately following each odd number to see if it is also odd.
A is 16th from the left end in a row of boys and V is 18th from the right end. G is 11th from A towards the right and 3rd from V towards the right end. How many boys are there in the row?
UPSC's answer: (b) — A is 16th from the left, so there are 15 boys to A's left. G is 11th from A towards the right, meaning G's position from the left is 16 + 11 = 27th. G is 3rd from V towards the right end, which implies V is 3 positions to the left of G. Therefore, V's position from the left is 27 - 3 = 24th.
Three Statements S1, S2 and S3 are given below followed by a Question : S1 : C is younger than D, but older than A and B. S2 : D is the oldest. S3 : A is older than B. Question : Who among A, B, C and D is the youngest? Which one of the following is correct in respect of the above Statements and the Question?
UPSC's answer: (d) — S1 states that C is younger than D but older than both A and B, establishing the partial order D > C > A and D > C > B. S3 states that A is older than B, which refines the relationship between A and B to A > B. Combining S1 and S3 yields the complete sequence: D > C > A > B.
How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?
UPSC's answer: (c) — List all integers from 1 to 100 containing the digit 4: 4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, 94, total 19. Identify those divisible by 4: 4, 24, 40, 44, 48, 64, 84, total 7. Subtract the divisible-by-4 numbers from the total: 19 - 7 = 12.
Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of Q is two times that of P. Let u = m / x and v = n / y. Which one of the following is correct?
UPSC's answer: (a) — Let each side of P be a. Then x = a³ and m is its mass. Each side of Q is 2a, so y = (2a)³ = 8a³, and its mass n = 2m. u = m/a³ and v = 2m/8a³ = m/(4a³) = u/4. So u = 4v — option (a).
The average age of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher?
UPSC's answer: (c) — Let each student be s years old and the teacher t years old. Average of four is 20, so t + 3s = 80. The teacher is 20 years older than each student, so t = s + 20. Then 4s + 20 = 80, s = 15 and t = 35. Hence option (c).
A person bought a car and sold it for ₹ 3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car?
UPSC's answer: (d) — Let the Cost Price (CP) of the car be denoted by x. A loss of 20% means the Selling Price (SP) is 80% of the Cost Price. Therefore, the equation is 0.80 * x = 3,00,000. Solving for x gives x = 3,00,000 / 0.80. This simplifies to x = 3,00,000 * (10/8) = 3,75,000.
Which one of the following statements best reflects the critical message of the passage?
UPSC's answer: (d) — The passage highlights that the Irish became 'almost wholly dependent' on the potato as their staple food. It specifies that they planted 'primarily one prodigious variety,' the 'Lumper' potato, creating a genetically uniform crop.
With reference to the above passage, which of the following is/are the most rational and practical implication/implications? 1. India's Public Distribution System should be monitored by the Union Government. 2. Girls should be encouraged to delay marriage and first pregnancy. 3. Mothers should be encouraged to breastfeed their children immediately after birth. 4. The supply of safe drinking water and proper sanitation facilities to all should be ensured. 5. Authorities should ensure the vaccination as prescribed. Select the correct answer using the code given below.
UPSC's answer: (b) — The passage highlights that malnutrition causes death and permanent damage to children's bodies and minds, leading to reduced lifetime earnings.
Which of the following are the most rational inferences that can be made from the passage? 1. Farmers' income will be higher with pulse cultivation than with paddy cultivation. 2. Pulse cultivation causes less pollution as compared to paddy cultivation. 3. Pulse straw can be used to improve soil quality. 4. In the context of northern Indian agriculture, paddy straw has no usefulness. 5. Mechanized agriculture is the main cause for stubble burning. Select the correct answer using the code given below.
UPSC's answer: (c) — Statement 2 is a rational inference because the passage states that Arhar straw decomposes fast and is ploughed back, whereas paddy straw is burned due to high silica content, implying pulse cultivation causes less pollution from burning.
With reference to the above passage, the following assumptions have been made : 1. High risks involved in holding maximum water in reservoirs are due to our over-dependence on hydropower projects. 2. Storage capacity of dams should not be fully used before or during monsoon season. 3. Role of dams in flood control is underestimated in India. Which of the above assumptions is/are valid?
UPSC's answer: (d) — Assumption 1 is valid because the passage states authorities store maximum water 'only to ensure greater electricity generation and irrigation,' implying that the drive to maximize storage stems from a heavy reliance on these outputs, particularly hydropower.
Which of the following is/are the most rational and logical inference/inferences that can be made from the passage? 1. It is essential to rethink and redefine the economic role of the State in the quest for development. 2. India has not made effective implementation of its policies in social sectors nor made sufficient investments in them. Select the correct answer using the code given below.
UPSC's answer: (c) — The passage states that economic liberalization was shaped by government economic problems rather than people's priorities or long-term development objectives, implying a misalignment in the State's role.
With reference to the above passage, the following assumptions have been made : 1. India's economy needs to be greatly integrated with global economy so as to create large number of jobs and to sustain its growth momentum. 2. Economic liberalization would cause large economic growth which would reduce poverty and create sufficient employment in the long run. Which of the above assumptions is/are valid?
UPSC's answer: (d) — The passage states that economic liberalization was driven by government economic problems, not people's priorities or long-term development objectives, implying a disconnect between policy and social needs.
A shop owner offers the following discount options on an article to a customer : 1. Successive discounts of 10% and 20%, and then pay a service tax of 10% 2. Successive discounts of 20% and 10%, and then pay a service tax of 10% 3. Pay a service tax of 10% first, then successive discounts of 20% and 10% Which one of the following is correct?
UPSC's answer: (d) — Let the marked price of the article be 100. For Option 1: A 10% discount reduces the price to 90; a subsequent 20% discount reduces it to 72; adding 10% service tax results in a final price of 79.2.
The letters from A to Z are numbered from 1 to 26 respectively. If GHI = 1578 and DEF = 912, then what is ABC equal to?
UPSC's answer: (d) — Write the letter positions side by side: G, H, I = 7, 8, 9 → 789, and D, E, F = 4, 5, 6 → 456. The given codes are exactly double these numbers: 2 × 789 = 1578 and 2 × 456 = 912. For ABC: A, B, C = 1, 2, 3 → 123, and 2 × 123 = 246. Hence option (d).
What is the missing term @ in the following? ACPQ : BESU :: MNGI : @
UPSC's answer: (d) — Analyze the first pair ACPQ : BESU to identify the pattern. The first letter A (1) becomes B (2), which is +1. The second letter C (3) becomes E (5), which is +2. The third letter P (16) becomes S (19), which is +3. The fourth letter Q (17) becomes U (21), which is +4.
What is the largest number among the following?
UPSC's answer: (c) — A negative power of a fraction inverts it: (1/k)⁻ⁿ = kⁿ. (a) 2⁶ = 64; (b) 4³ = 64; (c) 3⁴ = 81; (d) 6² = 36. The largest is 81. Hence option (c).
What is the greatest length x such that 3 1/2 m and 8 3/4 m are integral multiples of x?
UPSC's answer: (d) — Convert the mixed fractions to improper fractions: 3 1/2 m = 7/2 m and 8 3/4 m = 35/4 m. The problem asks for the greatest length x that divides both lengths exactly, which is the Highest Common Factor (HCF) of the two fractions.
Consider the following data : Year | Birthrate | Death rate 1911–1921 | 48·1 | 35·5 1921–1931 | 46·4 | 36·3 1931–1941 | 45·2 | 31·2 1941–1951 | 39·9 | 27·4 1951–1961 | 41·7 | 22·8 1961–1971 | 41·1 | 18·9 1971–1981 | 37·1 | 14·8 For which period was the natural growth rate maximum?
UPSC's answer: (d) — The natural growth rate is calculated by subtracting the death rate from the birth rate for each period. For 1911–1921, the growth rate is 48.1 - 35.5 = 12.6. For 1941–1951, the growth rate is 39.9 - 27.4 = 12.5. For 1961–1971, the growth rate is 41.1 - 18.9 = 22.2.
The recurring decimal representation 1·272727... is equivalent to
UPSC's answer: (b) — Let x = 1.272727..., where the digits '27' repeat indefinitely. Since the repeating block has two digits, multiply x by 100 to shift the decimal point: 100x = 127.272727... Subtract the original equation (x = 1.272727...) from the new equation: 100x - x = 127.272727... - 1.272727...
What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?
UPSC's answer: (b) — Find the Least Common Multiple (LCM) of the divisors 3, 4, 5, and 6, which is 60. Since the number leaves a remainder of 2 in each case, the number must be of the form 60k + 2.
In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers?
UPSC's answer: (c) — Each marriage pairs one man with one woman, so married men = married women. If there are M men and W women, 0·4M = 0·3W, so M : W = 3 : 4. Take 30 men and 40 women (70 adults): married men = 12 and married women = 12, i.e. 24 married adults. 24/70 × 100 = 240/7 = 34 2/7 %. Hence option (c).
What is the remainder when 51 × 27 × 35 × 62 × 75 is divided by 100?
UPSC's answer: (a) — To find the remainder when a product is divided by 100, we can determine the last two digits of the product. First, calculate the product of the first two numbers: 51 × 27 = 1377, which ends in 77. Next, multiply this result by the third number: 77 × 35 = 2695, which ends in 95.
A sum of ₹ 2,500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6. What is the difference between the maximum share and the minimum share?
UPSC's answer: (c) — Convert the fractional ratio 1/2 : 3/4 : 5/6 to whole numbers by multiplying by the LCM of the denominators (12), resulting in 6 : 9 : 10. Calculate the total number of parts in the ratio: 6 + 9 + 10 = 25 parts.
For what value of n, the sum of digits in the number (10ⁿ + 1) is 2?
UPSC's answer: (b) — For n = 0: 10⁰ + 1 = 2, digit sum 2. For n = 1, 2, 3, …: 10ⁿ + 1 = 11, 101, 1001, …, always two 1s and zeros, so the digit sum is 2. For a negative or fractional n, 10ⁿ + 1 is not a whole number (e.g. 1·1 or about 4·16), so 'for any real number' is wrong.
In a class, there are three groups A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight of the students of the class?
UPSC's answer: (c) — Shifting one student from group A and two students from group B to group C changes only group membership, not the class total. The total number of students in the class remains the same because no student enters or leaves the class.
How many different sums can be formed with the denominations ₹ 50, ₹ 100, ₹ 200, ₹ 500 and ₹ 2,000 taking at least three denominations at a time?
UPSC's answer: (a) — There are 5 denominations: ₹50, ₹100, ₹200, ₹500 and ₹2,000. Taking at least three denominations at a time means choosing subsets of size 3, 4 or 5. The number of such subsets is 5C3 + 5C4 + 5C5 = 10 + 5 + 1 = 16.
Which one of the following is the most logical and rational inference that can be made from the above passage?
UPSC's answer: (c) — The passage explicitly states that 'we cannot shut down banks because there is no proper system to shut them down.' It identifies the missing institutional change as the 'setting up of a resolution corporation for banks' following the 1991 reforms.
Which one of the following is the most logical and rational inference that can be made from the above passage?
UPSC's answer: (c) — The passage states that renewable resources are still 'going through their cost curves and learning curves' to achieve the required output, implying current inefficiencies.
With reference to the above passage, the following assumptions have been made : 1. Governments often provide inefficient and costly subsidies for technologies that may not be ready in the near future. 2. India's commitment of reducing emissions by 33% by 2030 shall be on the basis of gas-based economy. Which of the above assumptions is/are valid?
UPSC's answer: (a) — Assumption 1 is valid because the passage states that business houses are wary of investing in renewable energy as the technology is not yet ready, implying that government subsidies for such unready technologies can be inefficient and costly.
With reference to the above passage, the following assumptions have been made : 1. Genome editing does not require the transfer of genes from one plant to another. 2. Through genome editing, the chosen genes can be altered precisely in a manner akin to the natural process that helps plants to adapt to the environmental factors. Which of the above assumptions is/are valid?
UPSC's answer: (c) — Assumption 1 is valid because the passage describes genome editing as dissecting and repairing the existing plant genome using 'molecular scissors' to alter relevant genes, without mentioning the introduction of foreign genes from other plants.
In the context of India, which one of the following statements best reflects the critical message of the passage?
UPSC's answer: (c) — The passage highlights that unscientific solid waste management, when combined with poor drainage and untreated sewage, leads to choked drains and stagnant water. This combination creates breeding grounds for mosquitoes and spreads water-borne diseases.
What is the most logical inference from the above passage?
UPSC's answer: (b) — The passage states that Article 25 guarantees freedom of religion but is explicitly prefixed with the condition 'subject to public order, morality, health and to the other provisions of this Part'.
How many different 5-letter words (with or without meaning) can be constructed using all the letters of the word 'DELHI' so that each word has to start with D and end with I?
UPSC's answer: (d) — The word 'DELHI' contains 5 distinct letters: D, E, L, H, and I. Each required 5-letter word must begin with 'D' and end with 'I', which means the 1st position and the 5th position are fixed. This leaves the 2nd, 3rd, and 4th positions to be filled using the remaining 3 letters: E, L, and H.
A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?
UPSC's answer: (c) — Initial quantity of liquid A is 20 litres. After removing 4 litres and adding 4 litres of liquid B, the quantity of liquid A remaining is 20 - 4 = 16 litres. The concentration of liquid A in the mixture is now 16/20 = 4/5. In the second step, 4 litres of this mixture is removed.
The average score of a batsman after his 50th innings was 46·4. After 60th innings, his average score increases by 2·6. What was his average score in the last ten innings?
UPSC's answer: (c) — Calculate the total runs scored in the first 50 innings: 50 × 46.4 = 2320. Determine the new average after 60 innings: 46.4 + 2.6 = 49.0. Calculate the total runs scored in the first 60 innings: 60 × 49.0 = 2940.
As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for ₹ 1,200. What was the original price of rice per kg?
UPSC's answer: (b) — Let the original price of rice per kg be ₹x. The new price after a 25% hike is x + 0.25x = 1.25x. The quantity of rice purchased at the original price is 1200/x kg. The quantity of rice purchased at the new price is 1200/(1.25x) kg.
A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?
UPSC's answer: (a) — Person X completes 20% of the work in 8 days, so X's daily work rate is 20/8 = 2.5% per day. Person Y completes 25% of the work in 6 days, so Y's daily work rate is 25/6 ≈ 4.1667% per day.
A car travels from a place X to place Y at an average speed of v km/hr, from Y to X at an average speed of 2v km/hr, again from X to Y at an average speed of 3v km/hr and again from Y to X at an average speed of 4v km/hr. Then the average speed of the car for the entire journey
UPSC's answer: (b) — Let the distance XY be d. The car covers 4d in total. Time = d/v + d/2v + d/3v + d/4v = (d/v)(1 + 1/2 + 1/3 + 1/4) = 25d/(12v). Average speed = 4d ÷ 25d/(12v) = 48v/25 = 1·92v. 1·92v lies between v and 2v — option (b).
Consider the following statements : 1. The minimum number of points of intersection of a square and a circle is 2. 2. The maximum number of points of intersection of a square and a circle is 8. Which of the above statements is/are correct?
UPSC's answer: (b) — Statement 1 is incorrect because a circle can be placed entirely inside a square without touching it, resulting in 0 points of intersection, which is less than 2. A square consists of 4 straight line segments (sides), and a circle is a single continuous curve.
A man takes half time in rowing a certain distance downstream than upstream. What is the ratio of the speed in still water to the speed of current?
UPSC's answer: (d) — Let the speed in still water be b and the current c. Downstream speed = b + c and upstream speed = b − c. For the same distance, half the time means double the speed: b + c = 2(b − c). So b = 3c, and b : c = 3 : 1. Hence option (d).
How many pairs of natural numbers are there such that the difference of whose squares is 63?
UPSC's answer: (a) — x² − y² = (x − y)(x + y) = 63, with x > y natural numbers. Factor pairs of 63 with the smaller factor first: (1, 63), (3, 21), (7, 9). These give (x, y) = (32, 31), (12, 9) and (8, 1). So there are 3 pairs — option (a).
Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?
UPSC's answer: (d) — For a fraction a/b, adding 5 to both numerator and denominator gives (a+5)/(b+5), so the change is (a+5)/(b+5) - a/b. For 2/3: 7/8 - 2/3 = 5/24. For 3/4: 8/9 - 3/4 = 5/36. For 4/5: 9/10 - 4/5 = 1/10 = 5/50.
A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4?
UPSC's answer: (d) — The digits greater than 3 are 4, 5, 6, 7, 8, and 9. Among these, the digits divisible by 3 are 6 and 9. Since n is not divisible by 6, n cannot be 6, so n = 9. Substituting n = 9 gives 2n = 18, 3n = 27, 2n + 4 = 22, and 3n + 1 = 28. Only 28 is divisible by 4, so option (d) follows.
If 1 litre of water weighs 1 kg, then how many cubic millimetres of water will weigh 0·1 gm?
UPSC's answer: (c) — 1 litre of water weighs 1 kg, which is equivalent to 1000 grams. 1 litre is equal to 1000 cubic centimetres (cm³). Therefore, 1000 cm³ of water weighs 1000 grams, meaning 1 cm³ of water weighs 1 gram. The question asks for the volume of water that weighs 0.1 grams.
A vessel full of water weighs 40 kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?
UPSC's answer: (a) — Let the empty vessel weigh V kg and a full load of water W kg. Full: V + W = 40. One-third full: V + W/3 = 20. Subtracting, 2W/3 = 20, so W = 30 and V = 10. Hence option (a).
A frog tries to come out of a dried well 4·5 m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15 cm. What is the number of jumps required for the frog to come out of the well?
UPSC's answer: (b) — The well is 4.5 m deep, which equals 450 cm. In each jump, the frog climbs 30 cm but slides down 15 cm, resulting in a net gain of 15 cm per cycle. The frog must reach a height of at least 450 cm to escape; once it reaches or exceeds this height during a jump, it does not slide back.
Question paper and answer key: Union Public Service Commission. Explanations: UPSC Answer Check. Practise this paper with a timer →
Practise Prelims PYQs and the daily 21 free
Score the daily set, see your rank, and let Guru explain what you missed.
Already have an account? Log in