CSAT Paper II of the 2022 Preliminary examination, held on 5 June 2022. 80 questions · 200 marks · qualifying at 33%. The questions broke down as Comprehension 27, Basic Numeracy 22, Mental Ability 14, Logical Reasoning 8, Data Interpretation 7.
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.
Unsustainability in production pattern is due to which of the following? 1. Heavy dependence on fossil fuels 2. Limited availability of resources 3. Expansion of recycling Select the correct answer using the code given below.
UPSC's answer: (a) — The passage explicitly states that current production models rely heavily on fossil fuels, which is identified as a primary driver of unsustainability.
Consider the following statements : Developed countries can support developing countries' transition to sustainable human development by 1. making clean energy sources available at low cost 2. providing loans for improving their public transport at nominal interest rates 3. encouraging them to change their production and consumption patterns Which of the statements given above is/are correct?
UPSC's answer: (b) — The passage says most developing countries are hampered by the high costs and low availability of clean energy sources, so developed countries can support them by making clean energy sources available at low cost; statement 1 is correct.
According to the passage given above, deforestation and denudation will ultimately lead to which of the following? 1. Depletion of soil resource 2. Shortage of land for the common man 3. Lack of water for cultivation Select the correct answer using the code given below.
UPSC's answer: (c) — The passage warns that unchecked environmental destruction and lack of afforestation will increase harsh climatic conditions and soil erosion by wind and water. Soil erosion by wind and water directly means the loss or depletion of the soil resource, so statement 1 follows.
What is the value of X in the sequence 20, 10, 10, 15, 30, 75, X?
UPSC's answer: (d) — The sequence follows a pattern where each term is multiplied by an incrementing factor: 0.5, 1, 1.5, 2, 2.5, 3. 20 × 0.5 = 10 10 × 1 = 10 10 × 1.5 = 15 15 × 2 = 30 30 × 2.5 = 75 The next factor is 3, so 75 × 3 = 225. Therefore, X = 225, which corresponds to option (d).
Two friends X and Y start running and they run together for 50 m in the same direction and reach a point. X turns right and runs 60 m, while Y turns left and runs 40 m. Then X turns left and runs 50 m and stops, while Y turns right and runs 50 m and then stops. How far are the two friends from each other now?
UPSC's answer: (a) — Start at (0,0) and move 50 m east to (50,0). X turns right (south) 60 m to (50,-60), then left (east) 50 m to (100,-60). Y turns left (north) 40 m to (50,40), then right (east) 50 m to (100,40). Both final points have x-coordinate 100, so separation is |40 - (-60)| = 100 m.
Which date of June 2099 among the following is Sunday?
UPSC's answer: (d) — Use Zeller's congruence for the Gregorian date 7 June 2099, with q=7, m=6, K=99, and J=20. Compute floor(13(m+1)/5)=18, floor(K/4)=24, floor(J/4)=5, and 5J=100. Add the terms: 7 + 18 + 99 + 24 + 5 + 100 = 253. Divide 253 by 7: 253 = 7 × 36 + 1, and remainder 1 means Sunday.
A bill for ₹ 1,840 is paid in the denominations of ₹ 50, ₹ 20 and ₹ 10 notes. 50 notes in all are used. Consider the following statements : 1. 25 notes of ₹ 50 are used and the remaining are in the denominations of ₹ 20 and ₹ 10. 2. 35 notes of ₹ 20 are used and the remaining are in the denominations of ₹ 50 and ₹ 10. 3. 20 notes of ₹ 10 are used and the remaining are in the denominations of ₹ 50 and ₹ 20. Which of the above statements are not correct?
UPSC's answer: (d) — Let the number of ₹50, ₹20, and ₹10 notes be x, y, and z respectively. The total number of notes is 50, so x + y + z = 50. The total value is ₹1,840, so 50x + 20y + 10z = 1,840. Simplifying the value equation by dividing by 10 gives 5x + 2y + z = 184.
Which number amongst 2⁴⁰, 3²¹, 4¹⁸ and 8¹² is the smallest?
UPSC's answer: (b) — Write 4¹⁸ and 8¹² as powers of 2: 4¹⁸ = (2²)¹⁸ = 2³⁶ and 8¹² = (2³)¹² = 2³⁶, so both equal 2³⁶. 2⁴⁰ is larger than 2³⁶, so it cannot be the smallest. Compare 3²¹ with 2³⁶ by taking a common exponent of 3: 3²¹ = (3⁷)³ = 2187³ and 2³⁶ = (2¹²)³ = 4096³. Since 2187 < 4096, 3²¹ < 2³⁶ < 2⁴⁰.
The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the number formed in the second row is twice the number formed in the first row; and the number formed in the third row is thrice the number formed in the first row. Repetition of digits is not allowed. If only three of the four digits 2, 3, 7 and 9 are allowed to use in the first row, how many such combinations are possible to be arranged in the three rows?
UPSC's answer: (c) — Let the first-row number be N; the other rows are 2N and 3N, and together the nine digits must be 1 to 9 with no repetition. 3N must have three digits, so N ≤ 333; hence N starts with 2 or 3 and uses three of the digits 2, 3, 7, 9. The candidates are 237, 239, 273, 279, 293, 297, 327 and 329.
Which one of the following statements best reflects the message of the author of the passage?
UPSC's answer: (c) — The passage draws an analogy between medicine and politics, noting that we seek a trained physician for health, not just an eloquent one. It criticizes the current presumption that anyone who can get votes is qualified to administer a State.
Why is the methodology adopted in India to count the ‘poor’ debatable?
UPSC's answer: (d) — The passage explicitly states that the poverty line is unsatisfactory due to its 'extremely narrow definition' and 'debatable methodology'. It clarifies that this methodology exclusively relies on the notion of poverty as 'insufficient income or insufficient purchasing power'.
Why is income poverty only one measure of counting the 'poor'?
UPSC's answer: (a) — The passage defines the poverty line as relying exclusively on the notion of 'insufficient income or insufficient purchasing power,' which it categorizes as 'income poverty.' It argues that if poverty is about deprivations affecting human well-being, income poverty is only one aspect of it.
What does the author mean by 'poverty of a life'?
UPSC's answer: (a) — The passage explicitly defines 'poverty of a life' as lying not merely in the impoverished state but in the 'lack of real opportunity given by social constraints as well as personal circumstances'.
X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
UPSC's answer: (b) — The total distance of the race is 3 km, which equals 3000 meters. The length of the circular course is 300 meters. The number of laps required to complete the race is 3000 m / 300 m = 10 laps. Let the speed of X be 3v and the speed of Y be 2v. The relative speed is 3v - 2v = v.
If the order of the letters in the English alphabet is reversed and each letter represents the letter whose position it occupies, then which one of the following represents 'LUCKNOW'?
UPSC's answer: (d) — In a reversed alphabet, a letter at position n maps to position 27 - n. L (12) maps to 15 = O, U (21) maps to 6 = F, C (3) maps to 24 = X. K (11) maps to 16 = P, N (14) maps to 13 = M, O (15) maps to 12 = L. W (23) maps to 4 = D. Therefore LUCKNOW becomes OFXPMLD, which is option (d).
In a tournament of Chess having 150 entrants, a player is eliminated whenever he loses a match. It is given that no match results in a tie/draw. How many matches are played in the entire tournament?
UPSC's answer: (c) — In a single-elimination tournament, every match results in exactly one player being eliminated. To determine the winner from 150 entrants, 149 players must be eliminated.
How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5 ?
UPSC's answer: (b) — The number must be divisible by 5, so the units digit must be 5 (since 0 is not an odd digit and repetition is not allowed, but 0 is even anyway, so only 5 is possible for the units place among odd digits). The available odd digits are {1, 3, 5, 7, 9}.
Consider the Question and two Statements given below : Question : Is x an integer? Statement-1 : x/3 is not an integer. Statement-2 : 3x is an integer. Which one of the following is correct in respect of the Question and the Statements?
UPSC's answer: (d) — Statement-1 states that x/3 is not an integer, which implies x is not a multiple of 3, but x could still be an integer (e.g., x=1) or a non-integer (e.g., x=1/2), so it is insufficient alone.
The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?
UPSC's answer: (b) — Let the initial price of the item be 100. After a 25% increase, the price becomes 100 + 25 = 125. A subsequent 20% decrease on 125 is 25, making the new price 125 - 25 = 100. A final 10% increase on 100 is 10, resulting in a final price of 110.
Based on the above passage, the following assumptions have been made : 1. Development of agricultural technology is confined to developed countries. 2. Agricultural technology is not adapted in developing countries. Which of the above assumptions is/are valid?
UPSC's answer: (d) — Assumption 1 is invalid because the passage states that techniques developed in the West are being adapted in some places to make tropical crops more productive, implying technology is not confined to developed countries.
Based on the above passage, the following assumptions have been made : 1. Poor countries need to bring about change in their existing farming techniques. 2. Developed countries have better infrastructure and they waste less food. Which of the above assumptions is/are valid?
UPSC's answer: (a) — The passage explicitly states that in the developing world, adaptation applies to 'existing farming techniques' as much as to new genetic advances, supporting Assumption 1.
Based on the above passage, the following assumptions have been made : 1. Growing enough food for future generations will be a challenge. 2. Corporate farming is a viable option for food security in poor countries. Which of the above assumptions is/are valid?
UPSC's answer: (a) — The passage states that staple crop productivity has reached a plateau and suitable unfarmed land is scarce, implying that meeting future food demands will be difficult.
The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E. How many such arrangements are possible?
UPSC's answer: (c) — The condition 'exactly two letters between A and E' means A and E must occupy positions (1,4) or (2,5) in a 5-letter sequence. There are 2 possible position pairs for A and E: (1,4) and (2,5).
Consider the Question and two Statements given below : Question : Is Z brother of X ? Statement-1 : X is a brother of Y and Y is a brother of Z. Statement-2 : X, Y and Z are siblings. Which one of the following is correct in respect of the Question and the Statements?
UPSC's answer: (d) — To answer 'Is Z the brother of X?' we need to know that Z is male and that Z and X are siblings. Statement-1: 'X is a brother of Y and Y is a brother of Z' tells us X and Y are male and that X, Y and Z are siblings, but says nothing about Z's gender.
On one side of a 1·01 km long road, 101 plants are planted at equal distance from each other. What is the total distance between 5 consecutive plants?
UPSC's answer: (b) — The total length of the road is 1.01 km, which converts to 1010 meters. With 101 plants planted at equal distances on one side, there are 100 equal intervals between them (since the number of intervals is always one less than the number of plants).
A, B and C are three places such that there are three different roads from A to B, four different roads from B to C and three different roads from A to C. In how many different ways can one travel from A to C using these roads?
UPSC's answer: (c) — Direct travel from A to C is possible via 3 distinct roads. Indirect travel from A to C via B involves choosing one of the 3 roads from A to B and one of the 4 roads from B to C. The number of indirect routes is calculated as 3 (A to B) multiplied by 4 (B to C), which equals 12.
A has some coins. He gives half of the coins and 2 more to B. B gives half of the coins and 2 more to C. C gives half of the coins and 2 more to D. The number of coins D has now, is the smallest two-digit number. How many coins does A have in the beginning?
UPSC's answer: (d) — The smallest two-digit number is 10, so D has 10 coins. D received half of C's coins plus 2, so C had (10 - 2) * 2 = 16 coins. C received half of B's coins plus 2, so B had (16 - 2) * 2 = 28 coins. B received half of A's coins plus 2, so A had (28 - 2) * 2 = 52 coins.
In the series AABABCABCDABCDE..., which letter appears at the 100th place?
UPSC's answer: (c) — The series AABABCABCDABCDE... is built by concatenating groups where the n-th group contains the first n letters of the alphabet: Group 1 = A, Group 2 = AB, Group 3 = ABC, Group 4 = ABCD, and so on. The cumulative number of letters after completing n groups is 1 + 2 + 3 + … + n = n(n+1)/2.
Three persons A, B and C are standing in a queue not necessarily in the same order. There are 4 persons between A and B, and 7 persons between B and C. If there are 11 persons ahead of C and 13 behind A, what could be the minimum number of persons in the queue?
UPSC's answer: (a) — Number positions from the front. '11 persons ahead of C' puts C at position 12. 7 persons between B and C means B is 8 places from C: position 4 or 20. 4 persons between A and B means A is 5 places from B: if B = 4, A = 9 (A cannot be at −1); if B = 20, A = 15 or 25.
According to the passage, natural selection cannot anticipate future environments on the earth as 1. species not fully prepared to face the environmental changes that await them will face extinction 2. all the existing species would get extinct as their genomes will not withstand biological mishaps 3. inability of the genome to withstand environmental changes would result in extinction 4. extinction of species is a common feature Select the correct answer using the code given below.
UPSC's answer: (c) — The passage states that natural selection cannot anticipate future environments, so existing organisms can never be fully prepared for environmental catastrophes. It then says an outcome is extinction of those species which cannot overcome environmental adversity, supporting statement 1.
The passage suggests that Darwinian theory of evolution is not a theory at all because
UPSC's answer: (b) — The passage explicitly states that the Darwinian explanation for extinct life is that organisms go extinct as a function of environmental or biological assaults for which their inheritance deems them ill-equipped.
With reference to the passage, the following assumptions have been made : 1. Only species that have the ability to overcome environmental catastrophes will survive and perpetuate. 2. More than 90% of the species on the earth are in the danger of getting extinct due to drastic changes in the environment. 3. Darwin's theory explains all the natural phenomena. Which of the above assumptions is/are valid?
UPSC's answer: (a) — Assumption 1 is valid because the passage states that extinction occurs for species that 'cannot overcome environmental adversity' and that survival depends on genomes able to withstand such vagaries.
Which one of the following statements best reflects the crux of the passage?
UPSC's answer: (d) — The passage establishes a causal chain: economic growth and rising middle-class numbers lead to higher affluence. This affluence drives two specific changes: a shift to protein-rich diets (milk, fish, meat) and increased use of electronics and vehicles.
How many seconds in total are there in x weeks, x days, x hours, x minutes and x seconds?
UPSC's answer: (d) — Convert x weeks to seconds: 1 week = 7 days = 168 hours = 604,800 seconds, so x weeks = 604,800x seconds. Convert x days to seconds: 1 day = 24 hours = 86,400 seconds, so x days = 86,400x seconds. Convert x hours to seconds: 1 hour = 3,600 seconds, so x hours = 3,600x seconds.
Consider the Question and two Statements given below in respect of three cities P, Q and R in a State : Question : How far is city P from city Q? Statement-1 : City Q is 18 km from city R. Statement-2 : City P is 43 km from city R. Which one of the following is correct in respect of the Question and the Statements?
UPSC's answer: (d) — The Question asks for the distance between cities P and Q. Statement-1 gives only the Q–R distance (18 km), and Statement-2 gives only the P–R distance (43 km); neither alone mentions both P and Q. Together they fix how far P and Q each are from R, but not their directions.
Two Statements followed by four Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows/follow from the Statements, disregarding the commonly known facts : Statement-1 : All pens are books. Statement-2 : No chair is a pen. Conclusion-I : All chairs are books. Conclusion-II : Some chairs are pens. Conclusion-III : All books are chairs. Conclusion-IV : No chair is a book. Which one of the following is correct?
UPSC's answer: (d) — From Statement-1 ('All pens are books'), the set of pens is entirely contained within the set of books. From Statement-2 ('No chair is a pen'), the set of chairs and the set of pens are completely disjoint.
Three Statements followed by three Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows/follow from the Statements, disregarding the commonly known facts : Statement-1 : Some doctors are teachers. Statement-2 : All teachers are engineers. Statement-3 : All engineers are scientists. Conclusion-I : Some scientists are doctors. Conclusion-II : All engineers are doctors. Conclusion-III : Some engineers are doctors. Which one of the following is correct?
UPSC's answer: (c) — From Statement-1, some doctors are teachers, meaning there is an overlap between the set of doctors and the set of teachers. From Statement-2, all teachers are engineers, so the overlapping doctors who are teachers must also be engineers.
Eight students A, B, C, D, E, F, G and H sit around a circular table, equidistant from each other, facing the centre of the table, not necessarily in the same order. B and D sit neither adjacent to C nor opposite to C. A sits in between E and D, and F sits in between B and H. Which one of the following is definitely correct?
UPSC's answer: (d) — Fix A's seat. A sits between E and D, and F sits between B and H. B and D must be neither next to C nor opposite C. Checking every seating that meets these conditions gives exactly six arrangements.
The passage is based on the idea that
UPSC's answer: (b) — The passage opens by stating that for the last two or three generations, individuals have been living as 'workers merely' rather than as human beings. It explicitly identifies 'an excessive amount of labour' as the rule in every circle of society today.
Man does not seek self-improvement because he
UPSC's answer: (d) — The passage states that excessive labour prevents man's spiritual element from thriving and makes it difficult to spend leisure in serious activities. It explicitly notes that man 'does not want to think' or 'cannot even if he wants to' due to this exhaustion.
Which of the following would invariably happen in a country, when the demographic dividend has begun to operate? 1. The number of illiterate people will decrease. 2. The ratio of very old and very young will decrease for a while. 3. Population growth rate will quickly stabilize. Select the correct answer using the code given below.
UPSC's answer: (b) — The passage explicitly defines the demographic dividend as a swelling in the working-age population, which conversely means the relative ratio of very young and very old people will be on the decline for a while.
With reference to the passage, which of the following inferences can be drawn? 1. Demographic dividend is an essential condition for a country to rapidly increase its economic growth rate. 2. Promotion of higher education is an essential condition for a country for its rapid economic growth. Select the correct answer using the code given below :
UPSC's answer: (d) — Inference 1 claims demographic dividend is an 'essential condition' for rapid growth, but the passage states it is a 'window of opportunity' and an 'engine of growth,' not a strict prerequisite.
Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below : 1. Z purchased 8 notebooks more than X did. 2. P and Q together purchased 21 notebooks. 3. Q purchased 5 notebooks less than P did. 4. X and Y together purchased 28 notebooks. 5. P purchased 5 notebooks more than X did. If each notebook is priced ₹ 40, then what is the total cost of all the notebooks?
UPSC's answer: (a) — From statements 2 and 3, P + Q = 21 and P - Q = 5, which gives P = 13 and Q = 8. From statement 5, P purchased 5 more than X, so X = P - 5 = 13 - 5 = 8. From statement 1, Z purchased 8 more than X, so Z = X + 8 = 8 + 8 = 16. From statement 4, X + Y = 28, so Y = 28 - X = 28 - 8 = 20.
A man started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1·25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is
UPSC's answer: (d) — Let the outward drive take t minutes (by the home clock). The return route is 1·25 times as long and driven at twice the speed, so it takes 1·25 ÷ 2 = 5/8 of t. From 14:30 to 16:00 is 90 minutes: t + 25 (stay) + 5t/8 = 90, so 13t/8 = 65 and t = 40 minutes.
A person X wants to distribute some pens among six children A, B, C, D, E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?
UPSC's answer: (c) — A = 2B = 3C = 4D = 5E = 6F, so A must be a multiple of 2, 3, 4, 5 and 6, i.e. of their LCM 60. With A = 60: B = 30, C = 20, D = 15, E = 12, F = 10 — but D = 15 is odd. The next choice, A = 120, gives B = 60, C = 40, D = 30, E = 24, F = 20, all even.
Six persons A, B, C, D, E and F are sitting equidistant from each other around a circular table (facing the centre of the table). Consider the Question and two Statements given below : Question : Who is sitting on the immediate left of A? Statement-1 : B is sitting opposite to C and D is sitting opposite to E. Statement-2 : F is sitting on the immediate left of B. Which one of the following is correct in respect of the Question and the Statements?
UPSC's answer: (d) — With six seats, 'opposite' means three seats away. Statement-1 pairs B–C and D–E as opposites, so A and F must also be opposite each other; it does not fix who is next to A, so it is not sufficient.
Consider the Question and two Statements given below : Question : What is the age of Manisha? Statement-1 : Manisha is 24 years younger than her mother. Statement-2 : 5 years later, the ages of Manisha and her mother will be in the ratio 3 : 5. Which one of the following is correct in respect of the Question and the Statements?
UPSC's answer: (c) — Let Manisha's current age be M and her mother's current age be Mo. Statement-1 provides the equation: Mo = M + 24. Statement-2 provides the equation: (M + 5) / (Mo + 5) = 3 / 5. Substituting Mo from Statement-1 into Statement-2 gives: (M + 5) / (M + 24 + 5) = 3 / 5.
Six lectures A, B, C, D, E and F, each of one hour duration, are scheduled between 8:00 a.m. and 2:00 p.m. Consider the Question and two Statements given below : Question : Which lecture is in the third period? Statement-1 : Lecture F is preceded by A and followed by C. Statement-2 : There is no lecture after lecture B. Which one of the following is correct in respect of the Question and the Statements?
UPSC's answer: (d) — The six one-hour slots between 8:00 a.m. and 2:00 p.m. are numbered 1 through 6, and the question asks which lecture occupies slot 3.
Which of the following statements best reflects the underlying tone of the passage?
UPSC's answer: (a) — The passage argues that machine productivity leads to leisure, but leisure is tedious without intelligent activities and interests. It explicitly states that for a leisured population to be happy, it must be educated with a view to enjoyment and technical knowledge.
With reference to the passage, which one of the following statements is correct?
UPSC's answer: (b) — The passage opens by suggesting two possible reasons for the reduced thrill of presents in adulthood: having 'too much already' or losing the 'fullness of the joy of giving'.
The author of the passage is against
UPSC's answer: (a) — The passage states that children 'do not look too forward nor too far backward,' which implies that excessive focus on the past and future is a negative trait associated with adults.
Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition. Consider the following statements : 1. The 4-digit least value of x is 1332. 2. The 3-digit greatest value of x is 888. Which of the above statements is/are correct?
UPSC's answer: (a) — For any three distinct non-zero digits A, B, and C, there are 6 possible 3-digit numbers formed without repetition: ABC, ACB, BAC, BCA, CAB, and CBA. The sum of these numbers is calculated as 222(A + B + C), because each digit appears in the hundreds, tens, and units place exactly twice.
There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in the PIN differ by at least 2. How many maximum attempts does one need to find out the PIN with certainty?
UPSC's answer: (c) — The PIN is a 3-digit decreasing sequence chosen from digits 1 to 7, so once three digits are selected, their left-to-right order is fixed. The condition that any two digits differ by at least 2 means no two selected digits can be consecutive.
There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these points as vertices and taking the diameter as one side of the triangle?
UPSC's answer: (a) — There are 8 equidistant points on the circle, so opposite points form 4 diameters. For any chosen diameter, the third vertex can be any of the other 6 points on the circle. By Thales' theorem, a triangle inscribed in a circle with a diameter as one side is right-angled at the third vertex.
24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
UPSC's answer: (d) — The problem provides the combined work rate of 24 men and 12 women but does not specify the individual work rates of a man and a woman.
What is the remainder when 91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99 is divided by 1261?
UPSC's answer: (d) — Factorize the divisor 1261 to identify its prime components: 1261 = 13 × 97. Examine the product 91 × 92 × 93 × 94 × 95 × 96 × 97 × 98 × 99. Observe that the term 97 is explicitly present in the product.
Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm : 1. It is possible to cut the sheet exactly into 4 square sheets. 2. It is possible to cut the sheet into 10 triangular sheets of equal area. Which of the above statements is/are correct?
UPSC's answer: (c) — Area of the rectangular sheet = 20 cm × 8 cm = 160 cm². For statement 1, cut the 20 cm length into 8 cm + 8 cm + 4 cm, giving two 8 cm × 8 cm squares and one 4 cm × 8 cm rectangle. Cut the 4 cm × 8 cm rectangle into two 4 cm × 4 cm squares, giving exactly 4 square sheets.
When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. Which one of the following is correct?
UPSC's answer: (a) — From the first condition, 0.7x + y = 1.65y, so 0.7x = 0.65y, giving x = (65/70)y = (13/14)y, which means x is less than y. From the second condition, 0.6x + z = 1.65z, so 0.6x = 0.65z, giving x = (65/60)z = (13/12)z, which means x is greater than z.
Which one of the following is implied by the passage?
UPSC's answer: (c) — The passage begins with the statement: 'The majority of people who fail to accumulate money sufficient for their needs...'. This phrase presupposes the existence of a group of people who actually fail to accumulate sufficient money.
What is the main idea of the passage?
UPSC's answer: (a) — The passage opens by stating that people who fail to accumulate sufficient money are generally easily influenced by the opinions of others. It further explains that allowing newspapers and neighbors to do one's thinking leads to a lack of success in any undertaking.
With reference to the above passage, which of the following statements is/are correct? 1. Conventions are the sources of rights of man. 2. Rights of man can be exercised only when there is a social order. Select the correct answer using the code given below.
UPSC's answer: (c) — The passage states that the social order is the 'basis of all other rights,' which directly supports Statement 2 that rights can only be exercised within a social order.
Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?
UPSC's answer: (a) — Let the total number of voters be V. Since 80% of voters cast their votes, the total votes cast is 0.8V. Candidate X received 56% of the votes cast, so Candidate Y received the remaining 44% (100% - 56%). The difference in their vote shares is 56% - 44% = 12% of the total votes cast.
What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?
UPSC's answer: (c) — First, determine the Least Common Multiple (LCM) of the divisors 6, 9, 12, 15, and 18. The prime factorizations are: 6 = 2×3, 9 = 3², 12 = 2²×3, 15 = 3×5, 18 = 2×3². The LCM is the product of the highest powers of all primes involved: 2² × 3² × 5 = 4 × 9 × 5 = 180.
Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p × q = 2430, then what is the difference between p and q?
UPSC's answer: (d) — Let p = 10a + b and q = 10b + a, where a and b are non-zero digits, so that p and q are two-digit reverses of each other. The condition is (10a + b)(10b + a) = 2430; factoring 2430 = 2 × 5 × 3⁵, we search for a pair of two-digit factors that are digit-reverses.
Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number : 1. p × q can be an odd number. 2. q/p can be a prime number. 3. p + q can be a prime number. Which of the above statements are correct?
UPSC's answer: (d) — Statement 1 is correct: If p = 3 (prime) and q = 9 (composite), then p × q = 27, which is an odd number. Statement 2 is correct: If p = 2 (prime) and q = 6 (composite), then q/p = 3, which is a prime number.
Consider the following statements : 1. Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide. 2. Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide. Which of the above statements is/are correct?
UPSC's answer: (c) — The minute hand moves at 6° per minute and the hour hand at 0.5° per minute, giving a relative speed of 5.5° per minute. At 3:00 the hour hand sits at 90° while the minute hand is at 0°, so the minute hand must gain 90° to overtake it, which takes 90 ÷ 5.5 = 180/11 ≈ 16.36 minutes, placing the…
There are two containers X and Y. X contains 100 ml of milk and Y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which one of the following is correct?
UPSC's answer: (a) — Initially, X has 100 ml milk and Y has 100 ml water. 20 ml of milk is moved from X to Y, so X has 80 ml milk and Y has 20 ml milk + 100 ml water (total 120 ml). The mixture in Y is uniform, so 20 ml transferred back to X contains (20/120)*20 = 10/3 ml milk and (100/120)*20 = 50/3 ml water.
A pie chart gives the expenditure on five different items A, B, C, D and E in a household. If B, C, D and E correspond to 90°, 50°, 45° and 75° respectively, then what is the percentage of expenditure on item A?
UPSC's answer: (d) — The total angle of a pie chart is 360 degrees. The sum of the angles for items B, C, D, and E is 90 + 50 + 45 + 75 = 260 degrees. The angle corresponding to item A is 360 - 260 = 100 degrees. The percentage of expenditure on item A is calculated as (100 / 360) * 100.
The author's assumption about scientific research is that
UPSC's answer: (c) — The passage explicitly states that 'Scientific research is probably never completely valueless.' It argues that even if research seems silly, insignificant, or mechanical, there is always a chance the results may be of value.
According to the author
UPSC's answer: (c) — The passage states that scientific research is 'probably never completely valueless.' It explicitly mentions that 'there is always a chance that the results may be of value to the investigator of talent.' This implies that even if research seems silly or insignificant, it retains the potential to…
Which one of the following best reflects the practical, rational and lasting solution?
UPSC's answer: (d) — The passage highlights that India receives 75% of its annual precipitation in just 120 days (June-September), creating a severe temporal mismatch in water availability.
If 15 × 14 × 13 × ⋯ × 3 × 2 × 1 = 3ᵐ × n where m and n are positive integers, then what is the maximum value of m?
UPSC's answer: (b) — The expression 15 × 14 × 13 × ⋯ × 3 × 2 × 1 is the factorial of 15, denoted as 15!. To find the maximum value of m in 15! = 3ᵐ × n, we need to determine the highest power of 3 that divides 15!.
What is the value of X in the sequence 2, 12, 36, 80, 150, X ?
UPSC's answer: (b) — The sequence 2, 12, 36, 80, 150, X follows the pattern n²(n + 1) for the nth term: 1²×2 = 2, 2²×3 = 12, 3²×4 = 36, 4²×5 = 80, 5²×6 = 150.
One non-zero digit, one vowel and one consonant from English alphabet (in capital) are to be used in forming passwords, such that each password has to start with a vowel and end with a consonant. How many such passwords can be generated?
UPSC's answer: (c) — The password consists of three distinct characters: one non-zero digit, one vowel, and one consonant. The first position is fixed for a vowel, and the last position is fixed for a consonant. There are 5 vowels (A, E, I, O, U) and 21 consonants in the English alphabet.
There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should contain at least one cup of coffee?
UPSC's answer: (d) — 9 cups in equal rows and columns form a 3 × 3 grid. The arrangement is fixed by choosing which 3 of the 9 places hold tea: 9C3 = 84 ways. A row has no coffee only if all 3 of its cups are tea.
The sum of three consecutive integers is equal to their product. How many such possibilities are there?
UPSC's answer: (c) — Let the three consecutive integers be n-1, n, and n+1. Their sum is 3n, and their product is n(n-1)(n+1) = n(n² - 1). Equating sum and product gives 3n = n(n² - 1), so n(n² - 4) = 0. Therefore n = 0, n = 2, or n = -2.
What is the number of numbers of the form 0·XY, where X and Y are distinct non-zero digits?
UPSC's answer: (a) — The number is of the form 0.XY, where X and Y are digits in the tenths and hundredths places respectively. The problem states that X and Y must be non-zero digits, so the possible values for each are {1, 2, 3, 4, 5, 6, 7, 8, 9}, giving 9 options for each.
The average weight of A, B, C is 40 kg, the average weight of B, D, E is 42 kg and the weight of F is equal to that of B. What is the average weight of A, B, C, D, E and F?
UPSC's answer: (c) — The sum of the weights of A, B, and C is 3 × 40 = 120 kg. The sum of the weights of B, D, and E is 3 × 42 = 126 kg. Adding these two sums gives A + 2B + C + D + E = 120 + 126 = 246 kg.
Question paper and answer key: Union Public Service Commission. Explanations: UPSC Answer Check. Practise this paper with a timer →
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