CSAT Paper II of the 2026 Preliminary examination, held on 24 May 2026. 80 questions · 200 marks · qualifying at 33%. The questions broke down as Basic Numeracy 26, Comprehension 22, Mental Ability 9, Logical Reasoning 9, Interpersonal & Communication Skills 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.
Question : X receives three coins of different denominations : 1, 2, 5, 10 and 20. If the total amount received by X is m, does X receive a coin of denomination 5? Statement I : m is not a prime number. Statement II : The sum of the digits of m is greater than 5.
UPSC's answer: (a) — Three different coins from {1, 2, 5, 10, 20} give ten possible totals: 8 (1+2+5), 13 (1+2+10), 23 (1+2+20), 16 (1+5+10), 26 (1+5+20), 31 (1+10+20), 17 (2+5+10), 27 (2+5+20), 32 (2+10+20), 35 (5+10+20). Statement I (m not prime) leaves 8, 16, 26, 27, 32, 35.
Question : For two distinct real numbers x and y, which of them is bigger? Statement I : x² < y < 1 Statement II : y < √x < 1
UPSC's answer: (d) — Statement I (x² < y < 1): take y = 0.3. With x = 0.5 (x² = 0.25) x is bigger; with x = 0.1 (x² = 0.01) y is bigger. Not sufficient. Statement II (y < √x < 1): take x = 0.25, so √x = 0.5. With y = 0.3 y is bigger; with y = 0.1 x is bigger. Not sufficient.
Question : If x and y are integers, then is x even? Statement I : x²y² is even. Statement II : 1 + x² + y² is odd.
UPSC's answer: (c) — Statement I: x²y² even means xy is even, so at least one of x, y is even. x could be odd (x = 1, y = 2) or even. Not sufficient. Statement II: 1 + x² + y² odd means x² + y² is even, so x and y have the same parity (both odd or both even). Not sufficient.
Question : X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the numbers all of which are either from X or from Y. Is every number of T from Y? Statement I : The sum of any two numbers belonging to T is even. Statement II : If both p and q are picked from T, then (p - 1)q is even.
UPSC's answer: (d) — Statement I: the sum of any two numbers of T is even, so all numbers of T have the same parity. T could be all odd (from X) or all even (from Y). Not sufficient. Statement II: (p − 1)q is even for all p, q in T.
Question : If x, y and z are integers, each greater than 1, then is x a prime number? Statement I : xy² = 116 Statement II : xz = 261
UPSC's answer: (a) — Statement I: xy² = 116 = 2² × 29. With y > 1, the only square factor available is 4, so y = 2 and x = 29, which is prime. Sufficient. Statement II: xz = 261 = 3² × 29. With x, z > 1, x can be 3, 9, 29 or 87; 3 and 29 are prime but 9 and 87 are not. Not sufficient.
Which of the following conclusions are valid? 1. Seven Sanskriti Angans, representing different regions of India, had been showcased in Kalagram. 2. Regional artistry was recognised via the inspiration drawn from iconic temples. 3. India's ancient history had been crafted by the contemporary craftsmanship of 230 artisans into creations to behold. 4. Art forms from all regions of India had been showcased in these living galleries. Select the answer using the code given below.
UPSC's answer: (a) — Conclusion 1 is valid: the passage says Kalagram represented India's regions through seven Sanskriti Angans. Conclusion 2 is valid: the thematic zones, inspired by iconic temples such as Dakshineshwar Kali and Brahma Mandir, were "treasure troves of regional artistry".
The weight of X, in kg, is denoted by X. The weights of A, B, C, D, P, Q, R and S are measured. Given : A + B + C + D = 17 A + C = 6 P + Q + S + D = 15 P + Q + R + B = 17 P = R and Q = S Which one of the following statements is correct?
UPSC's answer: (b) — From A + B + C + D = 17 and A + C = 6: B + D = 11. Put R = P and S = Q: P + 2Q + D = 15 and 2P + Q + B = 17. Add them: 3P + 3Q + (B + D) = 32, so 3(P + Q) = 21 and P + Q = 7. P + Q = 7 is more than A + C = 6, so (b) is correct.
How many words can one form by shuffling the letters of the word QUEUE, if Q is always followed by U? The words thus formed need not necessarily have any meaning.
UPSC's answer: (d) — QUEUE has the letters Q, U, E, U, E. Q must be immediately followed by U, so treat "QU" as one block. The items to arrange are then QU, U, E, E. Four items with E repeated twice: 4! ÷ 2! = 12 arrangements.
X, Y and Z jump forward 4', 6' and 5', respectively. At 8 AM, they all land on mark 199'. How many times will they all land on the same mark (need not be at the same moment) between mark 195' and 1000', if all of them cross mark 1000' by 9 AM?
UPSC's answer: (d) — X lands on 199 + 4k, Y on 199 + 6k and Z on 199 + 5k. A mark is shared by all three when the distance from 199 is a multiple of LCM(4, 6, 5) = 60. The common marks are 199, 259, 319, …, 199 + 60k. They need not land at the same moment, so 199 itself counts, and it lies between 195 and 1000.
Which of the following conclusions are valid? 1. Sport is more than just games; it is a way of life. 2. Sport can help mitigate the problems of seclusion among the young. 3. Earning laurels in sport can help one secure a job on the basis of an assigned quota. 4. Standard corporate sector skills cannot be learnt through sport. Select the answer using the code given below.
UPSC's answer: (d) — Conclusion 1 is valid: the passage calls for a culture in which "sport is seen as a way of life". Conclusion 2 is valid: children who are inactive and rarely leave the house is a problem of seclusion, and the passage says sport can help tackle it.
Which of the following statements is/are correct? 1. Parents are not encouraging enough when it comes to children playing sport. 2. Participation in sporting activities can help develop life skills. 3. Sport as a way of life can help evolve the very nature of society itself. Select the answer using the code given below.
UPSC's answer: (b) — Statement 1 is not correct: the passage says parents complain that their children are inactive; it does not say parents fail to encourage them to play. Statement 2 is correct: time management, fitness, teamwork and coordination are life skills the passage says sport teaches.
A toy T jumps forward or backward. In each forward jump, it moves 5' forward whereas in each backward jump, it moves 2' backward. If in 31 jumps, T moves exactly 15' forward, then what is the difference of the number of forward and backward jumps?
UPSC's answer: (d) — Let f be the forward jumps and b the backward jumps: f + b = 31. Net movement: 5f − 2b = 15. Substituting b = 31 − f: 5f − 62 + 2f = 15, so 7f = 77, f = 11 and b = 20. The difference is 20 − 11 = 9: (d).
Eight persons P, Q, R, S, T, U, V and W sit around a round table in eight different seats placed with equal distance between any two consecutive seats. Both P and R are adjacent to Q. Both T and R are adjacent to S. Both U and W are adjacent to V. S and W are on opposite chairs. If while going in the clockwise direction around the table from P, one meets R before T, then how many persons shall Q cross while moving in the clockwise direction around the table before meeting W?
UPSC's answer: (a) — P and R are both next to Q, and R and T are both next to S, so P, Q, R, S, T sit in a row of five consecutive seats. U and W are both next to V, so U, V, W fill the other three seats as a block, and S must be opposite W.
The top of a table is rectangular and its dimensions are 6' × 10'. Two rectangular portions of the table top are painted in blue colour; both these portions have dimensions 2·5' × 8' and each of them has exactly two sides common with two edges of the table top. If the table is fixed to the ground and the remaining portion of the table top is painted in white, how many different patterns are possible when observed from above?
UPSC's answer: (b) — Each blue portion is 2·5′ × 8′ and shares two sides with two edges of the table, so it sits in a corner. Its 8′ side cannot lie along the 6′ edge, so it must run along a 10′ edge. Each portion therefore fills one corner, 8′ along the long edge and 2·5′ into the width.
Which of the following statements is/are correct? 1. Real value should not change in the instance of static output cost and unchanged quantities against falling oil prices. 2. Deflators are to be used separately for inputs and outputs, and this is a practice universally adopted by all economies. Select the answer using the code given below.
UPSC's answer: (d) — Statement 1 is not correct: the passage says real value ADDED should not change when oil (input) prices fall while OUTPUT PRICES and quantities stay the same. The statement speaks of "real value" and a "static output cost", which is not what the passage describes.
Which of the following assumptions is/are valid? 1. Deflation strategies can be used to make manufacturers appear to be doing better than they actually are. 2. When input and output prices are both deflated against a single input price, it is referred to as 'double deflation'. Select the answer using the code given below.
UPSC's answer: (a) — Assumption 1 is valid: using the same deflator for inputs and outputs "would look as if the manufacturer had become more productive", so a deflation method can make performance look better than it is.
A pattern formed by two characters a and b is repeated more than once in the following string : x b x a x a x x a x a x bab What is x x in the 7th and 8th positions from the left in the above string?
UPSC's answer: (d) — The string has 15 characters: x b x a x a x x a x a x b a b (x = unknown). A pattern repeated a whole number of times must have length 3 or 5. Length 3 fails: positions 4 and 13 would have to match, but they are a and b. Length 5 works.
If 10ᵐ × 1000 × n = 75²⁵ × 25³² × 32⁷⁵, where n is not divisible by 10, then the value of m is
UPSC's answer: (b) — Write each base in primes: 75 = 3 × 5², 25 = 5², 32 = 2⁵. So 75²⁵ × 25³² × 32⁷⁵ = 3²⁵ × 5⁵⁰ × 5⁶⁴ × 2³⁷⁵ = 3²⁵ × 5¹¹⁴ × 2³⁷⁵. The number of factors of 10 is the smaller of the powers of 2 and 5, i.e. 114. What is left, n = 3²⁵ × 2²⁶¹, is not divisible by 10.
The speed of a train T is 100 km per hour and the speed of a person P is 4 km per hour. T crosses P in 15 seconds, if P travels along the direction of motion of T. If P travels along the opposite direction of T, then in how much time does T cross P, in seconds, approximately?
UPSC's answer: (c) — Same direction: relative speed = 100 − 4 = 96 km/h. In 15 s the train covers its own length: L = 96 × 15/3600 = 0·4 km. Opposite direction: relative speed = 100 + 4 = 104 km/h. Time = 0·4/104 h = 0·4 × 3600/104 s ≈ 13·85 s: (c).
For 1/3 < x < y < 2, which of the following statements is/are always correct? I. x + 1/x < y + 1/y II. √(1 + y²)/y < √(1 + x²)/x Select the answer using the code given below.
UPSC's answer: (b) — Statement I is not always correct. t + 1/t falls for t < 1 and rises for t > 1. With x = 0·5 and y = 0·9: x + 1/x = 2·5 but y + 1/y ≈ 2·01, so the inequality fails. Statement II is always correct. √(1 + t²)/t = √(1/t² + 1), which keeps falling as t increases.
What is the minimum number of times one needs to measure to get 298 litres of water from a tank, if the measuring cylinders have capacities 1 litre, 6 litres, 25 litres and 100 litres?
UPSC's answer: (b) — Measuring can mean filling a cylinder from the tank or taking water back out with a cylinder. Only adding: 298 = 2 × 100 + 3 × 25 + 3 × 6 + 5 × 1, which takes 13 measurements.
There are four types of weights, namely 1 kg, 2 kg, 5 kg and 10 kg. What is the maximum number of different ways one can measure 20 kg, if at least eight but not more than eleven weights of 1 kg are to be used while measuring?
UPSC's answer: (b) — Let the number of 1 kg weights be a (8 to 11). The rest, 20 − a, must be made from 2, 5 and 10 kg weights. a = 8, rest 12: 6 × 2; 1 × 2 + 2 × 5; 1 × 2 + 1 × 10. Three ways. a = 9, rest 11: 3 × 2 + 1 × 5. One way. a = 10, rest 10: 5 × 2; 2 × 5; 1 × 10. Three ways. a = 11, rest 9: 2 × 2 + 1 × 5.
A cut on a solid object divides the object into two parts where the new surfaces thus produced are plane. On the other hand, one single cut can be used to cut more than one object at a time. In an experiment, the total number of pieces produced by applying n cuts is denoted by xₙ. The experiment is performed on a solid cube where pieces remain unmoved after each cut. In this experiment, if after the third cut, the pieces are identical, then which of the following is not a possible value for x₄?
UPSC's answer: (a) — With unmoved pieces, three cuts can give identical pieces in three ways: three parallel cuts (4 slabs), two parallel cuts and one across them (6 pieces), or three mutually perpendicular cuts through the centre (8 pieces).
The class average x in a test increases by 4 when the score of a student is rectified, whose corrected score is 100 instead of 0. Later, the score of another student was found to have been recorded as 81 in place of 56. If there are no other corrections and the final corrected average is y, then y - x is
UPSC's answer: (b) — Changing one score from 0 to 100 raises the total by 100 and the average by 4, so there are 100 ÷ 4 = 25 students. The second score was recorded as 81 but should be 56, so the total falls by 25 and the average by 25 ÷ 25 = 1. Final average y = x + 4 − 1 = x + 3, so y − x = 3: (b).
Which of the following reflect the intent of the writer in the above passage? 1. To evolve methodologies for objective analysis of the two viruses 2. To establish the epidemiological similarities and differences between the two viruses 3. To offer a better understanding of the remedies of HMPV when analysed in conjunction with SARS-CoV-2 Select the answer using the code given below.
UPSC's answer: (d) — Intent 1 is not reflected: the passage offers no method for analysing the viruses. Intent 2 is not reflected: the passage stresses only differences (virus family, seasonality, severity, long-term effects). It does not set out similarities.
Three variables x, y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression {(x × y) + z}; then M - N is
UPSC's answer: (c) — x, y, z are three different values from 2, 3, 4, 5. Largest (x × y) + z: multiply the two biggest and add the next: 5 × 4 + 3 = 23 = M. Smallest: multiply the two smallest and add the next: 2 × 3 + 4 = 10 = N (the alternatives 2 × 4 + 3 = 11 and 3 × 4 + 2 = 14 are larger). M − N = 23 − 10 = 13: (c).
Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x² and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?
UPSC's answer: (b) — y ∝ x² and x ∝ 1/z, so y ∝ 1/z², i.e. y × z² is constant. At the given point: 50 × (7/25)². For y = 98: z² = 50 × (7/25)² ÷ 98 = (7/25)² × (25/49), so z = (7/25) × (5/7) = 1/5: (b).
Which of the following assumptions is/are valid? 1. Agricultural productivity has marched ahead in the West because of the economies of scale facilitated by the adoption of AI tools. 2. Affordable AI tools rendered available in local languages can help AI-based solutions reach more and more small farmers. 3. Though penetration is as yet low, critical application areas deploying AI tools are already in use in India. Select the answer using the code given below.
UPSC's answer: (d) — Assumption 1 is not valid: the passage says generative AI tools have started offering precision farming in the US and Europe; it says nothing about economies of scale or productivity having "marched ahead" because of them.
P, Q, R, S and T are ranked 1 to 5 (not necessarily in that order). The rank of P is 4, the rank of Q is not 5, the rank of R is 1, the rank of S is not 2, the rank of T is not 3. Then which of the following is/are correct? I. If the rank of S is 3, then that of T is 2. II. If the rank of Q is 3, then that of T is 5. Select the answer using the code given below.
UPSC's answer: (d) — P = 4 and R = 1, so Q, S and T share ranks 2, 3 and 5. Q ≠ 5 gives Q = 2 or 3; S ≠ 2 gives S = 3 or 5; T ≠ 3 gives T = 2 or 5. I: if S = 3, then Q = 2 (Q cannot be 5) and T = 5. T is not 2, so I is not correct. II: if Q = 3, then S = 5 and T = 2. T is not 5, so II is not correct. Hence neither: (d).
Two identical straight rods are painted in five distinct colours so that each of them gets divided into five equal parts along the length. In one of them, the portions are marked P1, P2, P3, P4 and P5 (not necessarily in that order) whereas in the other, they are marked Q1, Q2, Q3, Q4 and Q5 (not necessarily in that order). When the rods are kept parallel to each other side by side, P1 and Q3 match, P4 matches Q1 or Q2, and Q4 matches P3 or P5. If Q3 and Q5 are adjacent, which of the following is/are possible? I. Q3 is marked at the middle portion of the straight rod. II. P2 is marked at one of the extreme portions of the straight rod. Select the answer using the code given below.
UPSC's answer: (c) — Number the five portions 1 to 5 along the rods. Q3 sits opposite P1; P4 is opposite Q1 or Q2; Q4 is opposite P3 or P5; Q3 and Q5 are next to each other. I is possible. Rod Q: Q1, Q2, Q3, Q5, Q4. Rod P: P4, P2, P1, P3, P5. Then P1–Q3, P4–Q1, P5–Q4, and Q3, Q5 are adjacent, with Q3 in the middle.
Seven persons A, B, C, D, E, F and G travel by three cars X, Y, Z. A and another two of them travel by X. Only E travels with G. C travels by Z, but B does not travel by Y. Besides, A and B do not travel by the same car. Then which of the following are correct? I. No one travels alone. II. Only D travels with F. III. Only C travels with B. Select the answer using the code given below.
UPSC's answer: (b) — B cannot be in Y, and cannot be in X because A is there, so B is in Z with C. "Only E travels with G" means E and G share a car with nobody else. X has A and Z has B and C, so E and G are in Y. D and F are left, and X needs A plus two others: X = {A, D, F}, Y = {E, G}, Z = {B, C}.
There are four statements X, Y, Z and W. Their relations are as follows : If X is incorrect, then so is Z; if Y is incorrect, then W is correct; if W is correct, then X is incorrect. Which of the following is/are correct? I. If X is correct, then so is Y. II. If Z is correct, then it is not necessary that Y is correct. Select the answer using the code given below.
UPSC's answer: (a) — The given rules are: X incorrect → Z incorrect; Y incorrect → W correct; W correct → X incorrect. I: suppose X is correct. By the third rule W cannot be correct, so W is incorrect. By the second rule, if Y were incorrect W would be correct, so Y must be correct. I holds. II: suppose Z is correct.
X and Y are two runners who run for the same duration of time on the same circular track. They started running at the same time in the same direction with uniform speeds. When X completed 7 rounds, Y did exactly 5. After completing 5 rounds, Y changed his direction and started running in the opposite direction with speed which is double of his earlier speed. On the other hand, X continued to run with the same speed. They stopped running when X completed exactly 21 rounds. How many times did X and Y meet after they had started and before they finally stopped?
UPSC's answer: (a) — Take the time X needs for 7 rounds as 1 unit: X runs 7 rounds and Y 5 rounds per unit. Phase 1, same direction, 1 unit: X gains 7 − 5 = 2 rounds, so they meet 2 times (the second at the starting point, just as Y finishes 5 rounds). Phase 2: Y turns back at 10 rounds per unit.
In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all the questions and got a score of 69. Had he been awarded 4 marks for a correct answer and 1 mark deducted for a wrong answer, he would have scored 84. How many questions were there in the question paper?
UPSC's answer: (b) — Let c be correct and w wrong answers (all questions attempted). 5c − 2w = 69 and 4c − w = 84, so w = 4c − 84. Substituting: 5c − 8c + 168 = 69, so 3c = 99, c = 33 and w = 48. Total questions = 33 + 48 = 81: (b).
Which of the following conclusions is/are valid? 1. Only a serious offence as categorised by the revised JJ Act, justifies the transfer of a case to the adult judicial system. 2. The JJ Act, 2021, categorises an offence as a serious offence based on the maximum sentence it carries, rather than on the minimum sentence. Select the answer using the code given below.
UPSC's answer: (b) — Conclusion 1 is not valid: under the JJ Act it is a heinous offence that allows trying a juvenile as an adult; the passage says activists think a serious offence does NOT merit transfer.
Which of the following statements is/are correct? 1. If an offence has no minimum prescribed punishment, it cannot be considered heinous as per the JJ Act, 2015. 2. As per the JJ Act, 2021, an offence for which there is a provision for a maximum sentence of seven years or more, but no minimum sentence, is to be considered a serious offence. Select the answer using the code given below.
UPSC's answer: (c) — Statement 1 is correct: a heinous offence has a minimum punishment of seven years, so an offence with no prescribed minimum cannot be heinous (the passage gives culpable homicide as an example).
An explosion takes place at a certain distance from an army camp. As soon as the sensor in the camp receives the sound of the explosion, a drone starts flying towards the spot of explosion. The drone clicks a picture from the spot and the camp receives it at the same time. Immediately another drone starts flying to the spot and it also sends a picture as soon as it reaches the spot. The two pictures were received at 5:02 PM and 5:05 PM, respectively. If the speed of the drones is 30 m/s, at what time did the explosion take place? Assume that the speed of sound is 300 m/s.
UPSC's answer: (c) — Let the spot be d metres from the camp. The second drone leaves at 5:02 PM, flies d metres at 30 m/s and sends its picture at 5:05 PM, so d/30 = 180 s and d = 5400 m. The first drone also needed 180 s, so it left, i.e. the sensor heard the sound, at 5:02 PM − 3 min = 4:59:00 PM.
The digit in the unit place of the number 6¹²⁹ × 7³⁰⁷ is
UPSC's answer: (c) — Any power of 6 ends in 6. Powers of 7 end in the cycle 7, 9, 3, 1. 307 ÷ 4 leaves 3, so 7³⁰⁷ ends in 3. 6 × 3 = 18, so the unit digit is 8: (c).
A person saves 10% of his salary every month. If his salary increases by 12% and the expenditure increases by 10%, then what will be the change in his saving per month?
UPSC's answer: (b) — Take salary 100: saving 10, expenditure 90. New salary 112; new expenditure 90 × 1·1 = 99; new saving 112 − 99 = 13. Saving rises from 10 to 13, i.e. by 30%: (b).
P has a son and a daughter. S is the mother of T. S is R's spouse. Q and R are children of P. Then how is Q related to S?
UPSC's answer: (d) — S is the mother of T, so S is a woman; S is R's spouse, so R is a man. P has one son and one daughter, and Q and R are P's children. R is the son, so Q is the daughter. Q is the sister of R, who is S's husband: (d).
How many three-digit numbers can be expressed as an integral power of 2?
UPSC's answer: (c) — 2⁶ = 64 has two digits and 2¹⁰ = 1024 has four. The three-digit powers are 2⁷ = 128, 2⁸ = 256 and 2⁹ = 512. So there are 3: (c).
Which of the following inferences is/are correct? 1. The source of the energy we consume is the key to the battle for cleaner air. 2. Bans are effective where the will is strong and the people are convinced that such bans are for the greater good of society. 3. There is judicial approval for a policy that intervenes fiscally to facilitate benevolent pricing for cleaner fuel. Select the answer using the code given below.
UPSC's answer: (c) — Inference 1 is correct: the passage opens by saying the key source of the battle for clean skies is the fuel we burn. Inference 2 is not correct: the passage's lesson is that bans work when people have ALTERNATIVES that are available and affordable, not when people are convinced of the greater…
Which of the following statements is/are correct? 1. Thermal power stations in Delhi were required to summarily shut down. 2. CNG supplies had to be assured once diesel vehicles were prohibited from plying. 3. The Supreme Court banned the use of coal across the National Capital Region. Select the answer using the code given below.
UPSC's answer: (c) — Statement 1 is not correct: it was agreed that thermal plants would "clean up or shut down"; they were not required to shut down summarily. Statement 2 is correct: when diesel buses were stopped, CNG supply had to be assured. Statement 3 is not correct: the Supreme Court banned pet coke.
Consider the following statements : Every red is blue. Every blue is green. Every green is yellow. Which of the following statements denoted by P, Q and R are correct? P. Every blue is yellow. Q. Every red is green. R. Every red is yellow. Select the answer using the code given below.
UPSC's answer: (d) — The statements form a chain: every red is blue, every blue is green, every green is yellow. P: blue → green → yellow, so every blue is yellow. Q: red → blue → green, so every red is green. R: red → blue → green → yellow, so every red is yellow. All three follow: (d).
How many times does 5 appear in all two-digit positive integers?
UPSC's answer: (b) — Two-digit numbers run from 10 to 99. 5 in the tens place: 50 to 59, i.e. 10 times. 5 in the units place: 15, 25, …, 95, i.e. 9 times (55 is already counted once in the tens place and again here, correctly, since it has two 5s). Total 10 + 9 = 19: (b).
X travels 6 km on a bicycle with average speeds of 5 km per hour, 10 km per hour and 4 km per hour during the first 1 km, the next 2 km and the remaining 3 km, respectively. Y travels the same distances with average speeds of 4 km per hour, 10 km per hour and 5 km per hour, respectively. How many minutes early will Y complete the journey if both X and Y start at the same time?
UPSC's answer: (d) — X's time: 1/5 + 2/10 + 3/4 = 0·20 + 0·20 + 0·75 = 1·15 h. Y's time: 1/4 + 2/10 + 3/5 = 0·25 + 0·20 + 0·60 = 1·05 h. Y finishes 0·10 h = 6 minutes earlier: (d).
Seven cubes are identical in shape. Out of these, the weight of each of the six cubes is equal and the weight of the remaining cube is less than the weight of any other cube. A balance is used to identify the lightest cube. What is the minimum number of attempts required to distinguish the odd cube with certainty?
UPSC's answer: (a) — Split the seven cubes into groups of 3, 3 and 1. Weighing 1: put 3 against 3. If they balance, the single cube left out is the light one. If one side rises, the light cube is among those 3. Weighing 2: put 1 against 1; the lighter pan shows it, and if they balance it is the third cube.
Which one among the following statements most appropriately reflects the point of view of the given passage?
UPSC's answer: (c) — The passage says earlier fears of job losses did not come true and, even if AI proves different, its effect "may be salutary": agents could spend more time on creative and rewarding tasks. (c) captures this: the value of human work can rise when it is redirected to more fulfilling tasks.
Which of the following conclusions, made on the basis of the given passage, is/are correct? 1. The advent of new customer-service technology had invariably sparked fears about job losses. 2. Often it is found that instead of job losses, alternative channels for employee engagement are discovered while certain tasks are replaced by technology. 3. The advent of technology inevitably leads to stressful outcomes. Select the answer using the code given below.
UPSC's answer: (d) — Conclusion 1 is correct: the passage says previous waves of customer-service technology, including email and voice menus, stoked concerns about job losses.
Which of the following conclusions is/are correct? 1. All landlords essentially have some goodness trapped within them. 2. The common grazing grounds of a village are intended for use by the cattle of that village. 3. Landlords who believe in tradition tend to be more concerned about their tenants. 4. Winds later in the day tend to be cooler post the hot winds of the morning. Select the answer using the code given below.
UPSC's answer: (c) — Conclusion 1 is not correct: the passage contrasts Rai Sahib with "selfish Zamindars", so not all landlords are good. Conclusion 2 is not correct: cattle "from the nearby villages" graze on the common ground, so it is not reserved for one village's cattle.
Which of the following statements are not correct? 1. The landholdings of Rai Sahib were currently not being used for farming. 2. Temperamentally, Rai Sahib was as greedy as other landlords. 3. It cannot be ascertained that Rai Sahib could have made some money by leasing out the grazing land. 4. It may be asserted that Rai Sahib valued his tenants and wanted to protect their livelihood. Select the answer using the code given below.
UPSC's answer: (d) — The question asks which statements are NOT correct. Statement 1 is not correct: the passage is only about one plot kept for grazing; it says nothing about Rai Sahib's other landholdings.
A person facing the East travels 4 km straight and then turns right and travels 3 km, then further turns left and travels 2 km and finally turns left and travels 3 km. The minimum distance between the final point and the initial point, and the direction in which the person is facing at the final point are, respectively
UPSC's answer: (d) — Start facing East: 4 km East. Turn right (now facing South): 3 km South. Turn left (facing East): 2 km East. Turn left (facing North): 3 km North. The 3 km South and 3 km North cancel, leaving 4 + 2 = 6 km East of the start. The person is 6 km away and facing North: (d).
The ratio of male to female workers in two companies A and B is 13 : 10 and 7 : 5, respectively. If both the companies have the same number of female workers, then what is the ratio of the total number of workers in A to those in B?
UPSC's answer: (b) — Make the female counts equal: A = 13 : 10; B = 7 : 5 = 14 : 10. With 10 women each, A has 13 + 10 = 23 workers and B has 14 + 10 = 24. Ratio A : B = 23 : 24: (b).
If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct? I. The difference of the numbers is an even number. II. One of the numbers is a perfect square. Select the answer using the code given below.
UPSC's answer: (c) — For any two numbers a and b, HCF × LCM = a × b. If a × b = a³, then b = a²: one number is the square of the other. II is always true. The difference is a² − a = a(a − 1), a product of two consecutive integers, which is always even. I is always true. Hence both: (c).
If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x + y is divided by 11?
UPSC's answer: (d) — Divisibility by 11: the difference between the sums of alternate digits must be a multiple of 11. In 4x5y790, counting from the right, the odd places hold 0, 7, 5, 4 (sum 16) and the even places hold 9, y, x (sum 9 + x + y). 16 − (9 + x + y) = 7 − (x + y) must be 0 or −11, so x + y = 7 or 18.
Which of the following statements is/are correct? 1. Radical action can also be attributed to mild surrender where one acts against societal expectations. 2. Submitting to one's limitations, given the effect of age and other factors, ought not to be conflated with laziness. 3. 'Leading man' usually refers to one who plays the lead role in a movie; in this instance the implication is that Hugh Grant is performing the role of not an action hero, but that of a resting one! Select the answer using the code given below.
UPSC's answer: (c) — Statement 1 is correct: the passage calls Grant's nap "quietly radical" and "an elegant case for surrender", an act that goes against society's performance expectations. Statement 2 is correct: the surrender is "not to laziness, but to limits", at a stage of life the passage links to age.
Which of the following conclusions are correct? 1. In the breakaway phase, economic progress is slow for the technology followers. 2. In the catch-up phase, leaders stagnate and followers, therefore, close the gap between them and the leaders. 3. In the fine-tuning phase, technology is exhausted, as it were, and both leaders and followers attempt to extract leftover benefits, leading to more or less similar per capita income levels. 4. Industrial technology followed scavenging, which preceded hunting, which itself was followed by farming. Select the answer using the code given below.
UPSC's answer: (a) — Conclusion 1 is not correct: in the breakaway phase the followers' per capita income is UNCHANGED, not merely slow-growing. Conclusion 2 is not correct: the passage does not say leaders stagnate; followers close the gap by adopting the new technology.
An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio, amounts of P and Q be mixed in order to get R?
UPSC's answer: (a) — P has 20% copper, Q has 60% copper, and R must have 50% copper (equal copper and zinc). By alligation, P : Q = (60 − 50) : (50 − 20) = 10 : 30 = 1 : 3. Check: 1 part P and 3 parts Q give (20 + 180)/4 = 50% copper: (a).
A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If A − B is a multiple of 27, where A > B, how many such different A's are possible?
UPSC's answer: (b) — Write A = 10a + b and B = 10b + a, so A − B = 9(a − b). 9(a − b) is a multiple of 27 when a − b is a multiple of 3. With a > b, a − b = 3, 6 or 9. a − b = 9 means A = 90 and B = 09, which is not a two-digit number, so it is ruled out. B two-digit also needs b ≥ 1.
If ZERO is encoded as ADSN, then how do you encode STOP?
UPSC's answer: (b) — ZERO → ADSN: Z + 1 = A, E − 1 = D, R + 1 = S, O − 1 = N. The letters alternately move forward and back by one. STOP: S + 1 = T, T − 1 = S, O + 1 = P, P − 1 = O. So STOP is coded TSPO: (b).
There are three types of rectangular tiles : 3' × 3', 3' × 7' and 3' × 11'. An area of rectangular shape of dimensions 3' × 100' is to be covered using these tiles without breaking them. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x - y is
UPSC's answer: (a) — All tiles are 3′ wide, so only their lengths matter: 3a + 7b + 11c = 100. Maximum number: use as many 3′ tiles as possible. 100 leaves remainder 1 on division by 3, and one 7′ tile fixes it: 7 + 31 × 3 = 100, i.e. 32 tiles. So x = 32. Minimum number: use as many 11′ tiles as possible.
In a recruitment process, the selection of candidates is based on their performance in three components. The weightages of the components 1, 2 and 3 are 0·2, 0·3 and 0·5, respectively. Use the data given below and find the cutoff score if exactly three candidates are to be selected : Candidate | Score in component 1 | Score in component 2 | Score in component 3 1 | 5 | 4 | 6 2 | 4 | 6 | 5 3 | 3 | 2 | 8 4 | 9 | 4 | 3 5 | 8 | 8 | 2
UPSC's answer: (a) — Weighted score = 0·2 × C1 + 0·3 × C2 + 0·5 × C3. Candidate 1: 1·0 + 1·2 + 3·0 = 5·2. Candidate 2: 0·8 + 1·8 + 2·5 = 5·1. Candidate 3: 0·6 + 0·6 + 4·0 = 5·2. Candidate 4: 1·8 + 1·2 + 1·5 = 4·5. Candidate 5: 1·6 + 2·4 + 1·0 = 5·0.
Consider the following three statements, namely S1, S2 and S3 : S1. Protecting the environment is an existential exigency for humans, given the impact of environmental degradation on climate change. S2. Scientific consensus has not been achieved with regard to the extent of the contribution of human intervention to climate change. S3. Environmental activism includes climate alarmism and other extremist points of view that often become the focus of climate change deniers. Which of the following relationships based on the statements given above is/are correct? 1. S3 is a counterpoint to S1 2. S3 is unconnected to S1 and S2 3. S2 could be the reason for S3 Select the answer using the code given below.
UPSC's answer: (d) — Relationship 1 is not correct: S3 does not dispute S1's point that protecting the environment is vital; it criticises extreme forms of activism. Relationship 2 is not correct: S3 is about climate activism and climate-change deniers, so it is clearly connected to S1 and S2.
Match List-I with List-II and select the answer using the code given below the Lists : List-I (Relationship category) A. Between cricket captain and team members B. Between judge and lawyers in court C. Between Vice Chancellor and Deputy Registrar D. Between peers and coworkers List-II (Communication type) 1. Informal and firm 2. Informal and open-ended 3. Formal and open-ended 4. Formal and firm Code :
UPSC's answer: (b) — A. A cricket captain talks to the team informally but must give firm instructions: informal and firm (1). B. A judge and lawyers in court communicate formally and the judge's orders are final: formal and firm (4). C.
Match List-I with List-II and select the answer using the code given below the Lists : List-I (Tool of communication) A. Memorandum B. Flyer C. Bcc D. Minutes List-II (Purpose) 1. To record decisions 2. To inform confidentially 3. To intimate a directive 4. To disseminate non-targeted information Code :
UPSC's answer: (c) — A. A memorandum is used inside an organisation to convey a directive or instruction (3). B. A flyer spreads information widely, without targeting particular people (4). C. Bcc sends a copy without other recipients seeing the address, i.e. confidentially (2). D.
Which among the following actions would constitute the most appropriate directive(s) in resolving interpersonal conflict in an office with culturally diverse personnel? 1. Direct personnel to practise activities that are the cultural markers of diverse groups 2. Allow conflicts to resolve naturally over time to set an appropriate precedent of leadership 3. Encourage personnel to seek each other's perspectives Select the answer using the code given below.
UPSC's answer: (c) — Action 3 is appropriate: getting people to understand each other's perspectives addresses the root of cross-cultural conflict. Action 1 is not: ordering people to practise other groups' cultural markers is imposed and can deepen resentment.
Match List-I with List-II and select the answer using the code given below the Lists : List-I (Barrier to communication) A. Semantic B. Cognitive C. Organisational D. Affective List-II (Example) 1. Lack of feedback 2. Misunderstanding the meaning of a word 3. Fear of social stigma 4. Information overload Code :
UPSC's answer: (d) — A. Semantic barriers concern the meaning of words: misunderstanding a word (2). B. Cognitive barriers concern the mind's capacity to process: information overload (4). C. Organisational barriers arise from structure and systems: lack of feedback (1). D.
You are required to design a 'questionnaire' to be filled on-location by visitors, based on the following objective while writing a report : "To determine the feasibility of setting up a family-oriented vacation resort in the vicinity of a lake destination in the mountains" Which of the following heads would you include in the questionnaire to make it most appropriate for your purpose? 1. Size of family 2. Budget 3. Number of earners in the family 4. Food allergies and dietary restrictions Select the answer using the code given below.
UPSC's answer: (c) — The aim is to judge whether a family resort near a mountain lake is feasible, from visitors filling the form on the spot. Size of family (1) is essential: it tells what kind of rooms and facilities families need. Budget (2) is essential: it tells what visitors are willing to spend.
With reference to 'circular letters', which of the following statements is/are correct? 1. Circular letters are usually addressed to a group of people. 2. Non-standard and customized content is typical of circular letters. 3. Circular letters are used to intimate appraisals and increments of employees within organisations. 4. Circular letters are less cost-effective than personalised and specific recipient-directed letters. Select the answer using the code given below.
UPSC's answer: (d) — Statement 1 is correct: a circular letter carries the same message to a group of people. Statement 2 is not correct: circulars use standard content, not customised content.
Three partners A, B and C entered into a business. A invested one-third of the capital for one-third duration. B invested one-fourth of the capital for one-fourth duration. C invested the remaining capital for the whole duration. Out of a profit of ₹ 17,000, how much profit will C get?
UPSC's answer: (a) — Profit is shared in the ratio capital × time. A: 1/3 × 1/3 = 1/9. B: 1/4 × 1/4 = 1/16. C invests the rest, 1 − 1/3 − 1/4 = 5/12, for the whole time: 5/12. Multiply by 144: A : B : C = 16 : 9 : 60, total 85. C's share = 60/85 × 17,000 = ₹12,000: (a).
There are two chemicals which do not react with each other. A container contains 10 litres of the chemical A. One litre of this chemical is removed from it and one litre of the chemical B is poured. Then one litre of the mixture is removed from the container and one litre of B is poured. If this process of replacing one litre of the mixture by one litre of B is performed once more, then what is the volume of B that is present in the container approximately (in percentage)?
UPSC's answer: (b) — Each replacement removes 1/10 of the mixture, so the amount of A left is multiplied by 9/10 each time. A is replaced three times in all: A left = 10 × (9/10)³ = 7·29 litres. B = 10 − 7·29 = 2·71 litres, i.e. about 27% of the 10 litres: (b).
A shopkeeper employs a delivery boy and gives him a motorcycle for home delivery. For every delivery, the boy is given ₹ 5. At the end of the day, he also gets ₹ 2 for every kilometre of the distance covered in the day. The boy wants to earn more than ₹ 500 a day, but does not want to travel more than 100 km. Which of the following numbers of deliveries would definitely meet his target?
UPSC's answer: (d) — Daily earnings = 5 × deliveries + 2 × kilometres, and he rides at most 100 km. The distance he actually covers is not given. If the distance is small, 80 deliveries give about ₹400 and 90 give about ₹450, both below ₹500. They exceed ₹500 only if he rides more than 50 km or 25 km respectively.
Question paper and answer key: Union Public Service Commission. Explanations: UPSC Answer Check. Practise this paper with a timer →
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