Civil Services (Preliminary) Examination 2026 — General Studies Paper II (CSAT) — Solved PYQ with Answer Key

Mental Ability & Logical Reasoning — Solved Questions

1. Q1: Directions: The question is followed by two statements. Answer using the codes given in the options. X receives three coins of different denominations from among 1, 2, 5, 10 and 20. If the total amoun
   Answer: A — The question can be answered using one of the statements alone, but cannot be answered using the other statement alone.
   The correct answer is Option A (one statement alone suffices, the other does not). Key Points - Any 3 distinct denominations from 1, 2, 5, 10, 20 give sums: 8, 13, 16, 17, 23, 26, 27, 31, 32, 35. - Statement II (digit-sum of m 5) alone is s
2. Q2: Directions: The question is followed by two statements. Answer using the codes given in the options. For two distinct real numbers x and y, which of them is bigger? Statement I: x² < y < 1 State
   Answer: D — The question cannot be answered even using both the statements together.
   The correct answer is Option D (cannot be answered even with both statements). Key Points - Statement I (x² < y < 1) and Statement II (y < √x < 1) each fail to fix the order of x and y individually. - Combining them: for 0 <
3. Q3: Directions: The question is followed by two statements. Answer using the codes given in the options. If x and y are integers, then is x even? Statement I: x²y² is even. Statement II: 1 + x² + y² is od
   Answer: C — The question can be answered using both the statements together, but cannot be answered using either statement alone.
   The correct answer is Option C (both together suffice, neither alone). Key Points - Statement I (x²y² even) means xy is even, i.e. at least one of x, y is even — but not necessarily x. Insufficient. - Statement II (1 + x² + y² odd) means x²
4. Q4: Directions: The question is followed by two statements. Answer using the codes given in the options. X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consi
   Answer: D — The question cannot be answered even using both the statements together.
   The correct answer is Option D (cannot be answered even together). Key Points - T is drawn entirely from the odd set X or the even set Y. - Statement I (sum of any two in T is even) forces all elements of T to share the same parity — but th
5. Q5: Directions: The question is followed by two statements. Answer using the codes given in the options. If x, y and z are integers, each greater than 1, then is x a prime number? Statement I: xy² = 116 S
   Answer: A — The question can be answered using one of the statements alone, but cannot be answered using the other statement alone.
   The correct answer is Option A (one statement alone suffices). Key Points - Statement I (xy² = 116): since 116 = 2² × 29 and y 1, the only square factor is 4, giving y = 2 and x = 29, which is prime — a definite "Yes". Sufficient.
6. Q8: 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 t
   Answer: B — P and Q together weigh more than the total weight of A and C.
   The correct answer is Option B. Key Points - Given P + 2Q + D = 15 (using S = Q) and 2P + Q + B = 17 (using R = P). - Adding them: 3P + 3Q + (B + D) = 32, and since B + D = 17 − 6 = 11, we get 3(P + Q) = 21, so P + Q = 7. - Compare with A +
7. Q10: 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
   Answer: D — 14
   The correct answer is Option D (14). Key Points - All three meet on a common mark only where the distance from 199 is a common multiple of their jumps 4, 6 and 5, i.e. a multiple of LCM(4, 6, 5) = 60. - Common marks = 199, 259, 319, …, i.e.
8. Q14: 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
   Answer: A — 5
   The correct answer is Option A (5 persons). Key Points - Q sits between P and R; S sits between R and T, giving the block P–Q–R–S–T. V sits between U and W, giving U–V–W. - With S and W opposite on 8 seats and R met before T clockwise, the
9. Q18: 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?
   Answer: D — bb
   The correct answer is Option D (bb). Key Points - Treat each 'x' in the string as a wildcard to be filled so that a fixed a/b pattern repeats. - The 15-character string is the block 'abbab' repeated three times — (abbab)(abbab)(abbab) = a b
10. Q29: 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 expr
    Answer: C — 13
    The correct answer is Option C (13). Key Points - x, y, z are distinct values from 2, 3, 4, 5 and we evaluate (x × y) + z. - Maximum: take the two largest for the product, 4 × 5 = 20, plus the largest remaining distinct value z = 3 → 23. -
11. Q33: 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 fo
    Answer: D — Neither I nor II
    The correct answer is Option D (Neither I nor II). Key Points - Fixed: R = 1, P = 4. The values 2, 3, 5 go to Q, S, T with Q ≠ 5, S ≠ 2, T ≠ 3. - If S = 3: remaining 2, 5 for Q, T with Q ≠ 5 ⇒ Q = 2, T = 5. So T = 5, not 2 → Statement I is
12. Q34: 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
    Answer: C — Both I and II
    The correct answer is Option C (Both I and II). Key Points - Placing the two rods side by side with P1 opposite Q3, then satisfying P4 ↔ (Q1 or Q2) and Q4 ↔ (P3 or P5) with Q3 and Q5 adjacent, yields valid layouts. - In those layouts it is
13. Q35: 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 tra
    Answer: B — I and III only
    The correct answer is Option B (I and III only). Key Points - A travels in X with two others; B ≠ A's car and B ∉ Y ⇒ B is in Z (with C). Only E travels with G ⇒ E and G form a pair (car Y). - This forces X = A, D, F, Y = E, G, Z = C, B. -
14. Q36: 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 follo
    Answer: A — I only
    The correct answer is Option A (I only). Key Points - Rules: ¬X → ¬Z; ¬Y → W; W → ¬X. - Statement I (X correct ⇒ Y correct): if Y were incorrect, then W is correct, which forces X incorrect — contradiction. So X correct ⇒ Y correct → true.
15. Q37: 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
    Answer: A — 35
    The correct answer is Option A (35 meetings). Key Points - Speeds are in ratio X : Y = 7 : 5 (X does 7 rounds while Y does 5). Same-direction meetings occur on each unit of relative rounds. - After Y's first 5 rounds it reverses and doubles
16. Q44: 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?
    Answer: D — Q is a sister of the husband of S
    The correct answer is Option D. Key Points - Q and R are children of P; S is R's spouse and the mother of T. - So R is S's husband, and Q (being R's sibling) is therefore the sister of S's husband. Additional Information - P has a son and a
17. Q48: 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
    Answer: D — P, Q and R
    The correct answer is Option D (P, Q and R). Key Points - The chain is red ⊂ blue ⊂ green ⊂ yellow. - P: every blue is yellow (blue ⊂ green ⊂ yellow) → true. - Q: every red is green (red ⊂ blue ⊂ green) → true. - R: every red is yellow (red
18. Q51: 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 iden
    Answer: A — 2
    The correct answer is Option A (2 attempts). Key Points - Six cubes weigh the same and one is lighter; a balance must isolate the light one. - Attempt 1: weigh 3 vs 3 (leave 1 aside). If they balance, the odd cube is the one left out (but c
19. Q56: 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
    Answer: D — 6 km, North
    The correct answer is Option D (6 km, North). Key Points - Facing East: go 4 (East) → (4, 0); turn right = South, go 3 → (4, −3); turn left = East, go 2 → (6, −3); turn left = North, go 3 → (6, 0). - Final point is (6, 0): straight-line dis
20. Q67: If ZERO is encoded as ADSN, then how do you encode STOP?
    Answer: B — TSPO
    The correct answer is Option B (TSPO). Key Points - ZERO → ADSN uses an alternating shift +1, −1, +1, −1: Z+1=A, E−1=D, R+1=S, O−1=N. - Apply the same to STOP: S+1=T, T−1=S, O+1=P, P−1=O → TSPO. Additional Information - Spotting the alterna
21. Q71: 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
    Answer: D — 3 only
    The correct answer is Option D (3 only). Key Points - Statement 2 is wrong — S3 (about climate alarmism/extremism) is clearly connected to S1 and S2, which are about the same climate-change debate; so any option containing 2 is ruled out. -
22. Q72: 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
    Answer: B — A-1, B-4, C-3, D-2
    The correct answer is Option B (A-1, B-4, C-3, D-2). Key Points - A. Cricket captain ↔ team members — informal (teammates) but firm (on-field instructions) → 1. - B. Judge ↔ lawyers in court — a formal setting with firm authority and proced
23. Q73: 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
    Answer: C — A-3, B-4, C-2, D-1
    The correct answer is Option C (A-3, B-4, C-2, D-1). Key Points - A. Memorandum — an official note used to intimate a directive → 3. - B. Flyer — mass-distributed to disseminate non-targeted information → 4. - C. Bcc — used to inform confid
24. Q74: 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
    Answer: C — 3 only
    The correct answer is Option C (3 only). Key Points - 3 — encouraging personnel to seek each other's perspectives directly builds cross-cultural understanding and is the most appropriate way to resolve interpersonal conflict. Additional Inf
25. Q75: 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. Lac
    Answer: D — A-2, B-4, C-1, D-3
    The correct answer is Option D (A-2, B-4, C-1, D-3). Key Points - A. Semantic barrier — misunderstanding the meaning of a word → 2. - B. Cognitive barrier — information overload straining processing → 4. - C. Organisational barrier — struct
26. Q76: 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-or
    Answer: C — 1 and 2 only
    The correct answer is Option C (1 and 2 only). Key Points - To judge the feasibility of a family-oriented lake resort, the relevant heads are 1. Size of family (market/demand sizing) and 2. Budget (willingness and ability to pay). Additiona
27. Q77: 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 typica
    Answer: D — 1 only
    The correct answer is Option D (1 only). Key Points - 1 — circular letters are, by definition, addressed to a group of people at once → correct. Additional Information - 2 is wrong — circulars use standard, uniform content, not customised t

Reading Comprehension — Solved Questions

1. Q6: Passage: 'Kalagram', the cultural village set up at the Maha Kumbh Mela, unfolded as a mosaic of India's diverse regions, each represented by seven meticulously crafted 'Sanskriti Angans'—stepping thr
   Answer: D — 1 and 3
   The correct answer is Option D (1 and 3). Key Points - 1 — the passage says seven 'Sanskriti Angans', each representing a region of India, were showcased in Kalagram → valid. - 3 — the 230 master artisans were shaping India's ancient histor
2. Q7: Passage: 'Kalagram', the cultural village set up at the Maha Kumbh Mela, unfolded as a mosaic of India's diverse regions, each represented by seven meticulously crafted 'Sanskriti Angans'—stepping thr
   Answer: A — Paintings from four States of India have been mentioned.
   The correct answer is Option A. Key Points - The question asks which statement is not correct about the Kalagram passage. - The passage names four regional art forms: Bengal's Pattachitra (painting), Assam's bamboo crafts, Tamil Nadu's Than
3. Q11: Passage: Sport is not just about winning medals or getting jobs through a sports quota. Today's generation is struggling with issues like depression and anxiety. Parents often say that their children
   Answer: D — 1, 2 and 3
   The correct answer is Option D. Key Points - Valid conclusions are 1, 2 and 3. - 1 — the passage explicitly urges seeing sport "as a way of life", so it is more than just games. - 2 — parents complain children are inactive and rar
4. Q12: Passage: Sport is not just about winning medals or getting jobs through a sports quota. Today's generation is struggling with issues like depression and anxiety. Parents often say that their children
   Answer: B — 2 and 3
   The correct answer is Option B. Key Points - Correct statements are 2 and 3. - 2 — the passage says sport builds time management, fitness, teamwork and coordination, i.e. life skills. - 3 — it calls for a culture where sport is a way of lif
5. Q16: Passage: How is deflation done? Most countries use a method called 'double deflation', where input and output prices are deflated separately. Consider a manufacturer importing oil for use in productio
   Answer: A — 1 only
   The correct answer is Option A (1 only). Key Points - 1 — the passage states that when output prices and quantities stay the same while oil (input) prices fall, real value added should not change, so statement 1 is correct. - 2 is wrong — t
6. Q17: Passage: How is deflation done? Most countries use a method called 'double deflation', where input and output prices are deflated separately. Consider a manufacturer importing oil for use in productio
   Answer: A — 1 only
   The correct answer is Option A (1 only). Key Points - 1 — the passage explains that using a single deflator makes a manufacturer "look as if" it had become more productive, so deflation strategies can make manufacturers appear to
7. Q26: Passage: When SARS-CoV-2 was first detected in 2019, it was a truly novel virus for the world. At that time, no one in the world had been exposed to SARS-CoV-2 or had specific immunity against it. In
   Answer: B — 2 only
   The correct answer is Option B. Key Points - Only conclusion 2 is valid. - 2 — the passage stresses the two viruses have fundamentally different characteristics, epidemiology and impacts, so they should not be handled the same way. - 1 is w
8. Q27: Passage: When SARS-CoV-2 was first detected in 2019, it was a truly novel virus for the world. At that time, no one in the world had been exposed to SARS-CoV-2 or had specific immunity against it. In
   Answer: D — None of the above
   The correct answer is Option D. Key Points - The intent behind the passage is none of the three given options. - The writer's purpose is simply to contrast the two viruses — their families, seasonality, severity and affected populations. -
9. Q28: Passage: When SARS-CoV-2 was first detected in 2019, it was a truly novel virus for the world. At that time, no one in the world had been exposed to SARS-CoV-2 or had specific immunity against it. In
   Answer: B — 1, 2 and 3
   The correct answer is Option B. Key Points - Statements 1, 2 and 3 are valid inferences. - 1 — HMPV has been studied for decades, giving it longer documentation than the 2019-novel SARS-CoV-2. - 2 — the two viruses are different, producing
10. Q31: Passage: India is starting to deploy AI for critical use cases such as weather forecasting, pest detection and control, and crop yield optimisation. However, penetration is limited to a small subset o
    Answer: D — 2 and 3 only
    The correct answer is Option D. Key Points - Valid assumptions are 2 and 3. - 2 — the passage recommends affordable, local-language AI tools to reach smallholder farmers, assuming this will widen access. - 3 — it states critical application
11. Q32: Passage: India is starting to deploy AI for critical use cases such as weather forecasting, pest detection and control, and crop yield optimisation. However, penetration is limited to a small subset o
    Answer: A — 1 and 3 only
    The correct answer is Option A. Key Points - The statements that are not correct are 1 and 3. - 1 — the passage says AI penetration is limited to tech-savvy farmers today, but never claims they will "drive the AgTech companies of the f
12. Q39: Passage: The Juvenile Justice (Care and Protection of Children) Act, or the JJ Act, 2015 allows for the possibility for trying adolescents above 16 as adults if they are accused of committing a heinou
    Answer: B — 2 only
    The correct answer is Option B. Key Points - Only conclusion 2 is valid. - 2 — the JJ Act, 2021 classifies an offence with no minimum sentence but a maximum of seven years or more as a serious offence, i.e. it uses the maximum sentence, not
13. Q40: Passage: The Juvenile Justice (Care and Protection of Children) Act, or the JJ Act, 2015 allows for the possibility for trying adolescents above 16 as adults if they are accused of committing a heinou
    Answer: C — Both 1 and 2
    The correct answer is Option C. Key Points - Both statements 1 and 2 are correct. - 1 — under the JJ Act, 2015, an offence with no minimum prescribed punishment cannot be treated as heinous (heinous needs a minimum of seven years). - 2 — un
14. Q46: Passage: The key source of the battle for clean skies and clear lungs is the fuel we burn—from household Chulhas to the thermal power plants. In most cases, it is biomass or coal. The Supreme Court ba
    Answer: C — 1 and 3
    The correct answer is Option C. Key Points - Correct inferences are 1 and 3. - 1 — the passage opens by saying the fuel we burn is the key source of the battle for clean air. - 3 — the Supreme Court agreed fiscal measures were needed to kee
15. Q47: Passage: The key source of the battle for clean skies and clear lungs is the fuel we burn—from household Chulhas to the thermal power plants. In most cases, it is biomass or coal. The Supreme Court ba
    Answer: C — 2 only
    The correct answer is Option C. Key Points - Only statement 2 is correct. - 2 — the passage says that when diesel buses were stopped, CNG supply had to be assured, i.e. alternatives are needed for a ban to work. - 1 is wrong — thermal plant
16. Q52: Passage: Previous waves of customer-service technology, including email and those pesky voice menus, stoked concerns of job losses, only for them to fail to materialise. AI could yet prove different.
    Answer: C — The value of human intervention in the workplace affected by AI might be enhanced through redirection towards more fulfilling tasks.
    The correct answer is Option C. Key Points - The passage's point of view is best captured by Option C: the value of human agents can be enhanced by redirecting them to more fulfilling tasks. - The passage says AI could free human agents to
17. Q53: Passage: Previous waves of customer-service technology, including email and those pesky voice menus, stoked concerns of job losses, only for them to fail to materialise. AI could yet prove different.
    Answer: D — 1 and 2
    The correct answer is Option D. Key Points - Correct conclusions are 1 and 2. - 1 — the passage notes each new wave of customer-service technology sparked job-loss fears. - 2 — those fears failed to materialise; instead work shifted to more
18. Q54: Passage: Cattle from the nearby villages came to the common ground to graze, and there was still a cool freshness in the air. Hori took several deep breaths and thought of sitting down for a while, si
    Answer: C — 3 only
    The correct answer is Option C. Key Points - Only conclusion 3 is valid. - 3 — Rai Sahib held to old values and felt a landlord who neglects tenants is "less than human", showing tradition-minded landlords are more concerned about
19. Q55: Passage: Cattle from the nearby villages came to the common ground to graze, and there was still a cool freshness in the air. Hori took several deep breaths and thought of sitting down for a while, si
    Answer: D — 1, 2 and 3
    The correct answer is Option D. Key Points - The statements that are not correct are 1, 2 and 3. - 1 — the grazing land was reserved for cattle, i.e. it was being used (for grazing), so "not being used for farming" as an implied i
20. Q61: Passage: Was it the sun-dappled ambience, the strawberries and cream, the frustration of Flavio Cobolli's unforced errors against Serbian Novak Djokovic on Centre Court or simply the crushing weight o
    Answer: C — 1, 2 and 3
    The correct answer is Option C. Key Points - All three statements 1, 2 and 3 are correct. - 1 — Hugh Grant's nap is framed as "quietly radical", so mild surrender against societal expectation is a form of radical action. - 2 — the
21. Q62: Passage: Was it the sun-dappled ambience, the strawberries and cream, the frustration of Flavio Cobolli's unforced errors against Serbian Novak Djokovic on Centre Court or simply the crushing weight o
    Answer: B — 3 only
    The correct answer is Option B. Key Points - Only statement 3 is correct — Grant lets the body's wisdom override society's performance metrics, exactly what the passage says. - 1 is wrong — he watched the quarterfinals, not the semifinal, a
22. Q63: Passage: The process by which countries close their labour-productivity gap with the technology leader is based on convergence theory. The convergence model divides economic eras into three phases: th
    Answer: A — 3 and 4 only
    The correct answer is Option A. Key Points - Correct conclusions are 3 and 4. - 3 — in the fine-tuning phase, technology is exhausted and both leaders and followers extract leftover benefits, reaching similar per capita incomes. - 4 — the t
23. Q64: Passage: The process by which countries close their labour-productivity gap with the technology leader is based on convergence theory. The convergence model divides economic eras into three phases: th
    Answer: B — 2 and 3
    The correct answer is Option B. Key Points - Correct statements are 2 and 3. - 2 — convergence theory is fundamentally about closing the labour-productivity gap with the technology leader. - 3 — technology leaders arrive earlier at each new

Quantitative Aptitude — Solved Questions

1. Q9: 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.
   Answer: D — 12
   The correct answer is Option D (12). Key Points - QUEUE has the letters Q, U, U, E, E. The condition "Q is always followed by U" means the pair QU is glued into one block. - Remaining units to arrange: [QU], U, E, E — that is 4 un
2. Q13: 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 differen
   Answer: D — 9
   The correct answer is Option D (9). Key Points - Let f = forward jumps, b = backward jumps. Then f + b = 31 and 5f − 2b = 15. - Substituting b = 31 − f: 5f − 2(31 − f) = 15 ⇒ 7f = 77 ⇒ f = 11, so b = 20. - Difference |f − b| = |11 − 20| = 9
3. Q15: 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
   Answer: B — 4
   The correct answer is Option B (4). Key Points - Each 2.5' × 8' blue strip must sit in a corner (two sides common with two edges); the 8' side runs along a 10' edge and the 2.5' side along a 6' edge. - Two such strips cannot share the same
4. Q19: If 10ᵐ × 1000 × n = 75²⁵ × 25³² × 32⁷⁵, where n is not divisible by 10, then the value of m is
   Answer: B — 111
   The correct answer is Option B (111). Key Points - Factorise the right side: 75²⁵ = 3²⁵·5⁵⁰, 25³² = 5⁶⁴, 32⁷⁵ = 2³⁷⁵. So RHS = 2³⁷⁵ · 3²⁵ · 5¹¹⁴. - The number of factors of 10 = min(power of 2, power of 5) = min(375, 114) = 114. So RHS = 10
5. Q20: 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 dire
   Answer: C — 13.85
   The correct answer is Option C (≈13.85 seconds). Key Points - Same direction: relative speed = 100 − 4 = 96 km/h. Crossing in 15 s gives train length = 96 × (15/3600) = 0.4 km. - Opposite direction: relative speed = 100 + 4 = 104 km/h. Time
6. Q21: 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.
   Answer: B — II only
   The correct answer is Option B (II only). Key Points - Statement I is not always true. The function f(t) = t + 1/t decreases on (0, 1) and increases on (1, ∞), so for x < y straddling 1 (e.g. x = 0.5, y = 1) we get f(x) f(y), violating I
7. Q22: 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?
   Answer: B — 5
   The correct answer is Option B (5). Key Points - With cylinders of 1, 6, 25 and 100 litres, aim for 298 litres in the fewest fills/pours. - Use three fills of 100 (= 300) and then remove 2 litres (two uses of the 1-litre): 300 − 2 = 298, a
8. Q23: 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 t
   Answer: B — 8
   The correct answer is Option B (8 ways). Key Points - Weights available: 1, 2, 5, 10 kg; total needed = 20 kg using 8 to 11 one-kg weights. - For each allowed count of 1-kg weights, the remaining kilograms must be formed from 2s, 5s and 10s
9. Q24: 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 exp
   Answer: A — 16
   The correct answer is Option A (16). Key Points - If the three cuts leave identical pieces, the cube is split into a small number of equal pieces (e.g. 4 slabs, or 8 small cubes by three perpendicular central cuts). - The fourth cut is a si
10. Q25: 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
    Answer: B — 3
    The correct answer is Option B (3). Key Points - The first correction adds (100 − 0) = 100 to the total and raises the average by 4, so 100/N = 4 ⇒ N = 25 students. - The second correction changes a recorded 81 to the true 56, i.e. −25 to t
11. Q30: 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
    Answer: B — 1/5
    The correct answer is Option B (1/5). Key Points - y ∝ x²: from x = 5, y = 50 we get 50 = k·25 ⇒ k = 2, so y = 2x². For y = 98: x² = 49 ⇒ x = 7. - x ∝ 1/z: from z = 7/25, x = 5 we get x·z = 5·(7/25) = 7/5, so x = (7/5)/z. - Then 7 = (7/5)/z
12. Q38: 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 awar
    Answer: B — 81
    The correct answer is Option B (81). Key Points - Let C = correct, W = wrong. Then 5C − 2W = 69 and 4C − W = 84. - From the second, W = 4C − 84; substitute: 5C − 2(4C − 84) = 69 ⇒ −3C + 168 = 69 ⇒ C = 33, so W = 48. - Total questions = C +
13. Q41: 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
    Answer: C — 4:58:42 PM
    The correct answer is Option C (4:58:42 PM). Key Points - Let the distance be d. Second drone's flight (d/30) took the gap between the two pictures: 5:05 − 5:02 = 180 s, so d/30 = 180 ⇒ d = 5400 m. - First picture time = explosion + sound t
14. Q42: The digit in the unit place of the number 6¹²⁹ × 7³⁰⁷ is
    Answer: C — 8
    The correct answer is Option C (8). Key Points - Unit digit of 6¹²⁹ is always 6 (every power of 6 ends in 6). - Unit digit of 7³⁰⁷: powers of 7 cycle 7, 9, 3, 1 with period 4; 307 mod 4 = 3, so it is the 3rd term = 3. - Product's unit digit
15. Q43: 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?
    Answer: B — 30% increase
    The correct answer is Option B (30% increase). Key Points - Saving = 10% of salary, so expenditure = 90%. Take salary = 100 ⇒ saving 10, expenditure 90. - New salary = 112; new expenditure = 90 × 1.10 = 99; new saving = 112 − 99 = 13. - Cha
16. Q45: How many three-digit numbers can be expressed as an integral power of 2?
    Answer: C — 3
    The correct answer is Option C (3). Key Points - Integral powers of 2 that are three-digit numbers: 2⁷ = 128, 2⁸ = 256, 2⁹ = 512. - 2⁶ = 64 (two-digit) and 2¹⁰ = 1024 (four-digit) fall outside the range. Additional Information - Exactly thr
17. Q49: How many times does 5 appear in all two-digit positive integers?
    Answer: B — 19
    The correct answer is Option B (19). Key Points - Two-digit numbers run 10–99. The digit 5 in the units place: 15, 25, …, 95 → 9 times. - The digit 5 in the tens place: 50, 51, …, 59 → 10 times. Additional Information - Total = 9 + 10 = 19
18. Q50: 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 distanc
    Answer: D — 6
    The correct answer is Option D (6 minutes). Key Points - X: 1 km at 5 (12 min) + 2 km at 10 (12 min) + 3 km at 4 (45 min) = 69 min. - Y: 1 km at 4 (15 min) + 2 km at 10 (12 min) + 3 km at 5 (36 min) = 63 min. Additional Information - Y is f
19. Q57: In a sequence of numbers, each number other than the first two is the sum of the two immediately preceding numbers from it. If the first two numbers in the sequence are 4 and 7, then the sixth number
    Answer: D — 47
    The correct answer is Option D (47). Key Points - Each term is the sum of the two before it, starting 4, 7: 4, 7, 11, 18, 29, 47. - The sixth term is 47. Additional Information - This is a Fibonacci-style rule with different seeds; the sixt
20. Q58: 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 numbe
    Answer: B — 23 : 24
    The correct answer is Option B (23 : 24). Key Points - A has male : female = 13 : 10, B has 7 : 5. Equalise the female counts: A → 13 : 10, B → 14 : 10 (multiplying B by 2). - Totals: A = 13 + 10 = 23, B = 14 + 10 = 24. Additional Informati
21. Q59: 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.
    Answer: C — Both I and II
    The correct answer is Option C (Both I and II). Key Points - HCF × LCM = product of the two numbers. If this product equals the cube of one number a, then a × b = a³, so b = a². - II — one number (b) is a perfect square → true. - I — the di
22. Q60: 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?
    Answer: D — 7
    The correct answer is Option D (7). Key Points - For 4x5y790 to be divisible by 11, the alternating digit sum must be a multiple of 11: (4 + 5 + 7 + 0) − (x + y + 9) = 7 − (x + y). - This is divisible by 11 when x + y = 7 (or 18); in both c
23. Q65: 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 co
    Answer: A — 1 : 3
    The correct answer is Option A (1 : 3). Key Points - Alloy R must be 50% copper. P is 20% copper, Q is 60% copper. - By alligation, P : Q = |60 − 50| : |50 − 20| = 10 : 30 = 1 : 3. Additional Information - Mixing one part P with three parts
24. Q66: 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?
    Answer: B — 9
    The correct answer is Option B (9). Key Points - If A = 10x + y then B = 10y + x and A − B = 9(x − y). For this to be a multiple of 27, (x − y) must be a multiple of 3, so x − y ∈ 3, 6, 9 (with A B ⇒ x y). - B must also be a genuine 2-digit
25. Q68: 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
    Answer: A — 20
    The correct answer is Option A (20). Key Points - The length 100 (width fixed at 3) must be tiled with pieces of length 3, 7 and 11. - Maximum tiles: use as many 3s as possible — 100 = 3 × 31 + 7 × 1 → 32 tiles. - Minimum tiles: use larger
26. Q69: A train has to complete a journey of 800 km. If it meets a minor accident, its speed becomes half of the existing speed. If there is a mechanical defect, the speed becomes one-fourth of the existing s
    Answer: A — 200
    The correct answer is Option A (200 km/h). Key Points - Let original speed = s. Actual run: 200 at s + 400 at s/2 + 200 at s/8 (accident then defect) = (200 + 800 + 1600)/s = 2600/s. - Hypothetical run: 200 at s + 400 at s/4 + 200 at s/8 (d
27. Q70: 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 gi
    Answer: A — 5.1
    The correct answer is Option A (5.1). Key Points - Weighted score = 0.2·(comp 1) + 0.3·(comp 2) + 0.5·(comp 3). - Candidate 1 = 5.2, Candidate 2 = 5.1, Candidate 3 = 5.2, Candidate 4 = 4.5, Candidate 5 = 5.0. Additional Information - The to
28. Q78: 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 ca
    Answer: A — ₹12,000
    The correct answer is Option A (₹12,000). Key Points - Profit shares ∝ capital × time. A: ⅓ × ⅓ = 1/9; B: ¼ × ¼ = 1/16; C: remaining capital (1 − ⅓ − ¼ = 5/12) × full time = 5/12. - Bringing to a common scale (×144): A : B : C = 16 : 9 : 60
29. Q79: 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. T
    Answer: B — 27
    The correct answer is Option B (≈27%). Key Points - Each replacement leaves 9/10 of chemical A. After three replacements, A remaining = 10 × (9/10)³ = 10 × 0.729 = 7.29 litres. - So B present = 10 − 7.29 = 2.71 litres ≈ 27%. Additional Info
30. Q80: 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 co
    Answer: D — The question cannot be answered due to insufficient data
    The correct answer is Option D (the question cannot be answered due to insufficient data). Key Points - Earnings = ₹5 per delivery + ₹2 per km, with distance capped at 100 km, and the target is to earn more than ₹500. - The number of kilome

Frequently Asked Questions

How many questions are there in the Civil Services (Preliminary) Examination 2026 — General Studies Paper II (CSAT)?

The Civil Services (Preliminary) Examination 2026 — General Studies Paper II (CSAT) has 80 questions. Every question is solved here with the correct answer and a detailed explanation.

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The Civil Services (Preliminary) Examination 2026 — General Studies Paper II (CSAT) was held on 24 May 2026.

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Yes. UPSC Civil Services Examination deducts 0.83 marks for every wrong answer, so accuracy matters as much as attempting more questions.

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