UPSC Prelims PYQs with explanations
Real questions from official papers, mapped to syllabus topics. Attempt each one; the answer and the reason appear instantly.
There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?
Answer (d) & explanation
There are more than 8 such sets (d). Step 1: 1001 = 7 × 11 × 13. Each number in a set must be made from these primes (or be 1). Step 2: LCM 1001 means every prime appears somewhere; HCF 1 means no prime is in all three. Step 3: list some sets: {7, 11, 13}, {1, 77, 91}, {1, 77, 143}, {1, 91, 143}, {7, 11, 1001}, {1, 7, 143}, {1, 11, 91}, {1, 13, 77}, {77, 91, 143}. That is already 9, so n is more than 8. Options (a), (b) and (c) are too small.
Tip: when an option says "more than", you only need to find enough cases to pass it; no full count is needed. 1001 = 7 × 11 × 13 is worth remembering.
Answer as per the official UPSC answer key.
What is X in the sequence 1, 3, 6, 11, 18, X, 42?
Answer (c) & explanation
X is 29 (c). Step 1: find the gaps: 3 − 1 = 2, 6 − 3 = 3, 11 − 6 = 5, 18 − 11 = 7. Step 2: the gaps are the prime numbers in order: 2, 3, 5, 7, so next come 11 and 13. Step 3: X = 18 + 11 = 29, and 29 + 13 = 42 ✓. Options (a) 26, (b) 27 and (d) 30 do not give 42 with a prime gap.
Tip: when gaps grow unevenly, check whether they are primes, squares or Fibonacci numbers. Always confirm with the last given term.
Answer as per the official UPSC answer key.
The irrigation device called ‘Araghatta’ was
Answer (b) & explanation
Araghatta was a wheel with pots tied to it (b). The araghatta, or rahat, was a large wheel fitted with a chain of earthen pots. As animals turned it, the pots dipped into a well and lifted water up. Early medieval texts and inscriptions mention it. Option (a) is wrong: a leather bag pulled over a pulley is the charas or mot, a different device. Option (c) is wrong: it was not a single large pot. Option (d) is wrong: a bucket pulled by hand is the simplest lift, not the araghatta.
Notice the later Persian wheel, with gears, which spread under the Delhi Sultanate and Babur describes in his memoirs. Water-lifting helped farmers grow crops in dry seasons in north India.
Answer as per the official UPSC answer key.
What is the common characteristic of the chemical substances generally known as CL-20, HMX and LLM-105, which are sometimes talked about in media?
Answer (b) & explanation
They are explosives used in military weapons (b). CL-20 (hexanitrohexaazaisowurtzitane), HMX (octogen) and LLM-105 are high explosives used in warheads and munitions. CL-20 is among the most powerful non-nuclear explosives. LLM-105 is valued because it is insensitive, so it does not go off easily by accident. Option (a) is wrong: they are not refrigerants. Options (c) and (d) are wrong: they are not fuels for cruise missiles or rockets, which burn steadily rather than detonate.
Notice India's interest: DRDO's High Energy Materials Research Laboratory in Pune works on such compounds. Other common military explosives include RDX and TNT. Some rocket propellants do add HMX for extra energy.
Answer as per the official UPSC answer key.
Consider the following pairs :
| Region | Country
| I. Mallorca | Italy
| II. Normandy | Spain
| III. Sardinia | France
In how many of the above rows is the given information correctly matched?
Answer (d) & explanation
None of the rows is correctly matched (d). Row I is wrong: Mallorca is a Balearic island of Spain, not Italy. Row II is wrong: Normandy is in northern France, not Spain. Row III is wrong: Sardinia is an island of Italy, not France. Each region has been paired with a wrong neighbour, so options (a), (b) and (c) fail.
Notice the nearby trap: Corsica, just north of Sardinia, belongs to France and was Napoleon's birthplace. Normandy is famous for the D-Day landings of June 1944 in World War II. Sicily is Italy's largest island. UPSC often tests islands of the Mediterranean that sit close to a different country.
Answer as per the official UPSC answer key.
How many possible values of (p + q + r) are there satisfying 1/p + 1/q + 1/r = 1, where p, q and r are natural numbers (not necessarily distinct)?
Answer (c) & explanation
Three values are possible (c). Step 1: arrange p ≤ q ≤ r. The smallest, p, has the biggest fraction, so 1/p ≥ 1/3. Since 1/p must be less than 1, p is 2 or 3. Step 2: if p = 3, then q = r = 3. If p = 2, then 1/q + 1/r = 1/2, giving (4, 4) or (3, 6). Step 3: the solutions are (3, 3, 3), (2, 4, 4), (2, 3, 6) with sums 9, 10 and 11: three values. Options (a), (b) and (d) fail.
Tip: in unit-fraction equations, order the variables and bound the smallest one first. This keeps the cases few and complete.
Answer as per the official UPSC answer key.
A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram?
Answer (c) & explanation
The tram is 20 m long (c). Step 1: the tram and walkers move the same way, so use relative speed = tram speed − walker speed. Length = (v − 3) × 8 = (v − 4) × 9, with speeds in km/hr and time in seconds. Step 2: 8v − 24 = 9v − 36, so v = 12 km/hr. Step 3: relative speed past X = 12 − 3 = 9 km/hr = 9 × 5/18 = 2.5 m/s. Length = 2.5 × 8 = 20 m. Check with Y: 8 km/hr = 20/9 m/s × 9 s = 20 m ✓. Options (a), (b) and (d) fail.
Tip: to change km/hr to m/s, multiply by 5/18. Passing a person (a point) means covering only the tram's own length.
Answer as per the official UPSC answer key.
Read the passage
A single number for inflation is aggregate across different commodities and Services the price rise differs for different items of consumption. So, the single number is arrived at by assigning weights to different commodities and services. For WPI, the weights in production are used; for CPI, the consumption basket is used. But people are not homogeneous.
The consumption basket is vastly different for the poor, the middle classes, and the rich. Hence, the CPI is different for each of these classes and a composite index requires averaging the baskets.
Which one of the following statements best reflects the most logical, rational and crucial message conveyed by the passage?
Answer (b) & explanation
The message is that the present single inflation number does not correctly show the price rise of individual items (b). Step 1: the passage says one inflation number is an average of many items, each given a weight. Prices of different items rise differently. Step 2: it adds that consumption baskets differ for the poor, middle class and rich, so one composite CPI averages them too. So the single number hides how individual prices move: (b). Step 3: option (a), scrap CPI and use only WPI, and (d), inflation data is useless, are extreme. Option (c), services under-represented, is not discussed.
Tip: WPI uses production weights; CPI uses consumption weights. Since 2014 the RBI targets CPI inflation at 4% (with a band of 2–6%).
Answer as per the official UPSC answer key.
Which of the following are the evidences of the phenomenon of continental drift?
- I. The belt of ancient rocks from Brazil coast matches with those from Western Africa.
- II. The gold deposits of Ghana are derived from the Brazil plateau when the two continents lay side by side.
- III. The Gondwana system of sediments from India is known to have its counterparts in six different landmasses of the Southern Hemisphere.
Select the correct answer using the code given below.
Answer (c) & explanation
All three are evidence for continental drift (c). Item I is right: the belt of ancient rocks on the coast of Brazil matches those of West Africa. Item II is right: Ghana's gold has no source rock in Ghana, but its source exists in the Brazil plateau, showing the two lands once lay side by side. Item III is right: India's Gondwana sediments have twins in six southern landmasses. So options (a), (b) and (d), which leave items out, fail.
Notice other proofs used by Alfred Wegener (1912): the "jig-saw fit" of coastlines, tillite from old glaciers, and fossils like Mesosaurus found on both sides of the Atlantic. His idea was later explained by sea-floor spreading and plate tectonics.
Answer as per the official UPSC answer key.
With reference to the Indian polity, consider the following statements :
- I. The Governor of a State is not answerable to any court for the exercise and performance of the powers and duties of his/her office.
- II. No criminal proceedings shall be instituted or continued against the Governor during his/her term of office.
- III. Members of a State Legislature are not liable to any proceedings in any court in respect of anything said within the House.
Which of the statements given above are correct?
Answer (d) & explanation
All three statements are correct (d). Statement I is right: Article 361 says the President and Governors are not answerable to any court for official acts. Statement II is right: under the same Article, no criminal case can be started or continued against them during their term. Statement III is right: Article 194(2) gives State legislators freedom of speech in the House, just as Article 105 does for MPs. So options (a), (b) and (c) fail.
Notice the limit on legislators: in Sita Soren (2024), a seven-judge Bench held that MPs and MLAs who take bribes to vote or speak get no immunity, overruling P.V. Narasimha Rao (1998). Civil cases against a Governor need two months' notice.
Answer as per the official UPSC answer key.
Consider the following statements :
- I. Panchayats at the intermediate level exist in all States.
- II. To be eligible to be a Member of a Panchayat at the intermediate level, a person should attain the age of thirty years.
- III. The Chief Minister of a State constitutes a commission to review the financial position of Panchayats at the intermediate levels and to make recommendations regarding the distribution of net proceeds of taxes and duties, leviable by the State, between the State and Panchayats at the intermediate level.
Which of the statements given above are not correct?
Answer (d) & explanation
All three statements are not correct (d). Statement I is wrong: Article 243B lets States with a population under 20 lakh skip the intermediate level, so it does not exist in all States. Statement II is wrong: the minimum age is 21, not 30 (Article 243F). Statement III is wrong: the State Finance Commission is set up by the Governor under Article 243I, not the Chief Minister, and it reviews all panchayats. So all three are not correct.
Notice the trap: the question asks which are not correct. Other 73rd Amendment (1992) features: a State Election Commission (Article 243K), one-third seats for women (many States give 50%), and the Eleventh Schedule with 29 subjects.
the question asks for statements that are not correct. Circle "not" before you start.
Answer as per the official UPSC answer key.
A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N?
Answer (c) & explanation
The smallest value of N is 1078 (c). Step 1: notice the remainders: 3 leaves 1, 5 leaves 3, 6 leaves 4, 9 leaves 7. Each remainder is 2 less than its divisor. So N + 2 is divisible by all of 3, 5, 6 and 9. Step 2: LCM(3, 5, 6, 9) = 90. So N = 90k − 2. Step 3: the smallest 4-digit value: 90 × 12 = 1080, so N = 1078. (90 × 11 − 2 = 988 is only 3 digits.) Options (a), (b) and (d) fail the remainder checks.
Tip: when divisor − remainder is the same in every case, N + (that gap) is a multiple of the LCM. This is a classic shortcut.
Answer as per the official UPSC answer key.
Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point. Which of the following statements is/are correct?
- I. The result of the match between P and Q is a draw with the score 0-0.
- II. The number of goals scored by R against Q is 1.
Which of the statements given above is/are correct?
Answer (c) & explanation
Both statements are correct (c). Step 1: points: P = 3 (a win and a draw), Q = 2, R = 1 (a draw and a loss). There are three matches: P–Q, P–R and Q–R. Step 2: suppose P beat Q and drew R. Then Q must beat R for 2 points. P has only one goal, so P–Q was 1–0 and P–R 0–0; R's one goal comes against Q, so Q needs 2 goals to win, but Q has only one. Impossible. So P drew Q, P beat R, Q drew R. Step 3: each team scored exactly one goal. P's single goal beat R 1–0, so P–Q was 0–0 (I true). Q's goal came against R in a 1–1 draw, so R scored 1 against Q (II true). Options (a), (b) and (d) fail.
Tip: in points tables, list each team's possible results first, then match goals.
Answer as per the official UPSC answer key.
Which of the following are the sources of income for the Reserve Bank of India?
- I. Buying and selling Government bonds
- II. Buying and selling foreign currency
- III. Pension fund management
- IV. Lending to private companies
- V. Printing and distributing currency notes
Select the correct answer using the code given below.
Answer (a) & explanation
Buying and selling government bonds and foreign currency earn the RBI income (a). Item I is right: the RBI earns interest on the government securities it holds and gains from trading them in open market operations. Item II is right: it earns from foreign exchange operations, such as interest on reserves and gains on selling dollars. Item III is wrong: pension funds are run under the PFRDA. Item IV is wrong: the RBI does not lend to private companies. Item V is wrong: printing notes is a cost for the RBI, not income.
Notice where the profit goes: the RBI pays a surplus (dividend) to the government each year. It paid a record ₹2.69 lakh crore for 2024-25, set under the Bimal Jalan committee framework.
statement V. Many think the RBI "makes money" by printing money. Printing is an expense; the income comes from the assets bought with that money.
Answer as per the official UPSC answer key.
With reference to ‘Direct Air Capture’, an emerging technology, which of the following statements is/are correct?
- I. It can be used as a way of carbon sequestration.
- II. It can be a valuable approach for plastic production and in food processing.
- III. In aviation, it can be a source of carbon for combining with hydrogen to create synthetic low-carbon fuel.
Select the correct answer using the code given below.
Answer (c) & explanation
All three statements are correct (c). Direct Air Capture (DAC) pulls CO₂ straight from the open air using chemical filters or liquids. Statement I is right: the gas can be stored underground, a way of carbon sequestration. Statement II is right: it can be used as a raw material for plastics, and in food processing and fizzy drinks. Statement III is right: joined with green hydrogen, it can make synthetic low-carbon aviation fuel. So options (a), (b) and (d) fail.
Notice the difference from carbon capture and storage (CCS) at a factory chimney, where CO₂ is far more concentrated. DAC is still very expensive and energy-hungry. The world's largest plant, Mammoth, runs in Iceland.
Answer as per the official UPSC answer key.
Consider the following statements about 'PM Surya Ghar Muft Bijli Yojana' :
- I. It targets installation of one crore solar rooftop panels in the residential sector.
- II. The Ministry of New and Renewable Energy aims to impart training on installation, operation, maintenance and repairs of solar rooftop systems at grassroot levels.
- III. It aims to create more than three lakhs' skilled manpower through fresh skilling, and up-skilling, under scheme component of capacity building.
Which of the statements given above are correct?
Answer (d) & explanation
All three statements are correct (d). PM Surya Ghar Muft Bijli Yojana (February 2024, MNRE). Statement I is right: it aims at rooftop solar for one crore households, with up to 300 units of free power a month. Statement II is right: the MNRE trains people at the grassroots to install, operate, maintain and repair the systems. Statement III is right: its capacity-building component targets over three lakh skilled workers through fresh skilling and up-skilling. So options (a), (b) and (c) fail.
Notice the money: a central subsidy of up to ₹78,000 for a 3 kW system, and cheap bank loans. Households can sell spare power to the grid through net metering. India's target is 500 GW of non-fossil capacity by 2030.
Answer as per the official UPSC answer key.
With reference to India, consider the following :
- I. The Inter-State Council
- II. The National Security Council
- III. Zonal Councils
How many of the above were established as per the provisions of the Constitution of India?
Answer (a) & explanation
Only one was set up under the Constitution (a). Item I is right: the Inter-State Council rests on Article 263, which lets the President set it up; it was formed in 1990, after the Sarkaria Commission advised it. Item III is wrong: Zonal Councils come from the States Reorganisation Act, 1956, an ordinary law, so they are statutory. Item II is wrong: the National Security Council (1998) was set up by an executive decision. So options (b), (c) and (d) fail.
Notice the pattern UPSC tests: constitutional bodies (Finance Commission, Election Commission, CAG), statutory bodies (NHRC, Zonal Councils) and executive bodies (NITI Aayog, NSC). The Union Home Minister chairs all five Zonal Councils. The North Eastern Council is a separate statutory body.
"council" in all three names. Ask where each one's power comes from: Constitution, Act or government order.
Answer as per the official UPSC answer key.
Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR − PS = PPT. If Q = 3 and T < 6, then what is the number of possible values of (R, S)?
Answer (b) & explanation
1. Write it as an ordinary subtraction: PQR − PS = PPT. The answer keeps P in front, and its middle digit is also P.
2. Middle column: 3 − P (minus 1 if we borrowed) must give P. Only P = 1 with a borrow works: 3 − 1 − 1 = 1.
3. Last column, after borrowing: (R + 10) − S = T. So S + T = R + 10.
4. T can be 2, 4 or 5 (not 1 or 3, which are taken, and less than 6). Try each, using only unused digits:
5. T = 2: S = R + 8 needs R = 1, which is taken. None.
6. T = 4: S = R + 6 gives R = 2, S = 8. One pair.
7. T = 5: S = R + 5 gives (R, S) = (2, 7) or (4, 9). Two pairs.
8. Total: 3 pairs. Check one: 132 − 18 = 114.
Count pairs (R, S), not separate digits: (2, 8), (2, 7) and (4, 9).
Answer as per the official UPSC answer key.
Read the passage
There has been no democracy that has grown economically without corporate capitalism. It helps in modernizing the economy and enabling the transition from rural to urban, and agriculture to industry and services, which are inevitable with growth. It generates jobs - and there is no other way to fix a country’s unemployment challenge without a further impetus to private business. Big companies can operate on a large scale and become competitive both domestically and externally. A vibrant corporate capitalist base also leads to additional revenues for the State - which in turn, can be used for greater welfare for the marginalized and creating a more level playing field in terms of opportunities.
Which one of the following statements best reflects the critical message conveyed by the author of the passage?
Answer (a) & explanation
The critical message is that corporate capitalism matters for economic growth and also for democracy (a). Step 1: the passage opens: "no democracy has grown economically without corporate capitalism." Step 2: it lists benefits: modernisation, jobs, global competitiveness, and revenue for welfare and a level playing field. So it supports both growth and democratic goals: (a). Step 3: option (b), political objectives, is not the focus. Option (c) widens the claim to "no State", though the passage speaks of democracies. Option (d) invents a two-way mutual dependence.
Tip: match the scope of the passage exactly. If it talks about democracies, reject options that talk about all States.
Answer as per the official UPSC answer key.
Who among the following rulers in ancient India had assumed the titles ‘Mattavilasa’, ‘Vichitrachitta’ and ‘Gunabhara’?
Answer (a) & explanation
Mahendravarman I took these titles (a). The Pallava king Mahendravarman I (c. 600–630) wrote the Sanskrit farce Mattavilasa Prahasana, which mocks monks of various sects. Vichitrachitta ("curious-minded") reflects his new rock-cut temples, such as the one at Mandagapattu, made without brick, timber or metal. Gunabhara was another title. Option (b) is wrong: Simhavishnu was his father. Option (c) is wrong: Narasimhavarman I was called Mamalla. Option (d) is wrong: Simhavarman was an earlier king.
Notice the rivalry: Mahendravarman fought the Chalukya king Pulakeshin II, and his son Narasimhavarman I took Vatapi in 642. Mamallapuram is named after him.
Answer as per the official UPSC answer key.