UPSC Prelims PYQs with explanations
Real questions from official papers, mapped to syllabus topics. Attempt each one; the answer and the reason appear instantly.
What is the remainder when 93 + 94 + 95 + 96 + … + 9100 is divided by 6?
Answer (a) & explanation
The remainder is 0 (a). Step 1: every power of 9 leaves remainder 3 when divided by 6. (9 = 6 + 3; 81 = 78 + 3; and so on, since 3 × 9 leaves 3 again.) Step 2: the terms run from 9³ to 9¹⁰⁰: that is 100 − 3 + 1 = 98 terms. Total remainder = 98 × 3 = 294. Step 3: 294 ÷ 6 = 49 exactly, so the remainder is 0. Options (b), (c) and (d) miscount the terms or the remainder.
Tip: count terms carefully: from a to b there are b − a + 1 terms. Then multiply by the common remainder and reduce.
Answer as per the official UPSC answer key.
Consider the following countries :
- I. Austria
- II. Bulgaria
- III. Croatia
- IV. Serbia
- V. Sweden
- VI. North Macedonia
How many of the above are members of the North Atlantic Treaty Organization?
Answer (b) & explanation
Four of the six are NATO members (b). Bulgaria (joined 2004), Croatia (2009), North Macedonia (2020) and Sweden (2024) are members. Item I is wrong: Austria is constitutionally neutral since 1955. Item IV is wrong: Serbia has declared military neutrality, partly due to NATO's 1999 bombing during the Kosovo war. Both work with NATO only through partnership programmes. So options (a), (c) and (d) fail.
Notice NATO's growth to 32 members: Finland joined in 2023 and Sweden in 2024, both ending long neutrality after Russia invaded Ukraine. Ireland, Switzerland and Malta also stay out. Article 5 says an attack on one is an attack on all.
Sweden joined only in March 2024, after Finland (2023). Older lists leave it out.
Answer as per the official UPSC answer key.
Consider the following pairs :
| Provision in the Constitution of India | Stated under
| I. Separation of Judiciary from the Executive in the public services of the State | The Directive Principles of State Policy
| II. Valuing and preserving of the rich heritage of our composite culture | The Fundamental Duties
| III. Prohibition of employment of children below the age of 14 years in factories | The Fundamental Rights
How many of the above pairs are correctly matched?
Answer (c) & explanation
All three pairs are correctly matched (c). Pair I is right: separation of the judiciary from the executive is Article 50, a Directive Principle. Pair II is right: valuing and preserving our composite culture is Article 51A(f), a Fundamental Duty. Pair III is right: no child below 14 may work in factories, mines or hazardous work under Article 24, a Fundamental Right. So options (a), (b) and (d) fail.
Notice related provisions: Article 21A gives free education for ages 6–14 (86th Amendment, 2002), and Article 51A(k) asks parents to educate their children. The Child Labour Amendment Act, 2016 banned all child labour below 14. Article 39(e) and (f) protect children too.
Article 45 (early childhood care, a DPSP) and Article 24 (a Fundamental Right) both talk about children. Keep them apart.
Answer as per the official UPSC answer key.
Consider the following statements :
- I. On the dissolution of the House of the People, the Speaker shall not vacate his/her office until immediately before the first meeting of the House of the People after the dissolution.
- II. According to the provisions of the Constitution of India, a Member of the House of the People on being elected as Speaker shall resign from his/her political party immediately.
- III. The Speaker of the House of the People may be removed from his/her office by a resolution of the House of the People passed by a majority of all the then Members of the House, provided that no resolution shall be moved unless at least fourteen days' notice has been given of the intention to move the resolution.
Which of the statements given above are correct?
Answer (c) & explanation
Statements I and III are correct (c). Statement I is right: under Article 94, on dissolution of the Lok Sabha the Speaker stays in office until just before the first meeting of the new House. Statement III is right: the Speaker may be removed by a resolution passed by a majority of all the then members, after at least 14 days' notice. Both lines are copied almost word for word from Article 94. Statement II is wrong: nothing in the Constitution asks the Speaker to leave the party.
Notice that resigning from the party is a convention in Britain, not a rule in India. The Speaker decides defection cases under the Tenth Schedule and certifies Money Bills. The Deputy Speaker post stayed vacant for the whole 17th Lok Sabha.
a good practice dressed as a constitutional rule. Ask, "Which Article says this?"
Fell for this one? Most aspirants do. The PYQ Book puts every UPSC trap side by side, so the pattern finally clicks. Try the free sample
Answer as per the official UPSC answer key.
Read the passage
If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty line, even those just over the poverty line are subject to multiple economic insecurities of various kinds (due to wealth and/or health risks, market fluctuations, job-related uncertainties). Many Government policies are actually intended towards mitigating these insecurities.
With reference to the above passage, the following assumptions have been made:
- I. People above the poverty line also are prone to suffer from anxiety about economic insecurity.
- II. Eradication of poverty can result in peace and social equality in the country.
Which of the above assumptions is/are valid?
Answer (a) & explanation
Only assumption I is valid (a). Step 1: the passage says "even those just over the poverty line are subject to multiple economic insecurities." So people above the line also worry about economic security (I). Step 2: assumption II says ending poverty will bring peace and social equality. But the passage says insecurity affects people beyond poverty, and treats social inequality as a separate problem. Ending poverty alone would not solve both. Step 3: so II overreaches. Options (b), (c) and (d) fail.
Tip: when a passage separates two problems, do not assume solving one solves the other. Look for the passage's own words to support each assumption.
Answer as per the official UPSC answer key.
If n is a natural number, then what is the number of distinct remainders of (1n + 2n) when divided by 4?
Answer (c) & explanation
There are two distinct remainders (c). Step 1: try n = 1: 1 + 2 = 3, which leaves remainder 3 when divided by 4. Step 2: for n = 2 or more, 2ⁿ is a multiple of 4 (4, 8, 16, …), so it leaves remainder 0. And 1ⁿ is always 1. So 1ⁿ + 2ⁿ leaves remainder 1. Step 3: the only remainders are 3 and 1: two values. Options (a), (b) and (d) fail.
Tip: test small values of n first; patterns usually settle after one or two steps. Remember any power of 2 from 2² onward is divisible by 4.
don't stop at n ≥ 2. The single case n = 1 adds a second remainder.
Answer as per the official UPSC answer key.
The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r?
Answer (a) & explanation
r equals k (a). Step 1: "p is as much more than the average as q is less" means p = k + d and q = k − d for some amount d. Step 2: then p + q = 2k. Step 3: the average of all three is k, so their sum is 3k. Hence r = 3k − 2k = k. Options (b) k − 1, (c) k + 1 and (d) k/2 do not follow. For example, p = 7, q = 3, r = 5 gives average 5 = r.
Tip: values that are equally above and below the average cancel out. The remaining value must then sit exactly at the average.
Answer as per the official UPSC answer key.
Consider the following statements :
- Statement I : At the 28th United Nations Climate Change Conference (COP28), India refrained from signing the ‘Declaration on Climate and Health’.
- Statement II : The COP28 Declaration on Climate and Health is a binding declaration; and if signed, it becomes mandatory to decarbonize health sector.
- Statement III : If India’s health sector is decarbonized, the resilience of its health-care system may be compromised.
Which one of the following is correct in respect of the above statements?
Answer (c) & explanation
Only Statement III is correct and it explains Statement I (c). Statement I is right: India stayed out of the COP28 (Dubai, 2023) Declaration on Climate and Health. Statement III is right and is the reason: India worried that cutting emissions from health care now could limit the growth of its still-expanding health system and its resilience. Statement II is wrong: the declaration is voluntary, not binding; signing it would not make decarbonisation mandatory. So options (a), (b) and (d) fail.
Notice the bigger picture: COP28 also launched the Global Stocktake call to "transition away" from fossil fuels and set up the Loss and Damage Fund. India stresses equity and common but differentiated responsibilities.
"binding" is the error. COP declarations are political pledges, not treaties.
Answer as per the official UPSC answer key.
Which of the following statements with regard to recommendations of the 15th Finance Commission of India are correct?
- I. It has recommended grants of ₹4,800 crores from the year 2022-23 to the year 2025-26 for incentivizing States to enhance educational outcomes.
- II. 45% of the net proceeds of Union taxes are to be shared with States.
- III. ₹45,000 crores are to be kept as performance-based incentive for all States for carrying out agricultural reforms.
- IV. It reintroduced tax effort criteria to reward fiscal performance.
Select the correct answer using the code given below.
Answer (c) & explanation
Statements I, III and IV are correct (c). The 15th Finance Commission, chaired by N.K. Singh, made these recommendations. Statement I is right: it gave ₹4,800 crore of grants for better educational outcomes. Statement III is right: it kept ₹45,000 crore as an incentive for agricultural reforms. Statement IV is right: it brought back tax effort, with a 2.5% weight, in the devolution formula. Statement II is wrong: it fixed the States' share at 41% for 2021-26, not 45%; the 14th FC had given 42%.
Notice the drop to 41%: it reflected the move of Jammu and Kashmir to a Union Territory. The 16th Finance Commission, under Arvind Panagariya, kept the share at 41% for 2026-31.
the number 45 appears twice. It is right for the agriculture incentive (₹45,000 crore), wrong for the tax share (41%).
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Answer as per the official UPSC answer key.
Consider the following statements about Lokpal :
- I. The power of Lokpal applies to public servants of India, but not to the Indian public servants posted outside India.
- II. The Chairperson or a Member shall not be a Member of the Parliament or a Member of the Legislature of any State or Union Territory, and only the Chief Justice of India, whether incumbent or retired, has to be its Chairperson.
- III. The Chairperson or a Member shall not be a person of less than forty-five years of age on the date of assuming office as the Chairperson or Member, as the case may be.
- IV. Lokpal cannot inquire into the allegations of corruption against a sitting Prime Minister of India.
Which of the statements given above is/are correct?
Answer (a) & explanation
Only statement III is correct (a). Statement III is right: the Chairperson or a Member must be at least 45 years old on taking office. Statement I is wrong: the Lokpal and Lokayuktas Act, 2013 covers public servants in India and abroad. Statement II is wrong: the Chairperson can be a former Chief Justice, a former Supreme Court judge, or an eminent person, so "only the CJI" is wrong. Statement IV is wrong: the Prime Minister is covered, with special safeguards, such as nothing on national security or foreign relations.
Notice the structure: a Chairperson and up to eight members, half of them judicial, and half from SC, ST, OBC, minorities and women. Justice Pinaki Chandra Ghose was the first Lokpal (2019).
"only" and "cannot". Absolute words in a Lokpal question are usually wrong.
One trap spotted is one mark saved. The PYQ Book lines up every trap UPSC has set, so you walk in prepared. Try the free sample
Answer as per the official UPSC answer key.
Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?
Answer (c) & explanation
1. 9 adds nothing new: anything divisible by 9 is already divisible by 3. So we need numbers not divisible by 2, 3, 5 or 7.
2. Any number up to 100 that is not prime has a factor of 2, 3, 5 or 7 (because 11 × 11 is already more than 100).
3. So the numbers we want are just 1 and the primes bigger than 7.
4. There are 25 primes up to 100. Leave out 2, 3, 5 and 7: 21 primes. Add the number 1: 22.
9 is in the list to make you count its multiples twice.
Answer as per the official UPSC answer key.
If FRANCE is coded as 654321 and GERMANY is coded as 9158437, then how is YEMEN coded ?
Answer (d) & explanation
YEMEN is coded as 71813 (d). Step 1: match letters to digits from FRANCE = 654321: F = 6, R = 5, A = 4, N = 3, C = 2, E = 1. Step 2: from GERMANY = 9158437: G = 9, E = 1 ✓, R = 5 ✓, M = 8, A = 4 ✓, N = 3 ✓, Y = 7. Step 3: YEMEN = Y E M E N = 7, 1, 8, 1, 3 = 71813. Option (c), 71913, takes M as 9 (that is G). Options (a) and (b) are wrong.
Tip: in letter-to-digit codes, line up each word with its code and check shared letters (here E, R, A, N) to confirm the mapping before answering.
Answer as per the official UPSC answer key.
Consider the following statements :
Statement I :
Circular economy reduces the emissions of greenhouse gases.
Statement II :
Circular economy reduces the use of raw materials as inputs.
Statement III :
Circular economy reduces wastage in the production process.
Which one of the following is correct in respect of the above statements?
Answer (a) & explanation
Both II and III are correct and both explain Statement I (a). A circular economy replaces "take, make, throw" with reduce, reuse, repair and recycle. Statement II is right: it cuts fresh raw material use, saving the energy of mining and processing. Statement III is right: it cuts waste in production, avoiding the emissions of landfills and burning. Both explain Statement I, that it lowers greenhouse gases, so options (b), (c) and (d) fail.
Notice India's tools: Extended Producer Responsibility (EPR) rules for plastic, e-waste and batteries, and Mission LiFE (Lifestyle for Environment). Steel scrap recycling and vehicle scrapping policy also fit this idea, as does biogas from waste under GOBARdhan.
Answer as per the official UPSC answer key.
In the context of electric vehicle batteries, consider the following elements :
- I. Cobalt
- II. Graphite
- III. Lithium
- IV. Nickel
How many of the above usually make up battery cathodes?
Answer (c) & explanation
Three of the four usually make up cathodes (c). A lithium-ion cathode is a lithium metal oxide, such as nickel-manganese-cobalt (NMC), nickel-cobalt-aluminium (NCA), or lithium iron phosphate (LFP). So lithium (III), nickel (IV) and cobalt (I) go into cathodes. Item II is wrong: graphite is the usual anode material, not the cathode. So options (a), (b) and (d) fail.
Notice the shift to LFP batteries, which avoid costly cobalt and are safer, now common in EVs. Sodium-ion batteries are an emerging cheaper option. India's PLI scheme for Advanced Chemistry Cell batteries aims to make cells at home, and the Kolar and Jammu lithium finds made news.
Answer as per the official UPSC answer key.
Consider the following statements :
- I. Anadyr in Siberia and Nome in Alaska are a few kilometers from each other, but when people are waking up and getting set for breakfast in these cities, it would be different days.
- II. When it is Monday in Anadyr, it is Tuesday in Nome.
Which of the statements given above is/are correct?
Answer (a) & explanation
Only statement I is correct (a). Statement I is right: the International Date Line runs through the Bering Strait between Anadyr in Siberia and Nome in Alaska, so at breakfast time the two places are on different days. Statement II is wrong: Anadyr, on the western (Asian) side, is a day ahead. So when it is Monday in Anadyr, it is still Sunday in Nome, not Tuesday. So options (b), (c) and (d) fail.
Notice the rule: crossing the Date Line westward, you add a day; crossing eastward, you subtract one. The line roughly follows the 180° meridian but zigzags to keep island groups like Kiribati on one date. The Diomede islands in the strait are just 4 km apart, but a day apart.
Answer as per the official UPSC answer key.
Read the passage
The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms’ green innovation is path-dependent: the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about 90% cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of path-dependent green investment without much disruption. A late, more chaotic transition is costlier.
With reference to the above passage, the following assumptions have been made:
- I. Path-dependent green investments will eventually most likely benefit growth as well as public finances in a country like India.
- II. If other green technologies follow the same pattern as that of solar energy, there will most likely be an easy green transition.
Which of the above assumptions is/are valid?
Answer (c) & explanation
Both assumptions are valid (c), as per UPSC's official key. Step 1: the passage says early, path-dependent green investment gives benefits "without much disruption", while a late transition is costlier. Lower costs and less disruption help both growth and public finances, including in a country like India (I). Step 2: solar became about 90% cheaper, beating forecasts. If other green technologies follow the same curve, the transition would likely be easier (II). Step 3: both follow from the passage's logic. Options (a), (b) and (d) fail. Some coaching keys printed (b), but the official answer is (c).
Tip: "most likely" softens an assumption, making it easier to accept. Note that solar's cost fall has made it one of India's cheapest new power sources.
Answer as per the official UPSC answer key.
What is X in the sequence 24, X, 12, 18, 36, 90?
Answer (b) & explanation
X is 12 (b). Step 1: look at the later terms: 12 → 18 is × 1.5, 18 → 36 is × 2, 36 → 90 is × 2.5. The multiplier rises by 0.5 each time. Step 2: go backwards: before 1.5 comes 1, and before that 0.5. Step 3: so 24 × 0.5 = 12 = X, and 12 × 1 = 12 ✓. Options (a) 18, (c) 9 and (d) 6 break the pattern.
Tip: if numbers rise unevenly, try ratios instead of differences. When the start of a pattern is missing, work backwards from the known part.
Answer as per the official UPSC answer key.
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: What is the smallest 1-digit number having exactly 4 distinct factors?
Statement I: 2 is one of the factors.
Statement II: 3 is one of the factors.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (d) & explanation
The question can be answered without either statement (d), as per the key: the statements are not needed. Step 1: one-digit numbers with exactly 4 factors: 6 (1, 2, 3, 6) and 8 (1, 2, 4, 8). The others have fewer (primes have 2; 4 and 9 have 3). Step 2: the smallest is 6, found directly from the question. Step 3: so the statements add nothing; UPSC marks this as (d). Options (a), (b) and (c) suggest the statements are needed.
Tip: in data sufficiency, first try to answer from the question alone. Numbers with exactly 4 factors are either p × q (two different primes) or p³.
read option (d) carefully. It is not the usual "cannot be answered" option.
Answer as per the official UPSC answer key.
Consider the following countries :
- I. Bolivia
- II. Brazil
- III. Colombia
- IV. Ecuador
- V. Paraguay
- VI. Venezuela
Andes mountains pass through how many of the above countries?
Answer (c) & explanation
The Andes pass through four of these countries (c). The Andes, the world's longest mountain range above sea, run down the west of South America through Venezuela, Colombia, Ecuador, Peru, Bolivia, Chile and Argentina. From this list, that is Bolivia, Colombia, Ecuador and Venezuela. Items II and V are wrong: Brazil and Paraguay lie east of the range, on the Brazilian Highlands and the Gran Chaco plains.
Notice the facts UPSC likes: Aconcagua in Argentina is the highest peak outside Asia; the Atacama Desert lies in their rain shadow; and Lake Titicaca, on the Peru–Bolivia border, is the highest navigable lake. The range is a fold mountain chain on the Pacific Ring of Fire.
Answer as per the official UPSC answer key.
Consider the following statements :
With reference to the Constitution of India, if an area in a State is declared as Scheduled Area under the Fifth Schedule
- I. the State Government loses its executive power in such areas and a local body assumes total administration
- II. the Union Government can take over the total administration of such areas under certain circumstances on the recommendations of the Governor
Which of the statements given above is/are correct?
Answer (d) & explanation
Neither statement is correct (d). Statement I is wrong: under the Fifth Schedule, the State's executive power still covers Scheduled Areas. No local body takes over total administration. What changes is that the Governor reports to the President, can modify laws for these areas, and a Tribes Advisory Council advises. Statement II is wrong: the Union can give the State directions on how to run these areas, but nothing lets it take over the administration. So options (a), (b) and (c) fail.
Notice the Sixth Schedule, for tribal areas of Assam, Meghalaya, Tripura and Mizoram, which does create Autonomous District Councils with law-making powers. PESA, 1996 extends panchayats to Fifth Schedule areas with strong gram sabha powers.
"directions" stretched into "take over". Strong verbs usually signal a wrong statement in this topic.
Answer as per the official UPSC answer key.