UPSC Prelims PYQs with explanations
Real questions from official papers, mapped to syllabus topics. Attempt each one; the answer and the reason appear instantly.
Question : Is p greater than q ?
Statement-1: p × q is greater than zero.
Statement-2: p2 is greater than q2.
Which one of the following is correct in respect of the above Question and the Statements ?
Answer (d) & explanation
The question cannot be answered even with both statements (d). Step 1: Statement-1: p × q is positive, so p and q have the same sign. Step 2: Statement-2: p² > q², so p is farther from zero than q. Step 3: together: both positive, like 3 and 2, gives p > q. Both negative, like −3 and −2, gives p < q. Two different answers, so the data are not enough. Options (a), (b) and (c) fail.
Tip: squares hide signs. Always test negative numbers in data sufficiency questions involving squares.
squaring hides the sign. Negatives reverse the order.
Traps like this come back in new clothes. The PYQ Book collects all of them, topic by topic, so none catch you twice. Try the free sample
Answer as per the official UPSC answer key.
Which one of the following is a part of the Congo Basin?
Answer (a) & explanation
Cameroon is part of the Congo Basin (a). The Congo Basin covers the DR Congo, the Republic of Congo, the Central African Republic, Gabon, Equatorial Guinea and south-eastern Cameroon. It holds the world's second-largest tropical rainforest after the Amazon, and its peatlands store huge amounts of carbon. Option (b) is wrong: Nigeria drains mainly to the Niger river. Option (c) is wrong: South Sudan drains to the White Nile. Option (d) is wrong: Uganda drains mostly to the Nile through Lake Victoria.
Notice that the Congo river crosses the Equator twice, so part of its basin always has a rainy season, giving it a steady flow. The basin is home to gorillas, bonobos and forest elephants.
Answer as per the official UPSC answer key.
Consider the following statements :
Statement-I :
- The Supreme Court of India has held in some judgements that the reservation policies made under Article 16(4) of the Constitution of India would be limited by Article 335 for maintenance of efficiency of administration.
Statement-II :
- Article 335 of the Constitution of India defines the term 'efficiency of administration'.
Which one of the following is correct in respect of the above statements?
Answer (c) & explanation
Statement I is correct but Statement II is wrong (c). Statement I is right: in cases such as Indra Sawhney (1992) and M. Nagaraj (2006), the Supreme Court held that reservation in posts under Article 16(4) must be weighed against the "efficiency of administration" under Article 335. Statement II is wrong: Article 335 only uses the phrase; it does not define it. Courts have had to give it meaning case by case.
Notice later rulings: Jarnail Singh (2018) dropped the need to show SC/ST backwardness for promotion quotas, and B.K. Pavitra (2019) said reservation does not by itself harm efficiency. The 82nd Amendment (2000) allowed relaxed qualifying marks for SC/STs in promotions, added as a proviso to Article 335.
"defines". The Constitution uses many phrases it never defines.
Answer as per the official UPSC answer key.
In the context of finance, the term 'beta' refers to
Answer (d) & explanation
Beta measures how a stock moves with the market (d). Beta tells how much a share price moves when the whole market moves. A beta of 1 means it moves in step with the market. Above 1, it swings more, so it is riskier, like many tech shares. Below 1, it is steadier, like utilities. Option (a) describes arbitrage: buying cheap on one platform and selling dear on another. Option (b) describes asset allocation. Option (c) describes basis risk, not beta.
Notice its partner, alpha: the extra return a fund manager earns beyond what beta predicts. Index funds aim for a beta of exactly 1 at low cost. Beta captures market risk only, not risks special to one company.
Answer as per the official UPSC answer key.
Read the passage
In India, a majority of farmers are marginal and small, less educated and possess low adaptive capabilities to climate change, perhaps because of credit and other constraints. So, one cannot expect autonomous adaptation to climate change. Even if it was possible, it would not be sufficient to offset losses from climate change. To deal with this, adaptation to climate change is paramount, alongside a fast mitigation response. Another solution is to have a planned or policy-driven adaptation, which would require the government to come up with policy recommendations. Perception is a necessary pre-requisite for adaptation. Whether farmers are adapting agricultural practices to climate change depends on whether they perceive it or not. However, this is not always enough for adaptation. It is important how a farmer perceives the risks associated with climate change.
Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage ?
Answer (c) & explanation
The message is that farmers' risk perceptions matter for motivating adaptation (c). Step 1: the passage says perception is a "necessary pre-requisite" for adaptation. Step 2: it ends with its key point: "It is important how a farmer perceives the risks" of climate change. That is (c). Step 3: option (a) says adaptation is only the government's job; the passage mentions policy as just one solution. Option (b) is not discussed. Option (d) says mitigation is not possible, but the passage calls for "a fast mitigation response".
Tip: the last line of a passage often carries its main message. Check options with "only" or "not possible" against the text.
Answer as per the official UPSC answer key.
Read the passage
Food consumption patterns have changed substantially in India over the past few decades. This has resulted in the disappearance of many nutritious foods such as millets. While food grain production has increased over five times since independence, it has not sufficiently addressed the issue of malnutrition. For long, the agriculture sector focussed on increasing food production particularly staples, which led to lower production and consumption of indigenous traditional crops/grains, fruits and other vegetables, impacting food and nutrition security in the process. Further, intensive, monoculture agriculture practices can perpetuate the food and nutrition security problem by degrading the quality of land, water and food derived through them.
Based on the above passage, the following assumptions have been made :
- 1. To implement the Sustainable Development Goals and to achieve zero-hunger goal, monoculture agriculture practices are inevitable even if they do not address malnutrition.
- 2. Dependence on a few crops has negative consequences for human health and the ecosystem.
- 3. Government policies regarding food planning need to incorporate nutritional security.
- 4. For the present monoculture agriculture practices, farmers receive subsidies in various ways and government offers remunerative prices for grains and therefore they do not tend to consider crop diversity.
Which of the above assumptions are valid ?
Answer (b) & explanation
Assumptions 2 and 3 are valid (b). Step 1: the passage says monoculture degrades the quality of land, water and food. So depending on a few crops harms health and the ecosystem (2). Step 2: it says grain output rose five times but did not fix malnutrition. So food planning must include nutritional security (3). Step 3: assumption 1 calls monoculture inevitable, which goes against the passage. Assumption 4, about subsidies and prices, is never mentioned. So options (a), (c) and (d) fail.
Tip: 2023 was the International Year of Millets, led by India at the UN. Millets are exactly the "disappearing nutritious foods" this passage mentions.
Answer as per the official UPSC answer key.
A rectangular floor measures 4 m in length and 2·2 m in breadth. Tiles of size 140 cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor ?
Answer (d) & explanation
1. Floor = 400 cm × 220 cm. One tile = 140 cm × 60 cm.
2. Neat rows (all tiles the same way) fit only 8 tiles.
3. Mixing the two directions in a staggered (pinwheel) pattern, as in the figure, fits 9 tiles.
4. 10 cannot fit: across the 220 cm width the tiles can fill at most 200 cm (140 + 60), so a strip of floor is always left empty and there is room for only 9.
don't stop at the neat grid answer 8. "Any orientation" is a hint to mix them.
Answer as per the official UPSC answer key.
Which one of the following makes a tool with a stick to scrape insects from a hole in a tree or a log of wood?
Answer (b) & explanation
The orangutan uses a stick as a tool (b). Orangutans, especially in Sumatra, shape sticks to pry insects and honey out of tree holes and to break open spiny fruits. Young ones learn the skill from their mothers, a sign of culture in apes. Option (d) is the trap: the sloth bear eats termites and ants, but it sucks them out of mounds through a gap in its front teeth; it makes no tool. The fishing cat (a) catches fish with its paws. Otters (c) use stones to crack shells but do not dig insects with sticks.
Notice the famous tool-users: chimpanzees "fish" for termites with stems, crows bend wires into hooks, and Egyptian vultures drop stones on eggs. Orangutans are critically endangered by palm oil plantations.
the sloth bear is famous for eating termites, which makes it tempting.
Answer as per the official UPSC answer key.
Consider the following statements in the context of interventions being undertaken under Anaemia Mukt Bharat Strategy :
- 1. It provides prophylactic calcium supplementation for pre-school children, adolescents and pregnant women.
- 2. It runs a campaign for delayed cord clamping at the time of child-birth.
- 3. It provides for periodic deworming to children and adolescents.
- 4. It addresses non-nutritional causes of anaemia in endemic pockets with special focus on malaria, hemoglobinopathies and fluorosis.
How many of the statements given above are correct?
Answer (c) & explanation
Three statements are correct (c). Anaemia Mukt Bharat (2018) uses a 6×6×6 strategy: six groups, six interventions, six institutional systems. Statement 2 is right: it promotes delayed cord clamping at birth, which gives the baby more iron-rich blood. Statement 3 is right: it gives periodic deworming, as worms cause blood loss. Statement 4 is right: it tackles non-nutritional causes in endemic pockets, such as malaria, haemoglobinopathies like sickle cell, and fluorosis. Statement 1 is wrong: it gives prophylactic iron and folic acid, not calcium.
Notice why it matters: NFHS-5 found about 57% of women and 67% of children aged 6–59 months anaemic. Fortified rice in public food schemes and the Sickle Cell Mission (2023) support the campaign.
Answer as per the official UPSC answer key.
Consider the following statements in respect of the Constitution Day :
Statement-I :
- The Constitution Day is celebrated on 26th November every year to promote constitutional values among citizens.
Statement-II :
- On 26th November, 1949, the Constituent Assembly of India set up a Drafting Committee under the Chairmanship of Dr. B. R. Ambedkar to prepare a Draft Constitution of India.
Which one of the following is correct in respect of the above statements?
Answer (c) & explanation
Statement I is correct but Statement II is wrong (c). Statement I is right: Constitution Day, or Samvidhan Divas, has been observed on 26 November since 2015 to promote constitutional values. That is the day in 1949 when the Constituent Assembly adopted the Constitution. Statement II is wrong: the Drafting Committee under Dr B.R. Ambedkar was set up much earlier, on 29 August 1947. The statement has the right person but the wrong event.
Notice the dates: the Constitution came into force on 26 January 1950, chosen because the Congress had declared Purna Swaraj on 26 January 1930. Some provisions, such as citizenship and elections, took effect on 26 November 1949 itself. 2025 marked 75 years of adoption.
26 November is real, so the date feels safe. Ask what happened on it.
Answer as per the official UPSC answer key.
Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following :
- 1. p + q + r – s – t is definitely even.
- 2. 2p + q + 2r – 2s + t is definitely odd.
Which of the above statements is/are correct ?
Answer (a) & explanation
Only statement 1 is correct (a). Step 1: subtracting a number has the same odd-even effect as adding it. So p + q + r − s − t has the same parity as the sum of all five. Step 2: the five include two odd numbers, and two odds make an even sum. So statement 1 is always even, and true. Step 3: in 2p + q + 2r − 2s + t, the doubled terms are even. The parity depends on q + t, which depends on which numbers are odd. So it is not definitely odd. Options (b), (c) and (d) fail.
Tip: for odd-even questions, ignore the signs and any doubled terms. Just count the odd numbers left.
Answer as per the official UPSC answer key.
Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements :
- 1. The number of possible values of p is 5.
- 2. The number of possible values of q is 6.
Which of the above statements is/are correct ?
Answer (c) & explanation
Both statements are correct (c). Step 1: pp = 11p, so 11(p + q + r) = tt0 = 110t. So p + q + r = 10t: either 10 or 20. Step 2: sum 10 with p < q < r: (1, 2, 7), (1, 3, 6), (1, 4, 5), (2, 3, 5). Sum 20: (3, 8, 9), (4, 7, 9), (5, 6, 9), (5, 7, 8). Step 3: p takes 1, 2, 3, 4, 5 (five values). q takes 2, 3, 4, 6, 7, 8 (six values). So options (a), (b) and (d) fail.
Tip: repeated-digit numbers like pp are 11 × p. Spotting this turns the puzzle into a simple sum.
Answer as per the official UPSC answer key.
Let P, Q, R, S and T be five statements such that :
- I. If P is true, then both Q and S are true.
- II. If R and S are true, then T is false.
Which of the following can be concluded ?
- 1. If T is true, then at least one of P and R must be false.
- 2. If Q is true, then P is true.
Select the correct answer using the code given below :
Answer (a) & explanation
Only conclusion 1 follows (a). Step 1: suppose T is true. By rule II, R and S cannot both be true. If S is false, then by rule I, P must be false (P true would make S true). If R is false, we are done. Either way, P or R is false. So conclusion 1 follows. Step 2: rule I says "if P then Q". This does not give "if Q then P". So conclusion 2 does not follow. Step 3: options (b), (c) and (d) fail.
Tip: "If A then B" also gives "if not B then not A". It never gives "if B then A".
reversing an 'if … then' (Q → P) is the classic mistake. Only the contrapositive (not Q → not P) is safe.
Answer as per the official UPSC answer key.
Consider the following infrastructure sectors :
- 1. Affordable housing
- 2. Mass rapid transport
- 3. Health care
- 4. Renewable energy
On how many of the above does UNOPS Sustainable Investments in Infrastructure and Innovation (S3i) initiative focus for its investments?
Answer (c) & explanation
S3i focuses on three of the four (c). The UN Office for Project Services (UNOPS) launched Sustainable Investments in Infrastructure and Innovation (S3i) in 2018 to bring private money into infrastructure in developing countries. Its three focus areas are affordable housing, renewable energy and health infrastructure. Item 2 is wrong: mass rapid transport is not one of them. So options (a), (b) and (d) are wrong.
Notice that S3i projects included plans for affordable homes in countries such as Ghana, Kenya and Pakistan, and renewable projects in the Caribbean. UNOPS itself is a UN body based in Copenhagen that manages projects for governments and other UN agencies. The initiative later ran into financial mismanagement concerns and was wound down.
Answer as per the official UPSC answer key.
Consider the following statements :
- Statement-I : The soil in tropical rain forests is rich in nutrients.
- Statement-II : The high temperature and moisture of tropical rain forests cause dead organic matter in the soil to decompose quickly.
Which one of the following is correct in respect of the above statements?
Answer (d) & explanation
Statement I is wrong but Statement II is correct (d). Statement II is right: the high heat and moisture of tropical rainforests make dead leaves and organic matter decompose very fast. Statement I is wrong: the nutrients released are taken up at once by the dense plant cover, and heavy rain washes, or leaches, the rest away. Most nutrients sit in the living plants, not the soil. So rainforest soil is poor, often red laterite rich in iron and aluminium.
Notice why clearing rainforest for farming fails: once trees are cut, the thin soil is exhausted in a few years. This explains shifting cultivation (jhum) in such areas. In contrast, cold temperate forests decompose slowly and build thick, fertile soils.
lush forest suggests rich soil. In rainforests the richness is in the plants, not the soil.
Answer as per the official UPSC answer key.
Consider the following statements in respect of the 44th Chess Olympiad, 2022:
- 1. It was the first time that Chess Olympiad was held in India.
- 2. The official mascot was named ‘Thambi’.
- 3. The trophy for the winning team in the open section is the Vera Menchik Cup.
- 4. The trophy for the winning team in the women’s section is the Hamilton-Russell Cup.
How many of the statements given above are correct?
Answer (b) & explanation
Two statements are correct (b). Statement 1 is right: the 44th Chess Olympiad, held at Mamallapuram near Chennai in 2022, was the first held in India. It moved there after Russia lost hosting rights. Statement 2 is right: its official mascot was a knight named "Thambi", meaning younger brother in Tamil. Statements 3 and 4 swap the trophies: the open section's trophy is the Hamilton-Russell Cup, and the women's section's is the Vera Menchik Cup.
Notice the torch relay, started for the first time at this Olympiad, beginning in India. At the 45th Olympiad in Budapest (2024), India won gold in both the open and women's sections, its best ever. D. Gukesh became world champion in 2024.
When two statements carry paired names, check whether they have simply been swapped.
Answer as per the official UPSC answer key.
Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible ?
Answer (c) & explanation
12 values of x are possible (c). Step 1: 7x is always divisible by x. So 7x + 96 is divisible by x only if x divides 96. Step 2: 96 = 2⁵ × 3. Step 3: the number of divisors = (5 + 1) × (1 + 1) = 12. So x can be any of 12 values: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96. Options (a), (b) and (d) miscount.
Tip: to count divisors, write the number as a product of prime powers. Add 1 to each power and multiply.
Answer as per the official UPSC answer key.
Question : Is (p + q – r) greater than (p – q + r), where p, q and r are integers ?
Statement-1: (p – q) is positive.
Statement-2: (p – r) is negative.
Which one of the following is correct in respect of the above Question and the Statements ?
Answer (c) & explanation
Both statements together are needed (c). Step 1: simplify the question first. p + q − r > p − q + r means 2q > 2r, that is, is q > r? Step 2: Statement-1 says p − q is positive, so q < p. Statement-2 says p − r is negative, so p < r. Neither alone links q and r. Step 3: together: q < p < r, so q < r. The question gets a definite "no". A definite "no" still answers it, so (c). Options (a), (b) and (d) fail.
Tip: always simplify the question before reading the statements. A firm "no" counts as an answer in data sufficiency.
Answer as per the official UPSC answer key.
Consider the following statements :
- 1. Amarkantak Hills are at the confluence of Vindhya and Sahyadri Ranges.
- 2. Biligirirangan Hills constitute the easternmost part of Satpura Range.
- 3. Seshachalam Hills constitute the southernmost part of Western Ghats.
How many of the statements given above are correct?
Answer (d) & explanation
None of the statements is correct (d). Statement 1 is wrong: Amarkantak, the source of the Narmada and Son, is where the Vindhya and Satpura ranges meet, through the Maikal hills; the Sahyadri is the Western Ghats. Statement 2 is wrong: the Biligirirangan Hills in Karnataka are where the Eastern and Western Ghats meet, not part of the Satpura. Statement 3 is wrong: the Seshachalam Hills, home of Tirumala, are part of the Eastern Ghats in Andhra Pradesh. The southern end of the Western Ghats is near Kanyakumari.
Notice the BRT Tiger Reserve in the Biligirirangan Hills, a vital wildlife corridor. Seshachalam is a biosphere reserve known for red sanders, the subject of much smuggling.
Answer as per the official UPSC answer key.
In which one of the following regions was Dhanyakataka, which flourished as a prominent Buddhist centre under the Mahasanghikas, located?
Answer (a) & explanation
Dhanyakataka was in Andhra (a). Dhanyakataka, today's Dharanikota next to Amaravati on the lower Krishna, was a capital of the Satavahanas and a great Buddhist centre of the Mahasanghika school, with sub-sects such as the Purvashaila and Aparashaila. Tradition links Nagarjuna and the Kalachakra teaching to the place. Option (b) is wrong: Gandhara, in the north-west, was a centre of Mahayana and Greco-Buddhist art. Option (c) is wrong: Kalinga is Odisha. Option (d) is wrong: Magadha is Bihar, home of Nalanda.
Notice the Amaravati school of art, in white marble-like limestone, one of three great schools along with Gandhara and Mathura. Andhra's new capital, Amaravati, is named after this ancient site.
Answer as per the official UPSC answer key.