UPSC Prelims PYQs with explanations
Real questions from official papers, mapped to syllabus topics. Attempt each one; the answer and the reason appear instantly.
Consider the following statements :
- 1. The Self-Help Group (SHG) programme was originally initiated by the State Bank of India by providing microcredit to the financially deprived.
- 2. In an SHG, all members of a group take responsibility for a loan that an individual member takes.
- 3. The Regional Rural Banks and Scheduled Commercial Banks support SHGs.
How many of the above statements are correct?
Answer (b) & explanation
Two statements are correct (b). Statement 1 is wrong: the SHG-Bank Linkage Programme was started by NABARD in 1992, not by the SBI. Statement 2 is right: in an SHG, members guarantee each other's loans, called joint liability; this peer pressure replaces collateral. Statement 3 is right: commercial banks, Regional Rural Banks and cooperative banks all lend to SHGs.
Notice the scale: India has over 90 lakh SHGs, mostly of women, under the DAY-NRLM. The Lakhpati Didi target aims to help 3 crore SHG women earn at least ₹1 lakh a year. SHGs have very low loan default rates, which shows how trust works as security. Kerala's Kudumbashree is a well-known model.
SBI is the biggest lender to SHGs today, but the scheme began with NABARD.
Answer as per the official UPSC answer key.
Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make?
Answer (d) & explanation
The maximum is 45 attempts (d). Step 1: think of the unluckiest case. First he picks every non-red shoe: 9 + 8 = 17 pairs = 34 shoes. Step 2: still unlucky, he then picks all 10 red shoes of the same foot (say all left shoes): 34 + 10 = 44. Step 3: the next shoe must be a red right shoe, which makes a pair. So 45 picks at most. Option (c), 44, stops one short. Options (a) and (b) ignore the left-right problem.
Tip: shoes have a left and a right, unlike socks. In worst-case questions, always ask what "a pair" really needs.
(c) 44 forgets that ten left shoes still do not make a pair.
Answer as per the official UPSC answer key.
A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements :
- 1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175.
- 2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167.
Which of the above statements is/are correct ?
Answer (c) & explanation
Both statements are correct (c). Step 1: think of the worst case. To avoid completing any colour, take one less than each group: 13 + 19 + 25 + 27 + 37 + 53 = 174. The next ball must complete a group, so n = 175 (statement 1 true). Step 2: to miss a colour as long as possible, take every ball except the smallest group (14 black): 180 − 14 = 166. Step 3: the next ball must be black, so m = 167 (statement 2 true). Options (a), (b) and (d) fail.
Tip: worst-case questions: give the unlucky picker everything except what you need, then add one.
for 'one of each colour', the worst case leaves out the smallest group, not the largest.
Answer as per the official UPSC answer key.
There are five persons P, Q, R, S and T each one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1. Task-2 must be assigned to either R or S. In how many ways can the assignment be done ?
Answer (d) & explanation
There are 24 ways (d). Step 1: Task-2 must go to R or S: 2 ways. Step 2: Task-1 cannot go to P, Q or the person who got Task-2. So only 2 people are left for it: 2 ways. Step 3: the other 3 tasks go to the remaining 3 people in 3 × 2 × 1 = 6 ways. Total = 2 × 2 × 6 = 24. Options (a), (b) and (c) miss a factor.
Tip: fill the most restricted task first. Then each later choice becomes simple counting.
Answer as per the official UPSC answer key.
Consider the following :
- 1. Aerosols
- 2. Foam agents
- 3. Fire retardants
- 4. Lubricants
In the making of how many of the above are hydrofluorocarbons used?
Answer (c) & explanation
HFCs are used in three of the four (c). Hydrofluorocarbons (HFCs) replaced the ozone-depleting CFCs. Besides refrigeration and air-conditioning, they are used as aerosol propellants, as foam-blowing agents for insulation, and as fire suppressants that put out fires without water damage. Item 4 is wrong: HFCs are not used in making lubricants. So options (a), (b) and (d) fall.
Notice the twist: HFCs do not harm the ozone layer, but they are powerful greenhouse gases, often thousands of times stronger than CO₂. The Kigali Amendment (2016) to the Montreal Protocol phases them down. India, in the third group, will freeze use in 2028 and cut 85% by 2047. Its India Cooling Action Plan (2019) supports this.
Answer as per the official UPSC answer key.
Consider the following statements :
- 1. Carbon fibres are used in the manufacture of components used in automobiles and aircrafts.
- 2. Carbon fibres once used cannot be recycled.
Which of the statements given above is/are correct?
Answer (a) & explanation
Only statement 1 is correct (a). Statement 1 is right: carbon fibre composites are very strong and light, so they are used in aircraft such as the Boeing 787 and Airbus A350, in racing and electric cars, wind turbine blades and sports gear like rackets and bicycles. Lighter vehicles burn less fuel. Statement 2 is wrong: carbon fibres can be recycled. Processes such as pyrolysis, which burns away the resin, and solvolysis, which dissolves it, recover the fibres, though these are costly and the fibres come out shorter.
Notice India's push: carbon fibre is a strategic material for missiles and space vehicles, and India still imports most of it. ISRO and DRDO have built their own, and private firms are setting up plants.
Answer as per the official UPSC answer key.
Consider the following statements :
Statement-I :
Switzerland is one of the leading exporters of gold in terms of value.
Statement-II :
Switzerland has the second largest gold reserves in the world.
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: Switzerland refines a huge share of the world's gold, at refineries in Ticino and elsewhere. It imports raw gold and old bars, and exports refined bars, so it is one of the largest exporters of gold by value. Statement II is wrong: the Swiss central bank's reserves, about 1,040 tonnes, rank around seventh or eighth, not second. The USA holds the most, over 8,000 tonnes, followed by Germany.
Notice India's place: the RBI holds about 880 tonnes, among the top ten, and has been buying and bringing gold home from London. India is also one of the world's two biggest gold consumers, along with China.
the export is from refining, not from a big vault. Trade and reserves are different things.
Answer as per the official UPSC answer key.
Consider the following in respect of prime number p and composite number c.
- 1. (p + c)/(p – c) can be even.
- 2. 2p + c can be odd.
- 3. pc can be odd.
Which of the statements given above are correct ?
Answer (d) & explanation
All three statements can be true (d). Step 1: "can be" needs only one example each. Step 2: statement 1: p = 11, c = 9. (11 + 9) ÷ (11 − 9) = 20 ÷ 2 = 10, which is even. Statement 2: c = 9. 2p is even, and even + 9 is odd. Step 3: statement 3: p = 3, c = 9. 3 × 9 = 27, odd. So options (a), (b) and (c) fail.
Tip: remember that composite numbers can be odd (9, 15, 21). Many "can be" traps assume composites are even.
Answer as per the official UPSC answer key.
What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated ?
Answer (a) & explanation
The sum is 7998 (a). Step 1: below 2000, the first digit must be 1. The other digits 2, 3 and 4 can be arranged in 3 × 2 × 1 = 6 ways. Step 2: thousands place: 6 numbers × 1000 = 6000. Step 3: each of 2, 3, 4 sits twice in each of the other three places: (2 + 3 + 4) × 2 × 111 = 1998. Total = 6000 + 1998 = 7998. Options (b), (c) and (d) miscount.
Tip: for sums of arranged numbers, handle the fixed digit separately, then use (sum of digits) × (times each appears) × 111.
Answer as per the official UPSC answer key.
A cuboid of dimensions 7 cm × 5 cm × 3 cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7 cm × 5 cm, 5 cm × 3 cm, 7 cm × 3 cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1 cm. Which of the following statements is/are correct ?
- 1. There are exactly 15 small cubes with no paint on any face.
- 2. There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green.
Select the correct answer using the code given below :
Answer (a) & explanation
Only statement 1 is correct (a). Step 1: unpainted cubes form the inner block: (7 − 2) × (5 − 2) × (3 − 2) = 5 × 3 × 1 = 15. So statement 1 is true. Step 2: blue faces (7 × 3) and green faces (5 × 3) meet along the four edges of length 3 cm. Step 3: each such edge has 3 − 2 = 1 middle cube with exactly those two colours. Four edges give 4 cubes, not 6. So statement 2 is false. Options (b), (c) and (d) fail.
Tip: two coloured faces meet along an edge. Cubes with exactly two colours on an edge = edge length − 2 (the corners have three colours).
corner cubes have three painted faces, so leave them out when you count 'exactly two'.
Answer as per the official UPSC answer key.
In essence, what does 'Due Process of Law' mean?
Answer (a) & explanation
Due process means the principle of natural justice (a). Due process of law, from the US Constitution, asks whether a law itself, and the way it is applied, is fair and reasonable. At its heart are the rules of natural justice: hear the other side (audi alteram partem) and no one should judge his own case. Option (b) is the opposite idea: procedure established by law, written in India's Article 21, which only asks whether a valid law was followed. Options (c) and (d) are parts of fairness but not its essence.
Notice the turn in Maneka Gandhi v Union of India (1978): the Supreme Court held that the procedure must be fair, just and reasonable, bringing due process into India in effect. Earlier, A.K. Gopalan (1950) had taken the narrow view.
option (b) is the Indian phrase, not its opposite number. UPSC asked what "due process" means, not what our text says.
Answer as per the official UPSC answer key.
Consider the following statements :
Statement-I : The temperature contrast between continents and oceans is greater during summer than in winter.
Statement-II : The specific heat of water is more than that of land surface.
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: water has a much higher specific heat than rock and soil, so the oceans warm and cool slowly, while land heats and cools fast. Statement I is marked wrong: UPSC's key treats the land–sea temperature contrast as greater in winter, when continental interiors such as Siberia become extremely cold while the oceans stay mild. So the difference in winter is larger than in summer.
Notice the effects: continental climates have a big range between summer and winter, while maritime climates stay mild. The land–sea contrast also drives land and sea breezes daily and the monsoon seasonally. The Siberian High in winter is the result of this deep cold.
Answer as per the official UPSC answer key.
Consider the following pairs :
| Area of conflict mentioned in news | Country where it is located
| 1. Donbas | Syria
| 2. Kachin | Ethiopia
| 3. Tigray | North Yemen
How many of the above pairs are correctly matched?
Answer (d) & explanation
None of the pairs is correctly matched (d). Pair 1 is wrong: Donbas, covering Donetsk and Luhansk, is in eastern Ukraine, at the heart of the war with Russia, not in Syria. Pair 2 is wrong: Kachin is a northern state of Myanmar, where the Kachin Independence Army fights the military junta, not in Ethiopia. Pair 3 is wrong: Tigray is a region of northern Ethiopia, which saw a brutal war in 2020–22, not in Yemen. Syria and Yemen are the decoy countries.
Notice that North Yemen no longer exists as a state; it merged with South Yemen in 1990. Kachin's rare earth mines, near China, have become a strategic prize in Myanmar's civil war.
Answer as per the official UPSC answer key.
If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q)(r + s)?
Answer (b) & explanation
The greatest value is 225 (b). Step 1: to make the product big, use the four largest digits: 9, 8, 7, 6. Their total is 30. Step 2: for a fixed total, a product of two parts is largest when the parts are equal. So make each bracket 15: 9 + 6 and 8 + 7. Step 3: 15 × 15 = 225. Option (a), 230, is impossible. Option (c), 224 = 16 × 14, is slightly less. Option (d), 221 = 17 × 13, is less again.
Tip: for a fixed sum, the product is greatest when the numbers are as close as possible.
Answer as per the official UPSC answer key.
In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.
Question: How many persons attended the party ?
Statement-1: 50 persons took milk.
Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.
Which one of the following is correct in respect of the above Question and the Statements ?
Answer (a) & explanation
Statement-2 alone answers it, but Statement-1 alone does not (a). Step 1: people who took tea or coffee = 75 + 60 − 15 = 120. No milk-taker takes tea, so total = 120 + (people who took milk only). Step 2: Statement-1 says 50 took milk. But some of them may also take coffee, so "milk only" is unknown. Not enough. Step 3: Statement-2: total = 5 × (milk only). So 120 + m = 5m, giving m = 30 and total = 150. Options (b), (c) and (d) fail.
Tip: in Venn questions, ask which region the given number covers. "Took milk" is not the same as "took milk only".
Answer as per the official UPSC answer key.
With reference to India's projects on connectivity, consider the following statements :
- 1. East-West Corridor under Golden Quadrilateral Project connects Dibrugarh and Surat.
- 2. Trilateral Highway connects Moreh in Manipur and Chiang Mai in Thailand via Myanmar.
- 3. Bangladesh-China-India-Myanmar Economic Corridor connects Varanasi in Uttar Pradesh with Kunming in China.
How many of the above statements are correct?
Answer (d) & explanation
None of the statements is correct (d). Statement 1 is wrong: the East-West Corridor links Silchar in Assam to Porbandar in Gujarat, and it was part of NHDP Phase II, not the Golden Quadrilateral, which links Delhi, Mumbai, Chennai and Kolkata. Statement 2 is wrong: the India–Myanmar–Thailand Trilateral Highway runs from Moreh in Manipur to Mae Sot in Thailand, not Chiang Mai. Statement 3 is wrong: the BCIM corridor was planned from Kolkata to Kunming, not from Varanasi.
Notice that each statement has one wrong end-point; UPSC tests exact names. India has gone cool on BCIM because it overlaps China's Belt and Road, preferring the Kaladan project and the Trilateral Highway.
each statement keeps one correct name. UPSC changed only one end of each route.
Answer as per the official UPSC answer key.
With reference to ancient India, consider the following statements :
- 1. The concept of Stupa is Buddhist in origin.
- 2. Stupa was generally a repository of relics.
- 3. Stupa was a votive and commemorative structure in Buddhist tradition.
How many of the statements given above are correct?
Answer (b) & explanation
Two statements are correct (b). Statement 1 is wrong: burial mounds over the remains of important people go back to Vedic and pre-Buddhist times. The Buddhists took up the stupa and made it their own, but they did not invent it. Statement 2 is right: stupas were usually built over relics of the Buddha or of revered monks. Statement 3 is right: stupas were also votive and commemorative: pilgrims offered small votive stupas as acts of merit, and some marked places linked to the Buddha's life.
Notice the parts of a stupa: the dome (anda), the railing (vedika), the gateways (torana) and the umbrella (chhatra). Great examples are Sanchi, Bharhut and Amaravati. Ashoka is said to have built 84,000 stupas.
Answer as per the official UPSC answer key.
Consider the following statements :
Statement-I : India’s public sector health care system largely focuses on curative care with limited preventive, promotive and rehabilitative care.
Statement-II : Under India’s decentralized approach to health care delivery, the States are primarily responsible for organizing health services.
Which one of the following is correct in respect of the above statements?
Answer (b) & explanation
Both statements are correct but II does not explain I (b). Statement I is right: the National Health Policy 2017 itself notes that public health care is mostly curative, treating illness after it strikes, with limited preventive, promotive and rehabilitative care. Statement II is right: public health and hospitals are on the State List, so States are mainly responsible for running health services. But II does not explain I: the curative focus comes from priorities and funding, not from decentralisation.
Notice the shift under Ayushman Bharat (2018): its Ayushman Arogya Mandirs, the former Health and Wellness Centres, push primary and preventive care, while PM-JAY pays for hospital treatment. Public health spending is still below the target of 2.5% of GDP.
Answer as per the official UPSC answer key.
In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots?
Answer (b) & explanation
1. Choose how many sixes and fours. The singles then fill up the rest of the 25, so they never cause a problem.
2. 0 sixes: fours can be 0 to 6 (up to 24 runs). That is 7 ways.
3. 1 six: 19 runs left, fours 0 to 4. 5 ways.
4. 2 sixes: 13 left, fours 0 to 3. 4 ways.
5. 3 sixes: 7 left, fours 0 or 1. 2 ways.
6. 4 sixes: 1 left, no four. 1 way.
7. Total: 7 + 5 + 4 + 2 + 1 = 19.
Answer as per the official UPSC answer key.
If 'ZERO' is written as 'CHUR', then how is 'PLAYER' written ?
Answer (d) & explanation
PLAYER is written SODBHU (d). Step 1: compare ZERO with CHUR. Z → C, E → H, R → U, O → R. Each letter moves 3 places forward, wrapping from Z back to A. Step 2: apply this to PLAYER: P → S, L → O, A → D, Y → B, E → H, R → U. Step 3: the code is SODBHU. Option (a) gets A and Y wrong. Options (b) and (c) go wrong on the last letters.
Tip: when a letter near Z changes to one near A, the code wraps around. Count forward: Y, Z, A, B is 3 steps.
Answer as per the official UPSC answer key.