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 :
- I. If any question arises as to whether a Member of the House of the People has become subject to disqualification under the 10th Schedule, the President's decision in accordance with the opinion of the Council of Union Ministers shall be final.
- II. There is no mention of the word 'political party' in the Constitution of India.
Which of the statements given above is/are correct?
Answer (d) & explanation
Neither statement is correct (d). Statement I is wrong: under the Tenth Schedule, the Speaker or Chairman decides defection cases, subject to judicial review (Kihoto Hollohan, 1992). The President decides other disqualifications under Article 103, and then on the Election Commission's opinion, not the Cabinet's. Statement II is wrong: "political party" appears many times in the Tenth Schedule, added by the 52nd Amendment in 1985. So options (a), (b) and (c) fail.
Notice the later change: the 91st Amendment (2003) removed the "split" exception (one-third), leaving only mergers backed by two-thirds of members. Courts have asked Speakers to decide defection petitions within a reasonable time, ideally three months.
two different routes mixed up: Article 103 (President, on EC's opinion) and the Tenth Schedule (presiding officer).
Answer as per the official UPSC answer key.
A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct?
- I. The minimum number of cuts is 9.
- II. The number of smaller pieces which are not painted on any face is 6.
Select the correct answer using the code given below:
Answer (c) & explanation
Both statements are correct (c). Step 1: for the fewest cuts, split the 60 pieces as evenly as possible across three directions: 60 = 3 × 4 × 5. Cuts needed = (3 − 1) + (4 − 1) + (5 − 1) = 2 + 3 + 4 = 9. So I is right. Step 2: pieces with no paint come from the inside: remove one layer from each side in every direction: (3 − 2) × (4 − 2) × (5 − 2) = 1 × 2 × 3 = 6. So II is right. Options (a), (b) and (d) fail.
Tip: for the minimum cuts, keep the three factors as close together as possible. Unpainted inner pieces = (a − 2)(b − 2)(c − 2).
Answer as per the official UPSC answer key.
Let P = QQQ be a 3-digit number. What is the HCF of P and 481?
Answer (c) & explanation
The HCF is 37 (c). Step 1: a number like QQQ (for example 555) equals Q × 111, and 111 = 3 × 37. So every QQQ has 37 as a factor. Step 2: 481 = 13 × 37. Step 3: the common part is 37. Could the HCF be bigger? Only if QQQ also had 13, but Q is a single digit (1–9) and 3 × Q cannot contain 13. So the HCF is always 37. Options (a), (b) and (d) fail.
Tip: remember 111 = 3 × 37, so every three-same-digit number (111, 222, …, 999) is divisible by 37. Also 1001 = 7 × 11 × 13.
Answer as per the official UPSC answer key.
Let x be a real number between 0 and 1. Which of the following statements is/are correct?
- I. x2 > x3
- II. x > √x
Select the correct answer using the code given below:
Answer (a) & explanation
Only statement I is correct (a). Step 1: for a number between 0 and 1, multiplying by it makes things smaller. Test x = 1/4. Step 2: statement I: x² = 1/16 and x³ = 1/64. Since 1/16 > 1/64, x² > x³: true. Step 3: statement II: √x = √(1/4) = 1/2, which is bigger than 1/4. So x > √x is false. Options (b), (c) and (d) fail.
Tip: between 0 and 1, higher powers get smaller and roots get bigger: √x > x > x² > x³. Above 1 the order flips. Test with an easy fraction like 1/4.
between 0 and 1 the usual "squaring makes it bigger" instinct runs backwards.
Answer as per the official UPSC answer key.
Consider the following statements :
- Statement I : Scientific studies suggest that a shift is taking place in the Earth’s rotation and axis.
- Statement II : Solar flares and associated coronal mass ejections bombarded the Earth’s outermost atmosphere with tremendous amount of energy.
- Statement III : As the Earth’s polar ice melts, the water tends to move towards the equator.
Which one of the following is correct in respect of the above statements?
Answer (b) & explanation
Both II and III are correct, but only III explains I (b). Statement I is right: studies show a shift in Earth's rotation and axis. Statement III is right and is the reason: melting polar ice moves mass towards the equator. Like a spinning skater stretching her arms, the Earth slows a little and its axis drifts. Statement II is right: solar flares and coronal mass ejections did hit the upper atmosphere hard, as in May 2024, but they do not move the planet's mass, so they do not explain I.
Notice another human factor: heavy pumping of groundwater has also shifted the axis, studies found. Solar storms instead cause auroras and can disrupt satellites, GPS and power grids.
Answer as per the official UPSC answer key.
Consider the following statements in respect of the International Bank for Reconstruction and Development (IBRD) :
- I. It provides loans and guarantees to middle income countries.
- II. It works single-handedly to help developing countries to reduce poverty.
- III. It was established to help Europe rebuild after the World War II.
Which of the statements given above are correct?
Answer (c) & explanation
Statements I and III are correct (c). Statement III is right: the IBRD, set up at Bretton Woods in 1944, was meant to rebuild war-torn Europe; its first loan went to France in 1947. Statement I is right: today it gives loans and guarantees to middle-income and creditworthy poorer countries. Statement II is wrong: it works with the IDA, IFC, MIGA and ICSID as the World Bank Group, so "single-handedly" is wrong.
Notice the split: the IDA gives soft loans and grants to the poorest countries, the IFC lends to the private sector, and MIGA gives risk insurance. India is one of the IBRD's largest borrowers, and is not a member of ICSID. The World Bank's twin is the IMF.
"single-handedly". A Bank with four sister bodies does not work alone.
Answer as per the official UPSC answer key.
Consider the following statements in respect of the first Kho Kho World Cup:
- I. The event was held in Delhi, India.
- II. Indian men beat Nepal with a score of 78-40 in the final to become the World Champion in men category.
- III. Indian women beat Nepal with a score of 54-36 in the final to become the World Champion in women category.
Which of the statements given above is/are correct?
Answer (a) & explanation
Only statement I is correct (a). Statement I is right: the first Kho Kho World Cup was held in New Delhi in January 2025, and India beat Nepal in both finals. Statements II and III are wrong: the question swaps the two scores. The women won 78-40 and the men won 54-36. So options (b), (c) and (d) fail.
Notice the game's roots: kho kho is an Indian tag game from Maharashtra, played by teams of 12, with nine on the field. It was shown at the 1936 Berlin Olympics as a demonstration sport. Ultimate Kho Kho, a professional league since 2022, has boosted its popularity. Trick: read sports scores carefully, as swaps are common.
Answer as per the official UPSC answer key.
If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x − y)?
Answer (d) & explanation
The ratio is −5, which is not listed, so the answer is (d). Step 1: the maximum of x + y uses the largest x and largest y: 8 + 7 = 15. Step 2: the minimum of x − y uses the smallest x and the largest y: 4 − 7 = −3. Step 3: ratio = 15 ÷ (−3) = −5. None of the options show −5. Option (c), −15/2, divides by −2 instead of −3. Options (a) and (b) ignore the minus sign.
Tip: to make a difference smallest, make the first number small and the subtracted number big. Always check "None of the above" before forcing a match.
to make x − y small you take y large, not small.
Answer as per the official UPSC answer key.
The 5-digit number PQRST (all distinct digits) is such that T ≠ 0, P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?
Answer (b) & explanation
Four such numbers are possible (b). Step 1: P = 3T with T not 0: (T, P) can be (1, 3), (2, 6), (3, 9). Step 2: Q = R + 3 and S = Q + 4 = R + 7. S is a digit, so R can be 0, 1 or 2: (R, Q, S) = (0, 3, 7), (1, 4, 8), (2, 5, 9). Step 3: combine and keep only numbers with all digits distinct: 35291 ✓, 63072 ✓, 64182 ✓, 94183 ✓. Others repeat a digit (for example 93073 repeats 3; 65292 repeats 2). So four. Options (a), (c) and (d) miscount.
Tip: list the few cases for each condition, then combine and strike out repeats. "All distinct" is the condition people forget.
Answer as per the official UPSC answer key.
Consider the following statements :
- I. Capital receipts create a liability or cause a reduction in the assets of the Government.
- II. Borrowings and disinvestment are capital receipts.
- III. Interest received on loans creates a liability of the Government.
Which of the statements given above are correct?
Answer (a) & explanation
Statements I and II are correct (a). Statement I is right: a capital receipt either creates a liability, such as borrowing, or reduces an asset, such as selling shares. Statement II is right: borrowings and disinvestment are capital receipts. Statement III is wrong: interest received on loans is a revenue receipt, the government's own income, and creates no liability. Taxes and dividends are revenue receipts too. So options (b), (c) and (d) fail.
Notice the matching spending terms: capital expenditure creates assets, like roads and dams, while revenue expenditure, like salaries and interest paid, does not. The fiscal deficit equals total spending minus revenue receipts and non-debt capital receipts, basically what the government borrows.
interest "on loans" makes one think of debt. The government is receiving the interest, so it is income.
Answer as per the official UPSC answer key.
Consider the following :
- I. Cigarette butts
- II. Eyeglass lenses
- III. Car tyres
How many of them contain plastic?
Answer (c) & explanation
All three contain plastic (c). Item I is right: cigarette filters are made of cellulose acetate, a plastic, and are among the most common litter on beaches. Item II is right: most spectacle lenses are polycarbonate or other plastics, not glass. Item III is right: tyres contain synthetic rubber and polymer fibres, and tyre wear is a big source of microplastics in air and water. So options (a), (b) and (d) fail.
Notice that microplastics, pieces under 5 mm, are now found in human blood, lungs and even the placenta. India banned many single-use plastic items from July 2022. Talks on a global plastics treaty have not yet reached agreement.
Answer as per the official UPSC answer key.
Who among the following was the founder of the ‘Self-Respect Movement’?
Answer (a) & explanation
Periyar founded the Self-Respect Movement (a). E.V. Ramaswamy, known as Periyar, left the Congress over caste discrimination and started the Self-Respect Movement in Tamil Nadu in 1925. It attacked Brahmin dominance, caste and religious ritual, and backed self-respect marriages without priests. Option (b) is wrong: Ambedkar led the Mahad Satyagraha and other movements. Options (c) and (d) are wrong: Bhaskarrao Jadhav and Dinkarrao Javalkar were non-Brahmin leaders in Maharashtra.
Notice what followed: Periyar led the Vaikom Satyagraha (1924) for temple road access, and founded the Dravidar Kazhagam (1944), the parent of Tamil Nadu's Dravidian parties. He also took over the Justice Party.
Answer as per the official UPSC answer key.
A natural number N is such that it can be expressed as N = p + q + r, where p, q and r are distinct factors of N. How many numbers below 50 have this property?
Answer (c) & explanation
Eight numbers below 50 have this property (c). Step 1: if p, q, r are factors of N, write them as N/a, N/b, N/c. Then N = N/a + N/b + N/c, so 1/a + 1/b + 1/c = 1 with a, b, c different. Step 2: the only set of different whole numbers that works is 2, 3, 6 (1/2 + 1/3 + 1/6 = 1). So N = N/2 + N/3 + N/6, and N must be divisible by 6. Step 3: multiples of 6 below 50: 6, 12, 18, 24, 30, 36, 42, 48 = 8 numbers. Example: 12 = 6 + 4 + 2. Options (a), (b) and (d) miscount.
Tip: turning factors into fractions of N often reveals a neat rule. Remember 1/2 + 1/3 + 1/6 = 1.
Answer as per the official UPSC answer key.
P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?
Answer (b) & explanation
They cross 13 times (b). Step 1: walking in opposite directions on a circle, their speeds add: 5 + 3 = 8 rounds per hour. So they cross every 1/8 hour = 7.5 minutes. Step 2: crossings happen at 7.5, 15, 22.5, 30, … minutes after 5:00. The first one after 5:20 is at 22.5 minutes (the 3rd crossing). Step 3: 7:00 is 120 minutes, which is the 16th crossing. Between 5:20 and 7:00 (not counting 7:00), crossings 3 to 15 occur: 13 times. Options (a), (c) and (d) miscount the ends.
Tip: opposite directions add speeds; same direction subtracts them. Count crossings carefully at the start and end of the time window.
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 : Let P, Q, R, S be distinct non-zero digits. If PP × PQ = RRSS, where P ≤ 3 and Q ≤ 4, then what is Q equal to?
Statement I : R = 1.
Statement II : S = 2.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (d) & explanation
Q can be found without either statement (d), as per the key. Step 1: P can be 1, 2 or 3, and Q at most 4. Step 2: if P = 1 or 2, then PP × PQ is at most 22 × 24 = 528, too small for a 4-digit number RRSS. So P = 3. Step 3: try 33 × 31 = 1023, 33 × 32 = 1056, 33 × 34 = 1122 (Q cannot be 3, as digits are distinct). Only 1122 has the RRSS shape. So Q = 4, found from the question alone. The statements (R = 1, S = 2) only confirm it.
Tip: when the conditions leave very few cases, check them all before reading the statements. If the answer comes out, neither statement is needed.
Do not jump to a statement before testing the question on its own. Small limits like P ≤ 3 often settle it.
Answer as per the official UPSC answer key.
Consider the following water bodies :
- I. Lake Tanganyika
- II. Lake Tonlé Sap
- III. Patos Lagoon
Through how many of them does the equator pass?
Answer (d) & explanation
The equator passes through none of them (d). Item I is wrong: Lake Tanganyika lies in the Rift Valley a few degrees south of the equator. Item II is wrong: Tonlé Sap is in Cambodia, at about 12°N. Item III is wrong: Patos Lagoon is in southern Brazil, near 31°S. The equator crosses Lake Victoria, not Tanganyika.
Notice Tonlé Sap's oddity: its river reverses flow in the monsoon, when the swollen Mekong pushes water back into the lake. Tanganyika is the world's longest freshwater lake and second deepest, after Baikal. The equator also passes through Ecuador, Colombia, Brazil, Kenya, the DR Congo and Indonesia.
Tanganyika is close to the equator and the trap. The East African lake on the equator is Victoria.
Answer as per the official UPSC answer key.
With reference to India, consider the following pairs :
| Organization | Union Ministry
| I. The National Automotive Board | Ministry of Commerce and Industry
| II. The Coir Board | Ministry of Heavy Industries
| III. The National Centre for Trade Information | Ministry of Micro, Small and Medium Enterprises
How many of the above pairs are correctly matched?
Answer (d) & explanation
None of the pairs is correctly matched (d). UPSC has rotated the ministries one step. Pair I is wrong: the National Automotive Board is under the Ministry of Heavy Industries, not Commerce. Pair II is wrong: the Coir Board is under the Ministry of MSME, not Heavy Industries. Pair III is wrong: the National Centre for Trade Information was set up by the Commerce Ministry, not MSME. Every pair is off by one, so options (a), (b) and (c) fail.
Notice the Coir Board's base: Kochi, Kerala, the heart of India's coir industry, which uses coconut husk fibre. The Khadi and Village Industries Commission is also under MSME. Spotting a "rotation" trick helps: if one pair is swapped, check the others.
rotated pairs. If you know just two of them, the third is often the leftover answer.
Answer as per the official UPSC answer key.
Consider the following statements :
Statement I :
- In India, State Governments have no power for making rules for grant of concessions in respect of extraction of minor minerals even though such minerals are located in their territories.
Statement II :
- In India, the Central Government has the power to notify minor minerals under the relevant law.
Which one of the following is correct in respect of the above statements?
Answer (d) & explanation
Statement I is wrong, Statement II is right (d). Under the Mines and Minerals (Development and Regulation) Act, 1957, Statement II is right: the Centre decides which minerals count as "minor" (Section 3(e)). Statement I is wrong: the States make the rules for granting minor mineral concessions (Section 15), and they keep the royalty. So options (a), (b) and (c) fail.
Notice examples of minor minerals: sand, gravel, building stone, marble and brick earth. Illegal sand mining is a big problem that States must police. Major minerals, such as coal, iron ore and bauxite, are regulated mostly by the Centre. In 2024, the Supreme Court held that States can tax mineral-bearing land.
in a Statement I/II question, check each statement alone first. Only then ask whether one explains the other.
Answer as per the official UPSC answer key.
If 7 * 24 = 25 and 12 * 16 = 20, then what is 16 * 63 equal to?
Answer (c) & explanation
1. Look at the first two: 7 × 7 + 24 × 24 = 49 + 576 = 625 = 25 × 25. And 12 × 12 + 16 × 16 = 144 + 256 = 400 = 20 × 20.
2. So the rule is: square both numbers, add, and find the number whose square is the total.
3. 16 × 16 + 63 × 63 = 256 + 3969 = 4225 = 65 × 65. Answer 65.
Answer as per the official UPSC answer key.
What is the 489th digit in the number 123456789101112...?
Answer (d) & explanation
The 489th digit is 9 (d). Step 1: the numbers 1 to 9 use 9 digits. The numbers 10 to 99 use 90 × 2 = 180 digits. Total so far: 189. Step 2: 489 − 189 = 300 digits remain. Each three-digit number uses 3 digits, so that is exactly 100 numbers: 100 to 199. Step 3: the 489th digit is the last digit of 199: 9. Options (a), (b) and (c) come from miscounting the blocks.
Tip: count digits block by block: 1-digit (9), 2-digit (180), 3-digit (2700). If the leftover divides exactly, the answer is the last digit of that number.
Answer as per the official UPSC answer key.