MP Police Constable Mock Test 2 — 100 MCQs in Exam Pattern

The correct answer is Son of Gautami. The word puta in Prakrit means son. Satavahana kings took names from their mothers, so Gautamiputra means son of Gautami.

The other options reverse or change the relation. The name always points to the king’s mother.

Memory hook: Putra means son, so Gautamiputra is Gautami’s son.

Macaulay wrote that English education should create a class ‘Indian in blood and colour, but English in taste, in opinions, in morals, and in intellect.’

He was Tenzing Norgay’s nephew, and was the youngest Sherpa on Tenzing’s own 1953 Everest expedition.

Man Singh I belonged to the Kachwaha Rajput clan, rulers of Amber, near present-day Jaipur.

The International Day of Yoga is observed every year on 21 June.

The date marks when the Constituent Assembly adopted Hindi in the Devanagari script as an official language, in 1949.

Rajasthan is India’s largest state by area, covering about 342,239 square kilometres, roughly 10.4% of the country’s land.

The correct answer is Megasthenes. He was the Greek ambassador at Chandragupta’s court and wrote the Indica. His account survives only in fragments.

The correct answer is (b) an early human species.

Denisovans were an early human group. They are named after Denisova Cave in southern Siberia, where their DNA was first read from a finger bone. They are not dinosaurs, not a cave system in North-East India, and not a geological period.

This question was asked in UPSC CSP 2019, GS Paper I.

The answer is Do not do to others what you would not want done to yourself. Hillel said what is hateful to you, do not do to another. Confucius said what you do not want done to yourself, do not do to others. Why the others fail: The first is the positive form from Matthew 7:12. The third is Leviticus 19:18. The fourth describes zakat, not the Golden Rule. Memory hook: Negative form means “do not”.

The answer is Contingency Fund of India. It is an imprest, a ready float of cash. The advance is made pending authorisation by Parliament by law. Why the others fail: the Public Account holds other public moneys, and the Consolidated Fund needs prior appropriation. Memory hook: contingency means emergency.

The Mango is India’s national fruit, reflecting its cultivation across the country for thousands of years and its cultural prominence.

The answer is that it’s a real image. A plane mirror actually forms a virtual image, one that cannot be projected onto a screen.

Article 21A was inserted by the 86th Amendment. It binds the State to provide free and compulsory education to children from six to fourteen years.

Karnataka Sangeeta Pitamaha is the traditional title, meaning the grandsire of Carnatic music. It honours Purandaradasa’s association with devotional composition and the organization of elementary teaching.

The title recognizes a foundational legacy within an older tradition of music. It does not mean that no musical forms existed before his lifetime.

Sangeeta Ratnakara names a musical treatise rather than this personal honorific. The Carnatic Trinity refers to Tyagaraja, Muthuswami Dikshitar and Syama Sastri.

Review Purandaradasa’s title and legacy. Read the Carnatic music lesson to place composers and teaching within the wider system.

The answer is the Constituent Assembly adopting the Constitution, on 26 November 1949. Why the others fail: the Constitution came into force on 26 January 1950, now Republic Day. The Drafting Committee was appointed on 29 August 1947. Memory hook: 26 November adopts, 26 January starts.

The correct answer is Bhubaneswar. It is the capital of Odisha. The new capital was built there after independence. Before that, Kataka (Cuttack) was the capital of the 1936 province. Puri and Konark are famous temple towns, not capitals. Memory hook: Kataka in 1936, Bhubaneswar after independence.

It marks the day in 1928 that C.V. Raman announced his discovery of the Raman Effect.

Timur sacked Delhi in December 1398. The Sultan then was Nasir-ud-Din Mahmud Shah Tughluq. Delhi took almost a century to recover.

Nek Chand created the Rock Garden from discarded domestic and industrial materials. He began secretly in his spare time in 1957. Le Corbusier led the master plan. The Rock Garden was Nek Chand’s separate creative project.

Review Nek Chand and the Rock Garden.

1826 is the answer. The East India Company and the King of Ava signed the treaty on 24 February 1826. It ended the First Anglo-Burmese War and ended Burmese influence in Assam. Memory hook: Yandabo, 1826, Burmese war ends.

Krishnadeva Raya belonged to the Tuluva dynasty. His reign is widely considered Vijayanagara’s golden age, combining military success, strong administration, and major patronage of the arts. Read more.

Chandigarh is the shared capital of Punjab and Haryana. Chandigarh itself remains a separate Union Territory. Using a city as a capital does not place that territory inside either state.

Review Chandigarh’s shared capital and UT status.

The date marks the UN General Assembly’s 1948 adoption of the Universal Declaration of Human Rights.

Tagore won Literature in 1913. Raman won Physics in 1930. Khorana won Medicine in 1968. Sen won Economics in 1998.

India became a major outsourcing destination for IT services and business process work, leveraging English-language skills and lower wage costs.

Russia spans roughly 17 million square kilometres, spread across both Europe and Asia. This makes it nearly twice the size of the next-largest country, Canada. Despite its enormous size, much of Russia’s territory, particularly Siberia, remains sparsely populated.

The correct answer is South America, Africa, and Asia. The equator crosses these three continents on its path around the globe.

She became the first female amputee in the world to summit Mount Everest, on 21 May 2013.

Article 39A is the directive. The 1987 Act implements it.

Statement 1 says all ledgers are folders. Statement 2 says all folders are archives. Chain these using the shared term folders. Every ledger is a folder, and every folder is an archive. So every ledger must be an archive. This makes conclusion I valid. Conclusion II reverses the last statement and claims all archives are ledgers. This is illicit conversion, a classic error. All folders are archives never means all archives are folders. Archives is the larger group here, so it can hold many non-ledgers. Conclusion II does not follow. The correct answer is: only conclusion I follows.

The given set is (23, 15, 47). Reverse the digits of the first number: 23 becomes 32. Now add the second number: 32 + 15 = 47. This matches. So the rule is: reverse the first number’s digits, then add the second number, to get the third. Test (34, 12, 46): reverse of 34 is 43, and 43 + 12 = 55, not 46. This fails. Test (52, 18, 70): reverse of 52 is 25, and 25 + 18 = 43, not 70. This fails. Test (27, 30, 57): reverse of 27 is 72, and 72 + 30 = 102, not 57. This fails. Test (41, 20, 34): reverse of 41 is 14, and 14 + 20 = 34. This matches, so it works. Only (41, 20, 34) follows the rule. So the answer is (41, 20, 34).

Under this rule, − actually means +, and + actually means −. Rewrite the expression with the real operations: 40 + 12 − 8 + 5. First, 40 + 12 = 52. Next, 52 − 8 = 44. Finally, 44 + 5 = 49. So the value of the expression is 49.

The number ‘5’ shows up in both views. In View 1, ‘5’ sits next to ‘1’ and ‘4’. In View 2, ‘5’ sits next to ‘2’ and ‘3’. A cube face touches four other faces and never touches the face opposite it. So ‘5’ is next to ‘1’, ‘4’, ‘2’ and ‘3’. The one face never seen next to ‘5’ is its opposite. That face is ‘6’, so the answer is 6.

Count the days between 12 March 2025 and 5 August 2025. March contributes 19 remaining days, since 31 minus 12 equals 19. April contributes 30 days, May contributes 31, and June contributes 30. July contributes 31 days, and August contributes 5 days, up to the target date. Adding these gives 19 plus 30 plus 31 plus 30 plus 31 plus 5, which is 146 days. The year 2025 is not a leap year, and February is not in this span anyway. Divide 146 by 7. That gives 20 full weeks, with a remainder of 6 days. This remainder of 6 is the number of odd days between the two dates.

Every other term in this series doubles the one before it. Check: 5×2=10, 10×2=20, and 80×2=160. Following that rule, 20 should double to 40, not 41. So 41 is the term that breaks the pattern.

A rectangle in this grid is fixed by choosing 2 horizontal lines and 2 vertical lines. A grid with 3 rows has 4 horizontal lines, so there are C(4,2) = 6 ways to pick 2 of them. A grid with 3 columns has 4 vertical lines, so there are C(4,2) = 6 ways to pick 2 of them. Multiply these two counts together: 6 times 6 equals 36. A common mistake is counting only the 9 smallest unit cells, and missing every larger rectangle. The correct total, across every size, is 36.

Statement 1 says all shards are fragments. Statement 2 says some shards are relics. The shared term is shards. Take the shards that are relics. Since all shards are fragments, those same items are also fragments. So those items are both fragments and relics. This means some fragments are relics. This makes conclusion I valid. Conclusion II claims all relics are fragments. Only the shard-relic overlap is confirmed to be fragments. Other relics, outside that overlap, are not accounted for at all. Conclusion II is too strong and does not follow. The correct answer is: only conclusion I follows.

Substitute the real operations: ÷ becomes ×, + becomes ÷, − becomes +, and × becomes −. The expression becomes: 8 × 5 ÷ 4 + 6 − 9. Multiplication and division come first, worked left to right. 8 × 5 = 40, then 40 ÷ 4 = 10. The expression is now: 10 + 6 − 9. Working left to right, 10 + 6 = 16, then 16 − 9 = 7. So the value of the expression is 7.

The given pair is Negligence : Accident. Negligence is a harmful practice, and an accident is its resulting outcome. We need the outcome that corruption produces. Bribery is one specific form of corruption, not its outcome. Wealth and Punishment describe what may happen to the corrupt person, not the outcome for society. Corruption in a system produces injustice for everyone affected by it. So the answer is Injustice.

The hands form a right angle 22 times in every 12-hour block, not 24 times. The gap between the hands sweeps a full circle every 12/11 hours. A right angle occurs twice in each such sweep, giving 22 occurrences in 12 hours. A full 24-hour day contains exactly 2 such 12-hour blocks. Total right angles equal 22 times 2, which is 44.

Check Row 1: 9 + 5 = 14, and 9 – 5 = 4. Multiply: 14 x 4 = 56. This matches. Check Row 2: 11 + 6 = 17, and 11 – 6 = 5. Multiply: 17 x 5 = 85. This also matches. The rule is: third number = (first plus second) multiplied by (first minus second). Apply it to Row 3: 13 + 7 = 20, and 13 – 7 = 6. So the answer is 20 x 6 = 120.

Count the days between 10 February 2028 and 22 July 2028. The year 2028 divides evenly by 4 and is not a century year, so it is a leap year. February 2028 therefore has 29 days, so 19 days remain after the 10th. March contributes 31 days, April contributes 30, and May contributes 31. June contributes 30 days, and July contributes 22 days, up to the target date. Adding these gives 19 plus 31 plus 30 plus 31 plus 30 plus 22, which is 163 days. Divide 163 by 7. That gives 23 full weeks, with a remainder of 2 days. This remainder of 2 is the number of odd days between the two dates.

Six relatives sit around a circular table, facing the centre. Number the seats 1 to 6 clockwise, starting from Chandan’s seat as seat 1. Facing the centre means a person’s left hand points to the next seat clockwise, and their right hand points to the previous seat. Deepa sits directly opposite Chandan. In a 6-seat circle, opposite means 3 seats away. So Deepa sits in seat 4. Eshwar sits immediately to the left of Chandan, one seat forward from seat 1. So Eshwar sits in seat 2. Falguni sits second to the right of Chandan, two seats back from seat 1. Moving back twice from seat 1 wraps around to seat 5. So Falguni sits in seat 5. Only seats 3 and 6 are left, for Hema and Girish. Girish does not sit next to Deepa. The seats next to Deepa’s seat 4 are seat 3 and seat 5. Seat 5 is already taken, so this rule means Girish cannot be in seat 3. So Girish sits in seat 6, and Hema sits in seat 3. Every seat is filled: Chandan 1, Eshwar 2, Hema 3, Deepa 4, Falguni 5, Girish 6. The seat immediately to Falguni’s right is the one just before seat 5, seat 4. Deepa sits in seat 4. So Deepa sits immediately to the right of Falguni.

The words ‘cats’ and ‘chase’ both appear in both sentences. Compare the two code groups: ‘ho mi lo ta’ and ‘ho su mi ka’. The codes common to both groups are ‘ho’ and ‘mi’, so these two codes belong to ‘cats’ and ‘chase’. The remaining codes in the first sentence, ‘lo’ and ‘ta’, must belong to the words that are not shared, which are ‘small’ and ‘mice’. So the answer is lo, ta.

The cube’s six faces show Circle, Square, Triangle, Diamond, Cross and Arrow. In View 1, Circle sits with Square and Triangle, so Circle is adjacent to both. In View 2, Circle sits with Cross and Arrow, so Circle is adjacent to both as well. Circle is now adjacent to four faces: Square, Triangle, Cross and Arrow. So Circle’s opposite must be Diamond. In View 1, Square sits with Circle and Triangle, so Square is adjacent to both. In View 3, Square sits with Diamond and Arrow, so Square is adjacent to both as well. Square is now adjacent to four faces: Circle, Triangle, Diamond and Arrow. So Square’s opposite must be Cross. Two opposite pairs are now fixed: Circle-Diamond, and Square-Cross. Only Triangle and Arrow remain unpaired. Since every face has exactly one opposite, Triangle and Arrow must be opposite each other. The symbol opposite Triangle is Arrow.

Statement 1 says all beams are frames. Statement 2 says all beams are panels. Here ‘beams’ is the shared term, and it is the subject in both statements. Every beam sits inside both frames and panels at the same time. Beams form a real, non-empty group, so frames and panels must overlap through it. So some frames are panels. This makes conclusion I valid. It is tempting to assume no conclusion is possible here, since beams is shared as a subject, not a predicate. That assumption is wrong in this exact case. Conclusion II claims all frames are panels, which is far too strong and unsupported. Many frames could exist outside the beam overlap. The correct answer is: only conclusion I follows.

The given set is (3, 4, 55). Cube the second number: 4 x 4 x 4 = 64. Now square the first number: 3 x 3 = 9. Subtract: 64 – 9 = 55. This matches. So the rule is: third number = (second cubed) minus (first squared). Test (4, 3, 13): 3 cubed is 27, and 4 squared is 16, so 27 – 16 = 11, not 13. This fails. Test (5, 6, 190): 6 cubed is 216, and 5 squared is 25, so 216 – 25 = 191, not 190. This fails. Test (1, 3, 27): 3 cubed is 27, and 1 squared is 1, so 27 – 1 = 26, not 27. This fails. Test (2, 5, 121): 5 cubed is 125, and 2 squared is 4, so 125 – 4 = 121. This matches, so it works. Only (2, 5, 121) follows the rule. So the answer is (2, 5, 121).

Sarita is the mother of Meenal, so Meenal is Sarita’s daughter. Meenal is married to Harish, and they have a daughter together. Meenal is the mother of Divya, so Divya is Meenal’s daughter. This makes Sarita the mother of Divya’s own mother. A mother’s mother is called a grandmother. So Sarita is related to Divya as her grandmother.

This sequence follows how a tree becomes a printed book. A tree is cut down, and its wood is the raw material. The wood is broken down chemically into wood pulp. The wood pulp is pressed and dried into sheets of paper. The paper is finally printed and bound into a book. So the order is Tree, Wood Pulp, Paper, Book, matching option A.

Five friends sit around a circular table, facing the centre. Number the seats 1 to 5 clockwise, starting from Ishwar’s seat as seat 1. Facing the centre means a person’s left hand points to the next seat clockwise, and their right hand points to the previous seat. Leela sits immediately to the left of Ishwar, one seat forward from seat 1. So Leela sits in seat 2. Kunal sits immediately to the right of Ishwar, one seat back from seat 1. Moving back once from seat 1 wraps around to seat 5. So Kunal sits in seat 5. Jaya sits second to the right of Ishwar, two seats back from seat 1. Moving back twice from seat 1 lands on seat 4. So Jaya sits in seat 4. Only seat 3 is left, so Manoj sits in seat 3. This also matches the last clue: Manoj sits immediately to the right of Jaya, landing on seat 3. Every seat is filled: Ishwar 1, Leela 2, Manoj 3, Jaya 4, Kunal 5. The seat immediately to Manoj’s left is the next seat clockwise from seat 3, seat 4. Jaya sits in seat 4. So Jaya sits immediately to the left of Manoj.

Nidhi is the wife of Amit, so Nidhi and Amit are married. Kunal is the brother of Nidhi, so Kunal and Nidhi are siblings. Kunal being the son of Prakash confirms Kunal’s own father. Amit’s father, Suresh, does not change this relationship. Kunal is the brother of Amit’s wife. A wife’s brother is called a brother-in-law. So Kunal is related to Amit as his brother-in-law.

Pooja’s rank from the left is 13. Her rank from the right is 25. Total = rank from left + rank from right − 1. Total = 13 + 25 − 1 = 37. So there are 37 contestants in the row.

A letter has the same water image only if it is symmetric top to bottom. The standard list is C, D, E, H, I, K, O, and X. The word ‘CHICKEN’ has 7 letters. Checking each one against that list gives a match every time it appears: C, H, I, C, K, E. That is 6 matching letters in total, so the answer is 6.

A letter has the same mirror image only if it is symmetric left to right. The standard list is A, H, I, M, O, T, U, V, W, X, and Y. The word ‘MOUNTAIN’ has 8 letters. Checking each one against that list gives a match every time it appears: M, O, U, T, A, I. That is 6 matching letters in total, so the answer is 6.

The given set is (4, 7, 14). Multiply the first two numbers: 4 x 7 = 28. Now halve that product: 28 / 2 = 14. This matches. So the rule is: third number = (first x second) divided by 2. Test (6, 5, 15): 6 x 5 = 30, and 30 / 2 = 15. This matches, so it works. Test (8, 3, 13): 8 x 3 = 24, and 24 / 2 = 12, not 13. This fails. Test (9, 4, 17): 9 x 4 = 36, and 36 / 2 = 18, not 17. This fails. Test (10, 3, 14): 10 x 3 = 30, and 30 / 2 = 15, not 14. This fails. Only (6, 5, 15) follows the rule. So the answer is (6, 5, 15).

Look at Row 1. Multiply the first number by 3: 10 x 3 = 30. Multiply the second number by 2: 4 x 2 = 8. Subtract: 30 – 8 = 22. This matches. The rule is: third number = (3 x first) – (2 x second). Apply it to Row 2: 9 x 3 = 27, and 5 x 2 = 10. So the answer is 27 – 10 = 17.

First convert Yash’s rank to a front-based rank. Rank from front = total − rank from back + 1 = 48 − 17 + 1 = 32. So Yash is 32nd from the front. Omkar walks 9 ranks behind Yash, so his rank is larger by 9. Omkar’s rank from the front = 32 + 9 = 41.

Statement 1 says all coils are conductors. Statement 2 says all coils are components. Here ‘coils’ is the shared term, and it is the subject in both statements. Every coil sits inside both conductors and components at once. Coils form a real, non-empty group, so this overlap between conductors and components must exist. So some conductors are components. This makes conclusion I valid. Conclusion II claims all conductors are components. Nothing tells us about conductors outside the coil group. Many conductors could exist that are not components at all. Conclusion II is too strong and does not follow. The correct answer is: only conclusion I follows.

Vinod is the father of Ashish, so Ashish is Vinod’s son. Vinod is the brother of Subhash, so they share the same parents. Subhash is the father of Reema, so Reema is Subhash’s daughter. Ashish’s father and Reema’s father are brothers. Children of two brothers are cousins to each other. So Ashish is related to Reema as her cousin.

The Venn diagram shows how many people like Chess, Carrom, and Badminton. Only Chess: 14. Only Carrom: 12. Only Badminton: 16. Chess and Carrom only: 6. Carrom and Badminton only: 5. Chess and Badminton only: 7. All three: 3. Add the three only-one regions, and leave out every overlap region. So the answer is 42.

The given set is (3, 6, 12). Multiply the first two numbers: 3 x 6 = 18. Now subtract 6: 18 – 6 = 12. This matches. So the rule is: third number = (first x second) – 6. Test (4, 5, 16): 4 x 5 = 20, and 20 – 6 = 14, not 16. This fails. Test (5, 4, 14): 5 x 4 = 20, and 20 – 6 = 14. This matches, so it works. Test (6, 3, 20): 6 x 3 = 18, and 18 – 6 = 12, not 20. This fails. Test (7, 2, 10): 7 x 2 = 14, and 14 – 6 = 8, not 10. This fails. Only (5, 4, 14) follows the rule. So the answer is (5, 4, 14).

A rectangle in this grid is fixed by choosing 2 horizontal lines and 2 vertical lines. A grid with 3 rows has 4 horizontal lines, so there are C(4,2) = 6 ways to pick 2 of them. A grid with 5 columns has 6 vertical lines, so there are C(6,2) = 15 ways to pick 2 of them. Multiply these two counts together: 6 times 15 equals 90. A common mistake is counting only the 15 smallest unit cells, and missing every larger rectangle. The correct total, across every size, is 90.

Statement 1 says all lanterns are beacons. Statement 2 says no signals are beacons. The shared term is beacons. Lanterns sit fully inside beacons, and signals never touch beacons at all. So signals can never touch lanterns either. This means no lanterns are signals. This makes conclusion I valid. A statement saying no X are Y always converts safely to no Y are X. So no lanterns are signals also means no signals are lanterns. This makes conclusion II valid too. Both conclusions follow from the statements. The correct answer is: both conclusions I and II follow.

Tea-only is 25-7=18, coffee-only is 23-7=16, so ‘one but not both’ totals 34. The union is 25+23-7=41, so ‘neither’ is 58-41=17. The ratio 34:17 simplifies to 2:1.

This sequence follows how an online order reaches a customer. A customer first places the order on a website. The seller then packs the item securely for transport. The packed item is shipped out through a courier service. The shipment finally reaches the customer, marked as delivered. So the order is Order Placed, Packed, Shipped, Delivered, matching option D.

The given pair is 20 : 4. Check the rule: 20 divided by 5 = 4, which matches. So the rule is: divide the first number by 5 to get the second. Apply the same rule to 45: 45 divided by 5 = 9. So the answer is 9.

The given set is (6, 7, 13). Add the first two numbers: 6 + 7 = 13. This matches. So the rule is: third number = first number plus second number. Test (10, 5, 16): 10 + 5 = 15, not 16. This fails. Test (12, 9, 20): 12 + 9 = 21, not 20. This fails. Test (14, 3, 18): 14 + 3 = 17, not 18. This fails. Test (9, 8, 17): 9 + 8 = 17. This matches, so it works. Only (9, 8, 17) follows the rule. So the answer is (9, 8, 17).

In BAT, the shift grows with each position: the 1st letter shifts by 1, the 2nd by 2, the 3rd by 3. B+1=C, A+2=C, T+3=W, giving CCW, which matches. So the rule is: shift the nth letter forward by n places. Apply the same rule to PEN: P+1=Q, E+2=G, N+3=Q. So the answer is QGQ.

Six friends sit around a circular table, and everyone faces away from the centre, outward. Number the seats 1 to 6 clockwise, starting from Neelam’s seat as seat 1. Facing outward flips the usual rule: a person’s right hand now points to the next seat clockwise. Their left hand points to the previous seat, going clockwise. Parul sits second to the right of Neelam, two seats forward from seat 1. So Parul sits in seat 3. Raghav sits immediately to the left of Neelam, one seat back from seat 1. Moving back once from seat 1 wraps around to seat 6. So Raghav sits in seat 6. Suman sits directly opposite Neelam. In a 6-seat circle, opposite means 3 seats away. So Suman sits in seat 4. Only seats 2 and 5 are left, for Urvashi and Tejas. Tejas does not sit next to Neelam. The seats next to Neelam’s seat 1 are seat 6 and seat 2. Seat 6 is already taken, so this rule means Tejas cannot be in seat 2. So Tejas sits in seat 5, and Urvashi sits in seat 2. Every seat is filled: Neelam 1, Urvashi 2, Parul 3, Suman 4, Tejas 5, Raghav 6. Opposite Tejas’s seat 5, three seats away, is seat 2. Urvashi sits in seat 2. So Urvashi sits directly opposite Tejas.

The typical human audible range spans roughly 20 Hz to 20,000 Hz. Sounds outside this range exist but go unheard by human ears.

Heat transfers by only three fundamental methods: conduction, convection, and radiation. Evaporation, revolution, and thermal expansion are separate physical phenomena, not heat-transfer mechanisms themselves.

Acceleration equals force divided by mass: 6 N ÷ 3 kg = 2 m/s².

Ethylene glycol dissolves readily in water and substantially lowers its freezing point, protecting car radiators from freezing in cold weather.

The sound travels to the wall and back in 0.3 s, so one-way distance = (340 × 0.3) ÷ 2 = 51 metres.

Species forms the fundamental, most specific unit around which the entire taxonomic hierarchy is built.

Pitch, how high or low a sound seems, depends mainly on the frequency of the sound wave. Higher frequency generally means higher perceived pitch.

A phone charger reduces mains AC voltage down to a much lower level, suitable for charging a phone’s battery, making its core function that of a step-down transformer.

Ethylene glycol is added mainly for its freezing-point-depression effect, keeping the radiator’s water from freezing solid in cold weather.

The desert-adapted kangaroo rat excretes highly concentrated urine to minimise water loss in its arid habitat.

Heating gypsum drives off part of its water content, converting it into the hemihydrate known as Plaster of Paris.

The upward force experienced by a body placed in a fluid is called upthrust, or buoyant force.

A transformer uses mutual induction between two coils to step AC voltage up or down, without changing the underlying frequency.

The stomach secretes hydrochloric acid, which helps digest food and creates a strongly acidic environment that kills many ingested pathogens.

Centrifugation spins a liquid at high speed, using centrifugal force to rapidly separate out suspended particles by density.

Let length = L = 12 m and breadth = B = 6 m. Area of a rectangle = L x B. So area = 12 x 6 = 72 sq m.

Let radius = R = 105 cm, and take pi = 22/7. Circumference of a circle = 2 x pi x R. So circumference = 2 x (22/7) x 105 = 660 cm.

Let downstream speed = 34 km/hr and upstream speed = 2 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Subtracting the upstream equation from the downstream one cancels B: (B+S) – (B-S) = 2S. So 34 – 2 = 2S, which gives 2S = 32. S = 32/2 = 16 km/hr. Check: 2 (upstream) + 32 (twice the stream speed) = 34, matching the downstream speed 34.

Let N = 144400. We need a whole number r such that r x r = N. Since 380 x 380 = 144400, r = 380 satisfies this exactly. So the square root of 144400 is 380. This confirms 380 is the correct square root.

Let base = b = 40 cm and height = h = 17 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 40 x 17 = 340 sq cm.

This is the zero-product property: if two numbers multiply to give 0, at least one of them must itself be 0 (since any nonzero number times another nonzero number is always nonzero). It does not require BOTH to be zero — for example, a=0, b=5 gives ab=0 with only a zero. So the correct conclusion is a=0, or b=0, or both.

Let area = A = 1089 sq m. Side of a square = sqrt(A). So side = sqrt(1089) = 33 m. Check: 33 x 33 = 1089 sq m, which matches A.

Let train length L = 875 m and train speed = 126 km/hr. Convert speed to m/sec: 126 x 5/18 = 35 m/sec. To pass a stationary man, the train only needs to cover its own length. So distance to cover = L = 875 m. Time = distance / speed = 875/35 = 25 seconds. Check: 35 m/sec x 25 sec = 875 m, which matches L.

Let length = L = 24 m, breadth = B = 20 m, rate = Rs 80 per sq m. Area of the room = L x B = 24 x 20 = 480 sq m. Cost of flooring = area x rate = 480 x 80 = Rs 38400.

Let Principal P = Rs 4500, Rate R = 6% per annum, Time T = 8 years. Simple interest formula: S.I. = (P x R x T)/100. P x R x T = 4500 x 6 x 8 = 216000. S.I. = 216000/100 = Rs 2160. Check: Amount = P + S.I. = 4500 + 2160 = Rs 6660.

Let boat speed in still water = B = 7 km/hr. Let stream speed = S = 3 km/hr. Downstream speed = B + S, because the current pushes the boat forward. So downstream speed = 7 + 3 = 10 km/hr. Upstream speed = B – S, because the current pushes against the boat. So upstream speed = 7 – 3 = 4 km/hr. The boat’s speed downstream is 10 km/hr.

Let length = L = 43 m, breadth = B = 7 m, rate = Rs 12 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (43+7) = 100 m. Cost of fencing = perimeter x rate = 100 x 12 = Rs 1200.

Let base = b = 37 cm and height = h = 17 cm. Area of a parallelogram = b x h. So area = 37 x 17 = 629 sq cm.

Let Principal P = Rs 17500, Rate R = 15% per annum, Time T = 6 years. Simple interest formula: S.I. = (P x R x T)/100. P x R x T = 17500 x 15 x 6 = 1575000. S.I. = 1575000/100 = Rs 15750. Check: Amount = P + S.I. = 17500 + 15750 = Rs 33250.

Let downstream speed = 37 km/hr and upstream speed = 29 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 37 + 29 = 2B, which gives 2B = 66. B = 66/2 = 33 km/hr. Check: this places B exactly halfway between the downstream speed 37 and the upstream speed 29.