UPSC Prelims — CSAT Paper II Mock (Free, Timed)

Question 1Governance

Passage: Decentralisation is often praised as a cure for distant, unresponsive government. Yet bringing power closer to people does not automatically make it more accountable. When local bodies lack independent revenue, they remain financially tethered to higher tiers and merely implement decisions taken elsewhere. Accountability requires not just proximity but the genuine authority to raise funds, set priorities and bear the consequences of failure. Where these conditions are absent, decentralisation can become an elaborate exercise that shifts blame downward while keeping real control upward. Q. Which one of the following best reflects the central idea of the passage?

Solution: The passage states accountability 'requires not just proximity but the genuine authority to raise funds, set priorities and bear the consequences,' making the key correct. The 'always improves' option is contradicted by 'does not automatically.' The 'never depend on higher tiers' option is too extreme; the passage notes dependence weakens accountability but never demands zero dependence. The 'distant government is more efficient' option is unstated.

Question 2Environment

Passage: Restoring a degraded forest is rarely as simple as planting trees. A monoculture plantation may green a satellite image, but it supports a fraction of the species a natural forest holds and is more vulnerable to a single pest. True restoration mimics the original mix of plants, the layered canopy and the soil life that took centuries to develop. It is slower, costlier and less photogenic, which is precisely why it is so often skipped in favour of quick planting drives that count seedlings rather than measure ecological recovery. Q. What does the passage imply about large tree-planting drives?

Solution: The passage contrasts monoculture drives that 'green a satellite image' and 'count seedlings' with true restoration that measures ecological recovery, implying appearance without substance, so the key is correct. The 'most reliable' option is contradicted. The 'illegal' option is unstated. The 'cost more than natural restoration' option reverses the passage, which calls true restoration 'costlier.'

Question 3Economy

Passage: A rising stock market is frequently treated as proof that an economy is thriving. But share prices reflect the expected future profits of listed companies, not the daily reality of most households. In economies where ownership of shares is concentrated among a small wealthy minority, a booming market can coexist with stagnant wages, rising joblessness and falling consumption. Mistaking the index for the economy can lead policymakers to celebrate while the broader population sees no improvement in its circumstances. Q. Which one of the following is the most logical inference from the passage?

Solution: The passage says a booming market 'can coexist with stagnant wages, rising joblessness,' so the key follows. The 'useless' option is too extreme; the passage critiques misreading, not the index entirely. The 'wages always fall' option overstates 'can coexist' into an always-relationship. The 'guarantees growth' option is unstated and contrary to the passage's concern.

Question 4Ethics

Passage: We tend to admire people who follow rules and condemn those who break them. Yet history is full of moments when breaking an unjust rule was the more ethical act. Obedience is a virtue only when the thing obeyed is itself just; otherwise it becomes a way of escaping personal responsibility by pointing to orders. The moral worth of an action lies not in whether a rule was followed, but in the judgement the person exercised about whether that rule deserved to be followed. Q. Which statement best reflects the author's view?

Solution: The author states 'obedience is a virtue only when the thing obeyed is itself just,' giving the key. The 'broken whenever convenient' option is far more extreme than the passage, which speaks of unjust rules specifically. The 'always the safest choice' and 'no place for judgement' options are directly contradicted, since the author elevates personal judgement over rule-following.

Question 5Science

Passage: A scientific theory earns trust not by being proven true forever, but by surviving repeated attempts to prove it false. Each failed attempt to refute a theory strengthens our confidence in it, yet leaves open the possibility that some future test will overturn it. This is why scientists speak of theories as the best current explanation rather than final truth. The willingness to be wrong is not a weakness of science but the very mechanism that allows it to correct itself over time. Q. What can be concluded from the passage?

Solution: The passage says trust comes from 'surviving repeated attempts to prove it false' while leaving open the possibility of being overturned, so the key is correct. The 'never change' option contradicts 'rather than final truth.' The 'avoids testing' option reverses the passage. The 'never tested is strongest' option is the opposite of the testing-based credibility described.

Question 6Society

Passage: Cities promise anonymity, and for many that is their attraction. You can reinvent yourself among strangers who carry no memory of who you used to be. But anonymity has a price. The same crowd that frees you from judgement also frees others from any sense of obligation toward you. In a village, a person who collapses on the road is known; in a vast city, they are simply one more body that others step around. The freedom of the city and its indifference are two faces of the same coin. Q. Which one of the following best captures the main idea of the passage?

Solution: The closing line calls freedom and indifference 'two faces of the same coin,' making the key correct. The 'villages always kinder' option overgeneralises beyond the single example. The 'inherently cruel' option attributes cruelty of character, but the passage speaks of structural indifference. The 'no drawbacks' option contradicts the stated 'price' of anonymity.

Question 7Governance

Passage: Transparency laws are designed to let citizens see how decisions are made, on the assumption that visibility breeds honesty. But officials who know every record may be requested can simply stop creating records. Verbal instructions replace written orders, meetings go undocumented, and the trail that transparency was meant to expose quietly disappears. A right to information is only as strong as the information that actually exists. Without a parallel duty to record decisions properly, transparency can hollow out the very thing it seeks to reveal. Q. Which one of the following is an assumption underlying the author's argument?

Solution: The argument that transparency 'is only as strong as the information that actually exists' rests on the assumption that documentation must exist, giving the key. The 'never misuse' and 'incapable of honesty' options are unrelated extremes. The 'always corrupt' option overstates; the passage notes verbal instructions evade trails, not that they are inherently corrupt.

Question 8Economy

Passage: Subsidies meant to help the poor often leak to those who need them least. A cheap fuel intended for a struggling household is just as cheap for a wealthy one, and the wealthy typically consume more of it. Universal price subsidies therefore spend the largest share of public money on the people with the largest capacity to pay. Targeted transfers, though harder to administer and more open to errors of exclusion, at least direct support toward those for whom it was designed. Q. What does the passage imply about universal price subsidies?

Solution: The passage states the wealthy 'consume more' and thus universal subsidies spend most money on 'people with the largest capacity to pay,' so the key is correct. The 'fairest' option is contradicted by the leakage argument. The 'cheaper to administer and reach poor better' option conflates ideas; admin ease is not claimed to improve targeting. The 'never reach' option is too absolute.

Question 9Technology

Passage: Recommendation algorithms learn what holds our attention and feed us more of it. Over time, this narrows what we see rather than broadening it, because the content most likely to keep us engaged is often that which confirms what we already believe. The result is not a marketplace of ideas but a hall of mirrors, where each user is shown a reflection of their own preferences. The technology is not malicious; it is simply optimising for engagement, indifferent to whether that engagement leaves us better informed. Q. Which one of the following is the most logical inference from the passage?

Solution: The passage says engagement-optimisation 'narrows what we see' and is 'indifferent to whether that engagement leaves us better informed,' so the key follows. The 'deliberately designed to misinform' option is contradicted by 'not malicious.' The 'seek out challenging content' option reverses the confirmation tendency. The 'more broadly informed' option is the opposite of 'narrows what we see.'

Question 10Environment

Passage: Water scarcity is often described as a problem of supply, prompting calls for more dams and deeper wells. But in many regions the deeper trouble is how water is used once it arrives. Crops unsuited to dry climates are grown because the water to sustain them is free or heavily subsidised, while leaking pipes lose a large share before it reaches any tap. Adding supply to a system that wastes what it already has is like pouring water into a bucket riddled with holes. Q. Which one of the following best reflects the author's view?

Solution: The author argues the 'deeper trouble is how water is used' and likens adding supply to filling a leaky bucket, supporting the key. The 'more dams only' option is contradicted. The 'natural phenomenon' option is unstated; the passage stresses human choices. The 'benefits poorest farmers' option is not addressed and contrary to the critique of wasteful subsidies.

Question 11Education

Passage: Examinations were introduced to make selection fair, replacing patronage with measurable merit. Over time, however, the test can quietly become the goal itself. Students learn to produce the answers an exam rewards rather than to understand the subject, and teachers narrow their lessons to what will be assessed. The instrument designed to measure learning begins to distort it. When a measure becomes a target, it often ceases to be a good measure, and an exam meant to reveal ability ends up shaping students to fit the exam. Q. What can be concluded from the passage?

Solution: The passage states the exam 'begins to distort' learning and 'ceases to be a good measure' when it becomes the goal, giving the key. The 'abolished entirely' option is too extreme; the author critiques distortion, not exams as such. The 'patronage fairer' option reverses the passage's praise of merit over patronage. The 'deliberately sabotage' option imputes intent not stated.

Question 12Ethics

Passage: Charity feels good to give and is easy to praise, but it can also conceal the conditions that make it necessary. When a community relies on donations to survive, attention shifts from why it is poor to how generous the donors are. The giver is celebrated; the structures that produce need remain unexamined. This is not an argument against helping people in distress, but a caution that relief, however kind, is not the same as justice, and may even delay it. Q. Which one of the following best captures the central idea of the passage?

Solution: The passage explicitly says it is 'not an argument against helping' but warns relief 'is not the same as justice, and may even delay it,' so the key is correct. The 'never given' option is contradicted. The 'donors create poverty' option is unstated. The 'identical' option is the very distinction the passage draws.

Question 13Governance

Passage: A law that is perfectly drafted but rarely enforced sends a peculiar message. It signals that the state disapproves of an act in principle while tolerating it in practice. Citizens learn to read not the words of the statute but the behaviour of the authorities, and they calibrate their own conduct accordingly. Selective enforcement can be worse than no law at all, because it grants officials the discretion to punish some while ignoring others, turning the law into an instrument of arbitrary power rather than equal treatment. Q. Which one of the following is the most logical inference from the passage?

Solution: The passage says selective enforcement 'grants officials the discretion to punish some while ignoring others,' turning law into 'arbitrary power,' supporting the key. The 'guarantee fair outcomes' option is contradicted by the gap between drafting and enforcement. The 'always obey' option reverses 'calibrate their own conduct.' The 'removing all laws' option is an unstated extreme.

Question 14Science

Passage: When a new disease emerges, the first instinct is to demand certainty before acting. But waiting for complete data can itself be a decision, one that allows the threat to spread while evidence accumulates. Public health often requires acting on incomplete information, accepting that some early measures may later prove unnecessary. The cost of overreacting to a false alarm is usually smaller and more reversible than the cost of underreacting to a real one. Caution, in such moments, can be the riskier path. Q. What does the passage imply about decision-making during an emerging disease?

Solution: The passage argues public health 'often requires acting on incomplete information' and that caution 'can be the riskier path,' so the key is correct. The 'delayed until certainty' option is contradicted. The 'overreaction always costlier' option reverses the stated comparison. The 'no evidence at all' option overstates; the passage assumes evidence accumulates, just not waiting for completeness.

Question 15Economy

Passage: Automation is often discussed as if machines simply destroy jobs. The reality is more tangled. Machines tend to take over specific tasks rather than whole occupations, and in doing so they change what a job involves rather than eliminating it outright. A role may shed its routine parts while gaining new responsibilities that require judgement a machine cannot supply. Whether workers benefit depends less on the technology itself than on whether they are given the chance and the training to move toward the tasks that remain valuably human. Q. Which statement best reflects the author's view?

Solution: The author says machines 'take over specific tasks rather than whole occupations' and outcomes depend on 'the chance and the training,' giving the key. The 'eliminates most occupations' option overstates the destroy-jobs claim the passage corrects. The 'technology alone' option is contradicted by 'depends less on the technology itself.' The 'all human judgement' option contradicts 'judgement a machine cannot supply.'

Question 16Society

Passage: We often assume that giving people more choices makes them freer and happier. Yet beyond a certain point, an abundance of options can become paralysing. Each additional choice demands comparison, raises the fear of choosing wrongly, and breeds regret about the paths not taken. A person facing dozens of nearly identical products may end up less satisfied than one who simply picked from a handful. Freedom, it turns out, is not the same as an unlimited menu; sometimes it lies in having enough good options, not endless ones. Q. What can be concluded from the passage?

Solution: The passage says abundance 'can become paralysing' and leave a person 'less satisfied,' supporting the key. The 'always greater happiness' option is directly contradicted. The 'no choices' option is an extreme the passage rejects ('enough good options'). The 'all identical' option misreads 'nearly identical,' which is an example, not a universal claim.

Question 17Environment

Passage: Recycling is widely treated as the citizen's main answer to waste, yet it sits last among the choices that actually matter. Reducing what we consume and reusing what we own prevent waste before it forms; recycling only manages what already exists, often imperfectly and at real energy cost. By framing recycling as the responsible act, the burden quietly moves from producers who design disposable goods to consumers who must sort the aftermath. The bin becomes a comfort that lets the deeper problem continue undisturbed. Q. Which one of the following best reflects the author's view?

Solution: The author ranks recycling 'last,' calls reduce and reuse better, and notes the burden 'moves from producers... to consumers,' so the key is correct. The 'most effective' option is contradicted. The 'consumers alone' option inverts the passage, which faults producers' designs. The 'producers no role' option contradicts the criticism of producers of 'disposable goods.'

Question 18Governance

Passage: Performance targets can sharpen the focus of a public service, but they also teach institutions to game the number. If hospitals are judged by waiting times, patients may be reclassified or shuffled to make the figures look better without anyone being treated faster. The target captures one slice of reality and turns it into the whole picture, while the parts it does not measure are quietly neglected. What gets measured gets managed; what does not get measured tends to get ignored, however important it may be. Q. Which one of the following is an assumption in the passage?

Solution: The argument rests on the assumption that institutions respond to what is measured, captured in 'what gets measured gets managed,' giving the key. The 'cannot be improved' option is contradicted by 'can sharpen the focus.' The 'unimportant' option misreads the example; waiting times matter, which is why gaming them is harmful. The 'all hospitals falsify' option overgeneralises 'may be reclassified.'

Question 19Technology

Passage: The promise of paperless offices was that digital files would be cheaper, searchable and instantly shareable. Much of that came true, yet paper consumption in many offices actually rose for years afterward. The ease of printing meant people printed more, not less; a document that once required a trip to a copier could now be produced at a desk with a click. Convenience, it turned out, did not reduce demand but multiplied it. A technology that makes an activity easier often increases how much of it we do. Q. Which one of the following is the most logical inference from the passage?

Solution: The passage concludes that easier activity 'often increases how much of it we do,' supporting the key. The 'failed to become searchable' option is contradicted by 'much of that came true.' The 'eliminated printing' option is false; paper use rose. The 'print less' option reverses the central observation that convenience multiplied demand.

Question 20Ethics

Passage: Loyalty is celebrated as a virtue, yet it can quietly corrode judgement. To be loyal is to favour a particular person or group, and that favour can blind us to their faults and to the harm they cause others. The loyal employee who covers for a dishonest colleague, the citizen who excuses a leader's abuses because of shared identity, both mistake a feeling of belonging for a moral compass. Loyalty without limits is not nobility; it is the surrender of conscience to attachment. Q. Which statement best reflects the author's view?

Solution: The author warns 'loyalty without limits... is the surrender of conscience to attachment,' supporting the key. The 'always noble' option is contradicted by the whole critique. The 'no attachment' option is an extreme not implied; the passage faults limitless loyalty, not all attachment. The 'same thing' option is the opposite of the passage, which distinguishes the two.

Question 21Economy

Passage: A country rich in a single valuable resource often grows poorer in unexpected ways. The wealth from oil or minerals can flood in so easily that other industries wither, unable to compete for workers and investment. Currencies strengthen, exports of everything else become costlier abroad, and the economy grows lopsided and fragile. When the resource price eventually falls, there is little else to fall back on. Abundance, paradoxically, can leave a nation more exposed than scarcity would have. Q. What does the passage imply about resource-rich economies?

Solution: The passage describes other industries withering and the economy growing 'lopsided and fragile,' leaving the nation 'more exposed,' so the key is correct. The 'guarantees prosperity' option is contradicted by the paradox. The 'falling prices benefit' option reverses 'little else to fall back on.' The 'never develop' option is unstated and contrary to the implied contrast with scarcity.

Question 22Society

Passage: Nostalgia paints the past in warm, flattering colours. We remember the songs and the gatherings, not the diseases that killed children or the rigid hierarchies that confined people to their place at birth. This selective memory is comforting, but it can be politically dangerous when it fuels demands to return to a golden age that never quite existed. The remembered past is an edited version, and policies built on that edited memory risk recreating the hardships the editing left out. Q. Which one of the following best captures the central idea of the passage?

Solution: The passage calls the remembered past 'an edited version' that can be 'politically dangerous' when guiding policy, supporting the key. The 'better in every way' option is exactly the illusion the passage critiques. The 'no useful purpose' option is too sweeping; the passage critiques selective memory, not all memory. The 'eliminated all hierarchies' option is unstated.

Question 23Science

Passage: Correlation tempts us toward stories of cause. When two things rise together, the mind reaches for a link, and often invents one. Ice cream sales and drowning deaths climb in the same months, yet neither causes the other; both follow the heat of summer. Many confident claims about what causes what are really observations of things that happen to move together, with a hidden third factor pulling the strings. Mistaking company for causation is among the most common and costly errors in reasoning. Q. What can be concluded from the passage?

Solution: The passage explains that ice cream and drowning 'both follow the heat of summer,' a 'hidden third factor,' supporting the key. The 'must cause each other' option is the very error warned against. The 'ice cream causes drowning' option is the absurd causal story the passage refutes. The 'never coexist' option overstates; the passage says correlation need not mean causation, not that the two cannot coexist.

Question 24Governance

Passage: Emergency powers are granted on the understanding that they are temporary, to be surrendered once the crisis passes. History suggests otherwise. Powers seized in a moment of danger tend to outlive the danger, because those who hold them rarely volunteer to give them up, and a frightened public is slow to demand their return. Each emergency leaves behind a residue of expanded authority that becomes the new normal, so that the state grows steadily more powerful one crisis at a time, never quite shrinking back. Q. Which one of the following is the most logical inference from the passage?

Solution: The passage says such powers 'tend to outlive the danger' and leave 'a residue of expanded authority that becomes the new normal,' so the key is correct. The 'relinquished promptly' option is contradicted by 'rarely volunteer to give them up.' The 'no effect' option reverses the central claim. The 'always demands return' option contradicts 'a frightened public is slow to demand their return.'

Question 25Health

Passage: A medicine that works on average may still fail the individual in front of you. Clinical trials report what happens to large groups, smoothing over the variation between one body and another. A drug that helps most people can harm a minority, and an average benefit can hide a wide spread of outcomes. Treating each patient as the statistical average is convenient but imperfect; good medicine reads the trial as a guide to probabilities, not as a guarantee about the particular person being treated. Q. Which statement best reflects the author's view?

Solution: The author says trials should be read 'as a guide to probabilities, not as a guarantee about the particular person,' supporting the key. The 'useless' and 'ignore entirely' options overstate; the passage values trials as guides. The 'helps every patient equally' option is contradicted by 'can harm a minority' and 'wide spread of outcomes.'

Question 26Society

Passage: Trust is often described as something earned slowly and lost quickly, but its deeper value lies in what it spares us. A society with high trust spends less on locks, contracts, audits and the endless verification that suspicion demands. People cooperate on a handshake, strangers extend credit, and energy that would go into guarding against betrayal flows instead into productive work. Where trust collapses, every transaction grows heavier with precaution, and the hidden tax of distrust quietly drags on everything a community tries to achieve. Q. What can be concluded from the passage?

Solution: The passage states high-trust societies 'spend less on locks, contracts, audits' and energy 'flows instead into productive work,' supporting the key. The 'no measurable effect' option is contradicted by the 'hidden tax of distrust.' The 'unnecessary in all societies' option overstates; the passage says less, not none. The 'distrust improves efficiency' option reverses 'every transaction grows heavier with precaution.'

Question 27Blood Relations

Pointing to a photograph, Ravi said, "She is the daughter of the only son of my grandmother." Assuming Ravi's father is that only son, how is the woman in the photograph related to Ravi?

Solution: The only son of Ravi's grandmother is Ravi's father. The daughter of Ravi's father is Ravi's sister. Hence the woman is Ravi's sister.

Question 28Blood Relations

A is the brother of B. B is the brother of C. C is the husband of D. E is the father of A. How is D related to E?

Solution: E is the father of A. A, B and C are brothers (all sons of E). C is the husband of D, so D is the wife of E's son, i.e. E's daughter-in-law.

Question 29Blood Relations

Introducing a man, a woman said, "His mother is the only daughter of my mother." How is the woman related to the man?

Solution: "The only daughter of my mother" - the woman's mother has only one daughter, which is the woman herself. So the man's mother is the woman; she is the man's mother.

Question 30Direction Sense

A man walks 5 km towards South, then turns left and walks 3 km, then turns left again and walks 5 km, and finally turns right and walks 2 km. In which direction is he now facing, and how far is he from the starting point along the straight line?

Solution: Start facing South, walk 5 (now 5 South). Turn left -> East, walk 3 (3 East). Turn left -> North, walk 5 (back to original latitude, 3 East of start). Turn right -> East, walk 2 (now 5 East of start). He faces East and is 3+2 = 5 km East of start.

Question 31Direction Sense

Starting from his house, Mohan walks 4 km North, then 3 km East, then 4 km South. How far and in which direction is he from his house?

Solution: 4 km North then 4 km South cancel out, leaving the 3 km East displacement. He is 3 km East of his house.

Question 32Direction Sense

Two friends start from the same point. A walks 6 km East, then 8 km North. B walks 6 km West, then 8 km North. What is the straight-line distance between A and B at the end?

Solution: A ends at (6, 8) and B ends at (-6, 8). Both are at the same height (8 North). Distance = horizontal gap = 6 - (-6) = 12 km.

Question 33Number Series

Find the next term in the series: 2, 6, 12, 20, 30, ?

Solution: Differences are 4, 6, 8, 10, so the next difference is 12. 30 + 12 = 42. (Also, terms are n(n+1): 1x2, 2x3, 3x4, 4x5, 5x6, 6x7 = 42.)

Question 34Number Series

Find the missing term: 3, 7, 15, 31, 63, ?

Solution: Each term is double the previous plus 1: 3x2+1=7, 7x2+1=15, 15x2+1=31, 31x2+1=63, 63x2+1=127.

Question 35Number Series

Find the odd one out: 4, 9, 16, 25, 35, 49

Solution: The sequence is of perfect squares: 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36, 7^2=49. The value 35 should be 36; 35 is the odd one out.

Question 36Letter Series

Find the next term in the series: B, D, G, K, P, ?

Solution: Positions: B(2), D(4), G(7), K(11), P(16). Differences increase 2, 3, 4, 5, so next is +6 -> 16+6 = 22 = V.

Question 37Coding-Decoding

If in a code MONDAY is written as NPOEBZ, then how is FRIDAY written in that code?

Solution: Each letter is shifted forward by 1: M->N, O->P, N->O, D->E, A->B, Y->Z. Apply to FRIDAY: F->G, R->S, I->J, D->E, A->B, Y->Z = GSJEBZ.

Question 38Coding-Decoding

In a certain code, FRIEND is written as HUMJTK (each letter shifted by 2, 3, 4, 5, 6, 7 respectively). How is CANDLE written in that code?

Solution: Shifts are 2,3,4,5,6,7. Verify FRIEND: F+2=H, R+3=U, I+4=M, E+5=J, N+6=T, D+7=K = HUMJTK. Apply to CANDLE: C+2=E, A+3=D, N+4=R, D+5=I, L+6=R, E+7=L = EDRIRL.

Question 39Letter-Number Coding

If A = 1, B = 2, C = 3, ... Z = 26, what is the sum of the letter-values of the word 'CAB'?

Solution: C = 3, A = 1, B = 2. Sum = 3 + 1 + 2 = 6.

Question 40Syllogism

Statements: (1) All pens are pencils. (2) Some pencils are erasers. Conclusions: (I) Some pens are erasers. (II) Some erasers are pencils. Which conclusion(s) logically follow?

Solution: All pens are pencils, and some pencils are erasers. The erasers that are pencils need not include any pens, so 'some pens are erasers' does not necessarily follow. 'Some pencils are erasers' converts to 'some erasers are pencils' (valid conversion of a particular affirmative). Only II follows.

Question 41Syllogism

Statements: (1) All cats are animals. (2) All animals are mortal. Conclusions: (I) All cats are mortal. (II) Some mortals are cats. Which conclusion(s) logically follow?

Solution: All cats are animals and all animals are mortal, so all cats are mortal (I follows). Since all cats are mortal and cats exist, some mortals are cats (II follows). Both follow.

Question 42Syllogism

Statements: (1) No teacher is rich. (2) Some rich people are wise. Conclusions: (I) Some wise people are not teachers. (II) No wise person is a teacher. Which conclusion(s) logically follow?

Solution: Some rich are wise; no teacher is rich, so those wise-and-rich people are not teachers. Hence some wise people are not teachers (I follows). But other wise people could be teachers, so II (no wise person is a teacher) does not follow. Only I follows.

Question 43Statements & Assumptions

Statement: "Please do not lean out of the moving train." - a notice in a railway compartment. Assumptions: (I) Leaning out of a moving train is dangerous. (II) Passengers will read and follow the notice. Which assumption(s) is/are implicit?

Solution: The notice is issued because leaning out is dangerous (I implicit). A notice is displayed expecting passengers to read and comply (II implicit). Both assumptions are implicit.

Question 44Seating Arrangement

Five people A, B, C, D and E sit in a row facing North. C sits at the middle (third position). A sits immediately to the left of C. E sits at the extreme right end. B sits to the immediate left of A. Who sits at the extreme left end?

Solution: Positions 1-5. C is at 3. A is immediately left of C, so A at 2. B immediately left of A, so B at 1. E at the extreme right (5). D takes the remaining position 4. Extreme left end is position 1 = B.

Question 45Arrangement Puzzle

Six books A, B, C, D, E, F are stacked in a pile. C is immediately above D. A is at the bottom. F is immediately above A. There are exactly two books between F and C. B is at the top. From bottom to top, what is the order?

Solution: A bottom (position 1), F immediately above A (position 2). B at top (position 6). Two books between F and C means C is at position 5 (positions 3 and 4 lie between F at 2 and C at 5). C immediately above D means D is at position 4. Position 3 is left for E. Order bottom to top: A, F, E, D, C, B.

Question 46Calendar

If 1st January 2024 was a Monday, what day of the week was 1st January 2025? (Note: 2024 is a leap year.)

Solution: 2024 is a leap year with 366 days, giving 2 odd days (366 mod 7 = 2). Monday + 2 days = Wednesday. So 1st Jan 2025 was a Wednesday.

Question 47Clocks

At what time between 3 o'clock and 4 o'clock will the hour hand and the minute hand of a clock coincide (overlap)?

Solution: At 3:00 the minute hand is 15 minute-spaces behind the hour hand. The minute hand gains 55/60 of a minute-space per minute relative to the hour hand, and must gain 15 minute-spaces. Time = 15 / (55/60) = 15 x 60/55 = 900/55 = 16 and 4/11 minutes. They coincide at 16 4/11 minutes past 3.

Question 48Analytical Decision Making

In a class, Ramesh ranks 7th from the top and 26th from the bottom. How many students are there in the class?

Solution: Total students = (rank from top) + (rank from bottom) - 1 = 7 + 26 - 1 = 32.

Question 49Probability

12 defective pens are accidentally mixed with 132 good ones. One pen is taken out at random. What is the probability it is a good pen?

Solution: Total pens = 12 + 132 = 144. Good pens = 132. Probability = 132/144 = 11/12.

Question 50Real Numbers

96 storybooks and 240 textbooks are stacked so every stack has the same number of books of one kind and is as tall as possible. Each stack has:

Solution: The greatest equal stack is HCF(96, 240) = 48 books.

Question 51Statistics

A 'less than' ogive is always:

Solution: Cumulative frequencies only build up, so the curve never falls.

Question 52Triangles

A 1.5 m tall person casts a 3 m shadow while a nearby tree casts a 12 m shadow. The tree's height is:

Solution: By similar triangles, height/12 = 1.5/3, so height = 6 m.

Question 53Surface Areas and Volumes

A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.

Solution: Volume of earth dug out = Volume of cylindrical well = πr²h = (22/7) × (3.5)² × 20 = (22/7) × 12.25 × 20 = 770 m³. Volume of platform = l × b × h = 22 × 14 × h = 308h. 308h = 770 → h = 770 / 308 = 2.5 m.

Question 54Polynomials

A ball thrown up has height h = −5t² + 20t metres after t seconds. It returns to the ground at:

Solution: h = 0 gives −5t(t − 4) = 0, so t = 0 (start) or t = 4 s (landing).

Question 55Areas Related to Circles

A bicycle wheel of radius 35 cm makes 5 revolutions. The distance moved (π = 22/7) is:

Solution: Distance = 5 × 2 × 22/7 × 35 = 5 × 220 = 1100 cm.

Question 56Pair of Linear Equations in Two Variables

A boat goes 12 km downstream and 8 km upstream in the same time pattern; if its speed in still water is 10 km/h, the stream speed (downstream 12, upstream 8) is:

Solution: Downstream 10 + s = 12 and upstream 10 − s = 8 both give s = 2 km/h.

Question 57Arithmetic Progressions

A child builds a triangle of coins: 1 in the top row, 2 in the next, and so on. To build 10 rows she needs:

Solution: 1 + 2 + … + 10 = 10 × 11 ÷ 2 = 55 coins.

Question 58Circles

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the centre of the circle.

Solution: Half of the chord = 8 cm. Using Pythagoras theorem in the right triangle formed by the radius, distance to chord, and half-chord: distance = √(10² − 8²) = √(100 − 64) = √36 = 6 cm.

Question 59Circles (Tangents)

A circle of radius 6 cm has two parallel tangents. The distance between them is:

Solution: Parallel tangents touch the ends of a diameter, so they are a diameter (12 cm) apart.

Question 60Number Systems

A circular garden has radius √7 m. If the radius is increased to 3√7 m, how many times does the area increase?

Solution: Area is proportional to radius². The radius becomes 3 times, so the area becomes 3² = 9 times.

Question 61Coordinate Geometry

A delivery van goes from (2, 1) to (2, 9) then to (8, 9). The total path length is:

Solution: Vertical leg 8 plus horizontal leg 6 gives 8 + 6 = 14 units.

Question 62Areas of Parallelograms and Triangles

A farmer has a triangular field with sides 50 m, 65 m, and 65 m. He leaves a 10 m wide straight path along the base (50 m) to the opposite vertex. Is it possible to find the exact area lost to the path without knowing the shape of the path?

Solution: The problem states 'straight path along the base to the opposite vertex' which is ambiguous in width configuration. However, assuming it's a constant width strip, area logic implies we need its geometric definition to calculate the intersection.

Question 63Heron's Formula

A floral design is made from 16 identical triangular tiles and has a total area of 576√6 cm². If polishing costs 50 paise per cm², what is the total polishing cost?

Solution: Total area = 576√6 cm². Cost in Rupees = 576√6 × 0.50 = ₹288√6.

Question 64Quadrilaterals

A line segment joins the mid-points of any two sides of a triangle. If the length of this segment is represented by x − 2 and the third side is 3x − 10, find the value of x.

Solution: By the mid-point theorem, the line segment joining the mid-points is half of the third side. So, x − 2 = (3x − 10) / 2 → 2(x − 2) = 3x − 10 → 2x − 4 = 3x − 10 → x = 6.

Question 65Linear Equations in Two Variables

A manufacturing unit produces items where the total cost y consists of a fixed setup expense of ₹5000 plus a raw material expense of ₹45 per item produced (x). Find the number of items produced if total cost is ₹9500.

Solution: The linear equation is y = 45x + 5000. Given total cost y = 9500, substitute to get 9500 = 45x + 5000 → 4500 = 45x → x = 100.

Question 66Euclid's Geometry

A mathematical statement whose truth has been logically established using axioms, definitions, and previously proven statements is called a:

Solution: A theorem is a mathematical statement that has been proven true using logical arguments based on axioms, definitions, and other established theorems.

Question 67DI-Table

A shop sold the following number of units of a product across a week - Mon: 40, Tue: 55, Wed: 30, Thu: 65, Fri: 50. What was the average number of units sold per day over these five days?

Solution: Total = 40 + 55 + 30 + 65 + 50 = 240. Average = 240 / 5 = 48 units per day.

Question 68DI-Percentage

A factory produced 800 units in January and 1000 units in February. What is the percentage increase in production from January to February?

Solution: Increase = 1000 - 800 = 200. Percentage increase = (200 / 800) x 100 = 25%.

Question 69DI-Table

Marks scored by four students in a test (out of 100) - Asha: 72, Bina: 85, Chitra: 64, Deepa: 79. By how many marks did the highest scorer exceed the lowest scorer?

Solution: Highest = Bina 85, lowest = Chitra 64. Difference = 85 - 64 = 21 marks.

Question 70DI-Ratio

In a college, the number of students enrolled in three streams is - Science: 360, Commerce: 240, Arts: 120. What is the ratio of Science to Commerce to Arts students in simplest form?

Solution: 360 : 240 : 120, divide each by 120 -> 3 : 2 : 1.

Question 71DI-Percentage

A company's monthly expenditure is distributed as - Salaries: 45%, Rent: 20%, Utilities: 10%, Marketing: 15%, Miscellaneous: 10%. If the total monthly expenditure is Rs 2,00,000, how much is spent on Marketing?

Solution: Marketing = 15% of 2,00,000 = 0.15 x 200000 = Rs 30,000.

Question 72DI-Table

Rainfall (in mm) recorded over five months - Jun: 150, Jul: 200, Aug: 180, Sep: 90, Oct: 60. What percentage of the total rainfall fell in July?

Solution: Total = 150 + 200 + 180 + 90 + 60 = 680 mm. July share = (200 / 680) x 100 = 29.41% ~ 29.6% is closest. Using exact total 680: 200/680 = 0.2941, i.e. about 29.4%, nearest given option 29.6%.

Question 73DI-Table

A car travels the following distances on four days - Day1: 180 km, Day2: 220 km, Day3: 150 km, Day4: 250 km. If petrol costs Rs 100 per litre and the car gives 20 km per litre, what is the total fuel cost for the four days?

Solution: Total distance = 180 + 220 + 150 + 250 = 800 km. Fuel used = 800 / 20 = 40 litres. Cost = 40 x 100 = Rs 4,000.

Question 74DI-Comparison

Sales of two products over three months - Product A: Jan 50, Feb 70, Mar 90. Product B: Jan 80, Feb 60, Mar 70. Over the three months combined, how many more units of Product B were sold than Product A?

Solution: Product A total = 50 + 70 + 90 = 210. Product B total = 80 + 60 + 70 = 210. Difference = 210 - 210 = 0. They sold the same number; B exceeded A by 0.

Question 75DI-Percentage

A book originally priced at Rs 500 is first discounted by 20%, then a further 10% is taken off the reduced price. What is the final price?

Solution: After 20% off: 500 x 0.8 = 400. After a further 10% off: 400 x 0.9 = 360. Final price = Rs 360.

Question 76DI-Table

Number of books issued by a library on five days - Mon: 35, Tue: 42, Wed: 28, Thu: 50, Fri: 45. On which day were the books issued closest to the daily average, and what was that average?

Solution: Total = 35 + 42 + 28 + 50 + 45 = 200. Average = 200 / 5 = 40. Differences from 40: Mon 5, Tue 2, Wed 12, Thu 10, Fri 5. Tuesday (42) is closest to the average of 40.

Question 77DI-Ratio

A sum of Rs 9,000 is divided among three people P, Q and R in the ratio 2 : 3 : 4. How much does R receive?

Solution: Total parts = 2 + 3 + 4 = 9. Each part = 9000 / 9 = 1000. R's share = 4 parts = 4 x 1000 = Rs 4,000.

Question 78DI-Table

A survey of 500 people on preferred drinks gave - Tea: 220, Coffee: 150, Juice: 80, Others: 50. What fraction of the surveyed people preferred Coffee?

Solution: Coffee = 150 out of 500. Fraction = 150 / 500 = 3 / 10.

Question 79DI-Percentage

A student scored the following in five subjects (each out of 100) - English: 68, Maths: 92, Science: 84, History: 56, Geography: 70. What is the student's overall percentage across the five subjects?

Solution: Total marks = 68 + 92 + 84 + 56 + 70 = 370 out of 500. Percentage = (370 / 500) x 100 = 74%.

Question 80DI-Comparison

Production of wheat (in tonnes) by a farm over four years - 2020: 400, 2021: 500, 2022: 450, 2023: 600. In which year was the percentage increase over the immediately preceding year the highest?

Solution: 2021 vs 2020: (500-400)/400 = 25%. 2022 vs 2021: production fell, so no increase. 2023 vs 2022: (600-450)/450 = 150/450 = 33.3%. The highest percentage increase was in 2023 (33.3%).