MBA4U.in – CAT Practice Mock Test 2

Full-Length Static CAT-Style Mock Paper with Answer Key & Detailed Solutions

Original practice material | 68 Questions | 120 Minutes | VARC 24 | DILR 22 | QA 22

Instructions

Total duration: 120 minutes. Suggested sectional time: 40 minutes each for VARC, DILR and QA.

MCQ: +3 for a correct answer and -1 for an incorrect answer. TITA/non-MCQ: +3 for a correct answer and no negative marking.

This is a static practice paper. No interactive response fields are included.

Difficulty labels (Easy / Moderate / Difficult) are provided for practice analytics and are not part of the CAT interface.

 

Section I – VARC (24 Questions)

RC Passage 1 – Restoration and Authenticity

Passage difficulty: Moderate

When a damaged historical building is restored, the word “authentic” is often invoked as though it points to a single, recoverable state. Yet old buildings rarely possess one uncontested original form. They are altered by repairs, new uses, changing materials and successive generations of taste. A medieval hall may contain a nineteenth-century roof, twentieth-century wiring and a staircase added after a fire. To remove every later intervention in search of an original object may produce something that never existed at any one moment.

This complicates a familiar contrast between preservation and change. Restoration itself is a form of change, because deciding what to retain requires selecting among layers of history. Even the decision to leave damage untouched can transform meaning: a crack that once signalled neglect may later be displayed as evidence of age and endurance. The restorer therefore does not simply reveal history; the restorer helps organise how history will be read.

Some conservationists respond by favouring minimal intervention and reversible techniques. These principles are valuable because they reduce the risk that present judgement will permanently erase future options. But reversibility is not always literal. Replacing a failing beam may be necessary for safety, and once removed, its exact material history cannot be restored. The more useful aim is intellectual reversibility: documenting decisions clearly enough that later generations can understand what was changed, why it was changed and what evidence supported the choice.

Authenticity, on this view, is less a property hidden inside an object than a disciplined relationship between evidence, intervention and disclosure. A credible restoration does not pretend that the present has vanished from the process. It acknowledges its own decisions while preserving as much of the building’s historical complexity as circumstances allow.

Q1. The passage’s central argument is that authenticity in restoration is best understood as:  [MCQ | Moderate]

1. the recovery of a building’s earliest documented state.
2. the removal of later alterations wherever possible.
3. a transparent, evidence-based negotiation among historical layers and present interventions.
4. the refusal to alter damaged historical material under any circumstances.

Q2. Why does the author say that removing later interventions can create something that never existed at one time?  [MCQ | Moderate]

1. Historical buildings often accumulated changes across different periods.
2. Modern restorers usually lack accurate architectural plans.
3. Later materials are always stronger than original materials.
4. Buildings were rarely completed according to their designers’ intentions.

Q3. The phrase ‘intellectual reversibility’ most nearly refers to:  [MCQ | Moderate]

1. using only materials that can be physically removed.
2. recording restoration choices so future observers can reconstruct the reasoning behind them.
3. returning a building to its condition before each major repair.
4. avoiding all structural changes that affect original fabric.

Q4. Which statement would the author most likely endorse?  [MCQ | Difficult]

1. A restoration can be historically responsible even when some physical changes cannot be undone.
2. Any visible modern intervention destroys authenticity.
3. Safety requirements should always override historical evidence.
4. The oldest surviving layer of a building should receive priority over all later layers.

RC Passage 2 – The Unequal Geography of Shade

Passage difficulty: Moderate

Cities frequently respond to rising temperatures by announcing tree-planting targets. The policy seems straightforward: more trees mean more shade, and more shade can reduce heat exposure. Yet the number of trees planted is a poor proxy for the cooling benefits residents actually receive. A sapling beside a wide highway may count toward a target while providing almost no useful shade for years; a mature tree over a crowded pavement can immediately affect hundreds of daily journeys.

The geography of shade is also shaped by the geometry of streets. Tall buildings may block afternoon sun in one district while broad roads expose another. Tree species differ in canopy width, water demand and survival rate. Maintenance matters too: planting campaigns attract publicity, whereas watering, pruning and replacing dead trees produce fewer photographs but determine whether a canopy survives.

These differences have distributional consequences. Heat risk is not uniform across a city. People who work outdoors, wait for buses, live in poorly insulated housing or lack access to air-conditioning can be more exposed. A city that distributes trees evenly by area may therefore distribute cooling benefits unevenly by need. Conversely, concentrating investment in the hottest districts may appear unequal on a map while reducing inequality in experienced heat.

This is why some planners argue that urban forestry should be evaluated less like a beautification programme and more like public-health infrastructure. The relevant questions change: Which walking routes lack shade? Where do vulnerable residents spend time? Which planting sites can sustain mature canopy? Such an approach does not make citywide targets useless. It makes them subordinate to a more demanding objective: reducing harmful heat exposure where the reduction matters most.

Q5. Which policy principle is most strongly supported by the passage?  [MCQ | Moderate]

1. maximise the number of trees planted per square kilometre.
2. treat shade as an outcome whose distribution and durability matter more than planting totals alone.
3. replace air-conditioning subsidies with tree-planting programmes.
4. concentrate all planting in the city’s hottest neighbourhood.

Q6. Which example best illustrates the author’s criticism of a simple tree-count target?  [MCQ | Easy]

1. A mature tree is pruned to protect electrical cables.
2. A city plants many saplings in sites where few survive or shade pedestrians.
3. Residents disagree about which tree species looks attractive.
4. A shaded street contains fewer shops than an unshaded one.

Q7. The statement that concentrating investment may ‘appear unequal on a map’ is used to show that:  [MCQ | Difficult]

1. spatial equality and equality of benefit are not necessarily the same.
2. urban maps exaggerate temperature differences.
3. public-health spending should never be geographically uniform.
4. tree planting is more effective in wealthy districts.

Q8. Which of the following is NOT identified as relevant to the cooling benefit of urban trees?  [MCQ | Easy]

1. Canopy maturity
2. Street geometry
3. Maintenance and survival
4. The commercial value of nearby buildings

RC Passage 3 – Models, Maps and Explanation

Passage difficulty: Difficult

Scientific models are sometimes criticised for being unrealistic, as though realism were a single scale on which better models always score higher. But a model that includes every known detail may be less useful than one that deliberately omits most of them. A subway map distorts distance and direction so that connections become legible. Its inaccuracies are not merely tolerated; they are part of what makes the map useful for a particular task.

The analogy should not be pushed too far. Scientific models do more than guide travellers. They support prediction, explanation and intervention, and these purposes can pull model design in different directions. A highly accurate forecasting model may contain thousands of parameters whose interactions are difficult to interpret. A simpler model may predict less precisely but reveal which mechanisms are sufficient to generate a pattern. Calling one model “better” without specifying the purpose therefore conceals an important judgement.

This does not mean that any simplification is acceptable. Omissions must be disciplined by evidence. If a climate model ignores a process known to dominate the phenomenon being studied, its simplicity is not illuminating but misleading. The challenge is to distinguish productive abstraction from convenient blindness.

The same issue appears when models travel from one context to another. A model built on one population may perform poorly elsewhere, not because modelling as such has failed, but because assumptions that were harmless in the original setting become consequential in the new one. Robust modelling therefore requires not only testing outputs but examining the conditions under which the model’s abstractions remain defensible.

A model should thus be judged neither by resemblance to reality alone nor by predictive performance alone. Its adequacy depends on what it is for, what it leaves out and whether those omissions remain reasonable in the context of use.

Q9. The subway-map analogy primarily demonstrates that:  [MCQ | Moderate]

1. all useful models must distort reality.
2. some departures from realism can improve usefulness for a specified purpose.
3. scientific prediction is no more reliable than navigation.
4. complex models are generally inferior to simple ones.

Q10. According to the passage, a simpler model may be preferable to a more accurate forecasting model when the aim is to:  [MCQ | Moderate]

1. maximise the number of parameters included.
2. identify mechanisms sufficient to generate an observed pattern.
3. avoid using empirical evidence.
4. transfer the model unchanged to a new population.

Q11. What does the author mean by ‘convenient blindness’?  [MCQ | Difficult]

1. Ignoring details merely because they complicate a model, even when they materially affect the phenomenon.
2. Using a model without understanding its mathematical notation.
3. Preferring prediction to explanation in every context.
4. Applying visual maps to non-spatial problems.

Q12. Which statement best captures the author’s position on model evaluation?  [MCQ | Moderate]

1. Predictive accuracy should be the sole criterion.
2. Realistic detail should always increase with computing power.
3. Adequacy depends on purpose, omissions and context as well as performance.
4. Models that travel across contexts are inherently unreliable.

RC Passage 4 – Translation and Productive Ambiguity

Passage difficulty: Moderate-Difficult

Readers often imagine translation as the replacement of one set of words by another. This picture works tolerably well for instructions, where precision is usually the dominant aim. Literary translation is more troublesome because a sentence may do several things at once. It can state a fact, echo an earlier phrase, sustain a rhythm and leave deliberately unresolved whether a speaker is sincere or ironic.

A translator who removes ambiguity can make a difficult sentence easier to understand while making the work less faithful. The paradox arises because fidelity is not always fidelity to a single meaning. Sometimes the original text is carefully constructed to support several readings, and choosing one of them in translation changes the reader’s task.

Literalness does not solve the problem. Words that are close dictionary equivalents may differ in tone, social register or historical association. Nor can a translator preserve every feature. Maintaining rhyme may require altering syntax; preserving syntax may flatten rhythm; retaining a culturally specific image may puzzle readers who lack the relevant background.

For this reason, translation is better understood as a series of accountable trade-offs than as a search for perfect equivalence. The translator asks which features are central in a particular passage and which losses can be compensated elsewhere. A pun that cannot survive in one sentence may be echoed through wordplay later; a formal register may be recreated with different grammatical resources.

Such choices inevitably make the translator visible, even when the prose appears effortless. This visibility need not be treated as failure. The more useful question is whether the translation’s interventions are responsive to the structure of the original rather than merely smoothing away whatever resists immediate comprehension.

Q13. The passage suggests that literary translation differs from instruction translation mainly because literary language:  [MCQ | Moderate]

1. uses older vocabulary.
2. often performs several functions simultaneously, including preserving ambiguity.
3. cannot be translated without adding explanatory notes.
4. depends more heavily on dictionary equivalents.

Q14. Why can removing ambiguity make a translation less faithful?  [MCQ | Moderate]

1. Because all literary ambiguity is accidental.
2. Because the original may intentionally require readers to hold more than one interpretation open.
3. Because ambiguous translations are always more elegant.
4. Because translators should never choose among dictionary meanings.

Q15. The discussion of rhyme, syntax and cultural images supports which broader point?  [MCQ | Moderate]

1. Every translation inevitably requires trade-offs among features that cannot all be preserved equally.
2. Rhymed texts should be translated only into rhymed forms.
3. Cultural references should generally be replaced by local equivalents.
4. Literal translation is preferable whenever syntax can be preserved.

Q16. The author’s view of translator visibility is best described as:  [MCQ | Difficult]

1. necessarily evidence of poor translation.
2. acceptable when interventions respond responsibly to the original’s structure.
3. irrelevant because readers cannot detect translation choices.
4. desirable only when the translator adds explanations.

Q17. Choose the option that best summarises the paragraph: ‘Efficiency is often defined as producing more output with fewer inputs. But when an organisation optimises a process, it may also remove spare capacity. That spare capacity can look wasteful during normal periods yet become crucial when demand suddenly rises or a supplier fails. A system can therefore become more efficient in routine conditions while becoming less resilient to shocks.’  [MCQ | Moderate]

1. Efficient organisations should always maintain large inventories.
2. Removing apparent slack may improve routine efficiency but can reduce resilience when conditions change.
3. Resilience and efficiency are identical once output is measured correctly.
4. Unexpected demand is caused mainly by excessive optimisation.

Q18. Choose the option that best summarises the paragraph: ‘Experts often communicate uncertainty by presenting ranges or probabilities. Non-experts may interpret this as weakness, preferring a confident single number. Yet uncertainty can be information rather than ignorance: it shows how strongly evidence supports different possibilities. Hiding uncertainty may make a forecast easier to communicate while making it less honest and less useful for decisions.’  [MCQ | Moderate]

1. Forecasts should avoid numbers because probabilities confuse the public.
2. A confident single estimate is more useful than an uncertain range.
3. Explicit uncertainty can improve decision-making by representing the strength and limits of available evidence.
4. Experts use uncertainty mainly to protect themselves from criticism.

Q19. Select the sentence that best completes the paragraph: ‘A city may widen a road to reduce congestion. Initially, vehicles move faster and travel times fall. But the lower cost of driving can encourage some commuters to switch from public transport, change routes, or make trips they previously avoided. Over time, traffic volumes rise. ____’  [MCQ | Moderate]

1. Road construction is therefore never justified.
2. The original improvement can partly disappear because capacity changes travel behaviour as well as traffic flow.
3. Public transport always becomes faster after roads are widened.
4. Congestion can be measured only through fuel consumption.

Q20. Select the sentence that best completes the paragraph: ‘A scientific replication is sometimes described as successful only when it produces the same numerical result as the original study. That is too narrow. Differences in population, measurement or context can legitimately alter the estimated effect. What matters is whether the new evidence is consistent with the underlying claim once those differences are considered. ____’  [MCQ | Difficult]

1. Replication is therefore a test of the robustness of an explanation, not merely an exercise in numerical copying.
2. All studies should use exactly the same sample size.
3. Original research is more reliable than replication by definition.
4. Numerical disagreement proves that at least one study is fraudulent.

Q21. Five sentences are given below. Four form a coherent paragraph. Identify the odd sentence out and enter its number.
1. Coral reefs are built by organisms whose growth depends on a narrow range of environmental conditions.
2. Rising sea temperatures can disrupt the symbiosis that supplies corals with much of their energy.
3. Some coastal cities use concrete barriers to reduce damage from storm surges.
4. Repeated bleaching events can leave insufficient time for reefs to recover.
5. The loss of reef structure can also reduce habitat for many marine species.  [TITA | Moderate]

Q22. Five sentences are given below. Four form a coherent paragraph. Identify the odd sentence out and enter its number.
1. Archives do not preserve the past in a neutral or complete form.
2. Decisions about what to collect determine which experiences are easier for later researchers to study.
3. Digital storage has made every historical record permanently accessible.
4. Cataloguing practices also influence what researchers are likely to discover.
5. Historical absence in an archive can therefore reflect past institutional choices rather than absence from society.  [TITA | Moderate]

Q23. The four sentences below form a coherent paragraph when rearranged. Enter the correct sequence as a four-digit number.
1. Once established, these conventions can make an arbitrary system feel natural to later users.
2. Many standards begin not because one design is inherently superior but because early coordination requires everyone to choose something.
3. This path dependence explains why technically better alternatives can struggle to replace familiar standards.
4. As more people build tools and habits around the initial choice, switching becomes increasingly costly.  [TITA | Difficult]

Q24. The four sentences below form a coherent paragraph when rearranged. Enter the correct sequence as a four-digit number.
1. The result is that a price can transmit information without any participant knowing the whole system.
2. A farmer observes local weather, a transporter knows route conditions, and a retailer sees neighbourhood demand.
3. Markets can aggregate fragments of knowledge that are dispersed among many participants.
4. Their separate decisions affect supply and demand, which in turn influence the price others observe.  [TITA | Moderate]

Section II – DILR (22 Questions)

Set 1 – Beverage Kiosks

The table gives cups sold by four kiosks over four days.

Kiosk	Mon	Tue	Wed	Thu
A	80	120	100	140
B	100	90	130	110
C	70	110	120	150
D	90	100	110	130

Q25. Which kiosk sold the highest total number of cups over the four days?  [MCQ | Easy]

1. A
2. B
3. C
4. D

Q26. What was the combined number of cups sold by all kiosks on Tuesday and Thursday?  [TITA | Easy]

Q27. Which kiosk recorded the greatest percentage increase in sales from Monday to Thursday?  [MCQ | Moderate]

1. A
2. B
3. C
4. D

Q28. Suppose profit per cup is Rs 2 at A, Rs 3 at B, Rs 4 at C and Rs 5 at D. What is the total profit over all four days?  [TITA | Moderate]

Q29. What is the ratio of total Wednesday sales to total Monday sales?  [MCQ | Moderate]

1. 23:17
2. 17:23
3. 46:35
4. 35:46

Set 2 – Conference Schedule

Six speakers P, Q, R, S, T and U are scheduled in Slots 1 to 6, one per slot. Conditions: (i) R is immediately before S; (ii) Q is exactly two slots after P; (iii) T is after Q; (iv) U is before R.

Q30. In which slot must U appear?  [TITA | Easy]

Q31. Which statement must be true?  [MCQ | Moderate]

3. Q is in Slot 3.
4. R is in Slot 4.
5. T is in Slot 6.
6. S is in Slot 5.

Q32. If T occupies Slot 4, who occupies Slot 5?  [MCQ | Moderate]

1. P
2. Q
3. R
4. S

Q33. Which pair lists the two people who can occupy Slot 4 in different valid schedules?  [MCQ | Moderate]

1. P and Q
2. R and T
3. S and U
4. Q and U

Q34. The stated conditions permit how many complete assignments of the six speakers to the six slots?  [TITA | Difficult]

Set 3 – Project Portfolio

Exactly three projects are selected from A, B, C, D, E and F. Conditions: (i) if A is selected, B is selected; (ii) C and D cannot both be selected; (iii) if E is selected, B is not selected; (iv) if F is selected, at least one of C or D is selected; (v) at least one of D or E is selected.

Q35. How many valid 3-project selections are possible?  [TITA | Moderate]

Q36. If A is selected, which two projects must accompany it?  [MCQ | Moderate]

1. B and D
2. B and F
3. C and E
4. D and F

Q37. How many projects are tied for the highest frequency of appearance across all valid selections?  [TITA | Difficult]

Q38. Under the additional condition that E is chosen, which of the following is forced into the portfolio?  [MCQ | Moderate]

1. A
2. B
3. C
4. F

Set 4 – Delivery Routes

A delivery company is comparing four routes. Fuel costs Rs 96 per litre on every route.

Route	Distance (km)	Average speed (km/h)	Toll (Rs)	Mileage (km/l)
P	180	60	240	12
Q	150	50	300	15
R	210	70	180	14
S	160	40	120	16

Q39. Which route has the lowest total monetary cost, including fuel and toll?  [MCQ | Easy]

1. P
2. Q
3. R
4. S

Q40. Among routes requiring at most 3 hours at the stated average speed, what is the minimum total monetary cost in rupees?  [TITA | Moderate]

Q41. What is the difference, in rupees, between the total monetary cost of Route P and Route S?  [TITA | Moderate]

Q42. If the average speed on Route S rises by 25% with distance unchanged, by how many minutes does its travel time fall?  [TITA | Moderate]

Set 5 – Four-Team League

Teams W, X, Y and Z play each other exactly once. A win gives 3 points, a draw 1 point to each team and a loss 0 points. W beat X, Y beat Z, and W drew with Y. Final points were W=4, X=4, Y=5 and Z=3.

Q43. What was the result of the match between W and Z?  [MCQ | Moderate]

1. W won
2. The match was drawn
3. Z won
4. Cannot be determined

Q44. What was the result of the match between X and Y?  [MCQ | Moderate]

1. X won
2. The match was drawn
3. Y won
4. Cannot be determined

Q45. How many of the six matches were drawn?  [TITA | Moderate]

Q46. How many teams recorded a win against W?  [TITA | Easy]

Section III – QA (22 Questions)

Q47. An article is marked 40% above cost price and then sold after successive discounts of 10% and 5%. What is the profit percentage?  [MCQ | Moderate]

17. 17.0%
18. 19.7%
19. 20.0%
20. 23.0%

Q48. How many integers n satisfy n^2 – 7n + 10 < 0?  [TITA | Easy]

Q49. A 20-litre mixture is made using a 30% solution and a 50% solution so that the final concentration is 42%. How many litres of the 30% solution are used?  [MCQ | Moderate]

1. 6
2. 8
3. 10
4. 12

Q50. Find the least positive integer n that is divisible by both 8 and 12 and leaves remainder 5 when divided by 7.  [TITA | Moderate]

Q51. A rectangle has area 60 square units and diagonal 13 units. What is its perimeter?  [MCQ | Moderate]

1. 26
2. 30
3. 34
4. 36

Q52. For positive p and q, if p/q + q/p = 5/2, then (p-q)^2/(pq) equals:  [MCQ | Moderate]

1. 1/4
2. 1/2
3. 3/4
4. 1

Q53. A tank is filled by Pipe A in 10 hours and emptied by Pipe B in 15 hours. Both are opened together for 3 hours, after which B is closed. How many more hours will A take to fill the tank?  [TITA | Moderate]

Q54. The average score of 9 students is 64. If the highest score, 88, is excluded, what is the average score of the remaining 8 students?  [MCQ | Easy]

1. 60
2. 61
3. 62
4. 63

Q55. How many positive integer triples (x,y,z) satisfy x+y+z=10, x≥2, y≥3 and z≥1?  [TITA | Difficult]

Q56. If log base 2 of x plus log base 2 of (x-2) equals 3, then x equals:  [MCQ | Moderate]

1. 3
2. 4
3. 5
4. 6

Q57. The incomes of A and B are in the ratio 5:6 and their expenditures are in the ratio 4:5. If they save equal amounts, A’s savings are what percentage of A’s income?  [MCQ | Moderate]

1. 10%
2. 16⅔%
3. 20%
4. 25%

Q58. In an arithmetic progression, the sum of the first 10 terms is 230 and the sum of the next 10 terms is 630. Find the common difference.  [TITA | Moderate]

Q59. A bag contains 2 red, 3 blue and 4 green balls. Two balls are drawn without replacement. What is the probability that they are of the same colour?  [MCQ | Moderate]

1. 5/18
2. 7/18
3. 4/9
4. 1/3

Q60. A line of slope -2 passes through (2,3). Its x-intercept is:  [MCQ | Moderate]

1. 3
2. 7/2
3. 4
4. 9/2

Q61. How many integers from 1 to 600, inclusive, are divisible by exactly one of 8 and 15?  [TITA | Difficult]

Q62. For a principal of Rs 10,000, the difference between compound interest and simple interest for 2 years at the same annual rate is Rs 144. What is the annual rate?  [MCQ | Moderate]

1. 10%
2. 12%
3. 14%
4. 16%

Q63. If 2^x=5 and 5^y=8, then xy equals:  [MCQ | Moderate]

1. 2
2. 3
3. 4
4. 5

Q64. How many positive divisors does 756 have?  [TITA | Moderate]

Q65. The volume of a right circular cylinder of radius 3 units and height 8 units is:  [MCQ | Easy]

1. 48π
2. 60π
3. 72π
4. 96π

Q66. The perpendicular sides of a right triangle differ by 7 units and its area is 60 square units. Find its hypotenuse.  [TITA | Moderate]

Q67. The minimum value of f(x)=x^2-4x+7 for real x is:  [MCQ | Easy]

1. 2
2. 3
3. 4
4. 7

Q68. How many five-digit numbers divisible by 5 can be formed from the digits 0, 1, 2, 3, 4 and 5 without repetition?  [MCQ | Moderate]

1. 192
2. 204
3. 216
4. 240

 

 

Answer Key

Q1	C	Q19	B	Q37	2	Q55	15
Q2	A	Q20	A	Q38	D	Q56	B
Q3	B	Q21	3	Q39	D	Q57	C
Q4	A	Q22	3	Q40	1260	Q58	4
Q5	B	Q23	2143	Q41	600	Q59	A
Q6	B	Q24	3241	Q42	48	Q60	B
Q7	A	Q25	C	Q43	C	Q61	105
Q8	D	Q26	950	Q44	B	Q62	B
Q9	B	Q27	C	Q45	2	Q63	B
Q10	B	Q28	6120	Q46	1	Q64	24
Q11	A	Q29	A	Q47	B	Q65	C
Q12	C	Q30	2	Q48	2	Q66	17
Q13	B	Q31	A	Q49	B	Q67	B
Q14	B	Q32	C	Q50	96	Q68	C
Q15	A	Q33	B	Q51	C
Q16	B	Q34	2	Q52	B
Q17	B	Q35	4	Q53	9
Q18	C	Q36	A	Q54	B

 

Detailed Solutions

VARC Solutions

Q1. Answer: C | Difficulty: Moderate

The passage rejects a single ‘original’ state and defines authenticity through evidence, intervention and disclosure. Hence C.

Q2. Answer: A | Difficulty: Moderate

The building can contain valid historical layers from different periods; stripping later layers can fabricate a state that never existed simultaneously. Hence A.

Q3. Answer: B | Difficulty: Moderate

The author defines intellectual reversibility as documenting choices and evidence so later generations can understand and reassess them. Hence B.

Q4. Answer: A | Difficulty: Difficult

The beam example explicitly shows that irreversible physical intervention can still be responsible if necessary and transparently documented. Hence A.

Q5. Answer: B | Difficulty: Moderate

The passage argues that planting totals should be subordinate to actual, durable reductions in harmful heat exposure. Hence B.

Q6. Answer: B | Difficulty: Easy

Counting saplings that fail or do not shade people is precisely the proxy problem described. Hence B.

Q7. Answer: A | Difficulty: Difficult

Equal geographic allocation can produce unequal experienced benefit; targeted allocation can look unequal yet reduce exposure inequality. Hence A.

Q8. Answer: D | Difficulty: Easy

Commercial value of nearby buildings is never presented as a determinant of cooling benefit. Hence D.

Q9. Answer: B | Difficulty: Moderate

The subway map is useful partly because task-relevant distortion improves legibility; realism is not the only criterion. Hence B.

Q10. Answer: B | Difficulty: Moderate

The passage says simpler models can reveal mechanisms sufficient to generate patterns even if prediction is weaker. Hence B.

Q11. Answer: A | Difficulty: Difficult

‘Convenient blindness’ means omitting a consequential process merely for simplicity rather than as a defensible abstraction. Hence A.

Q12. Answer: C | Difficulty: Moderate

The conclusion explicitly says purpose, omissions, context and performance all matter. Hence C.

Q13. Answer: B | Difficulty: Moderate

Literary sentences can simultaneously carry fact, rhythm, echo, tone and ambiguity, making one-for-one replacement inadequate. Hence B.

Q14. Answer: B | Difficulty: Moderate

When ambiguity is intentional, resolving it removes part of the reader’s interpretive task. Hence B.

Q15. Answer: A | Difficulty: Moderate

The examples show that preserving one feature often costs another, so translation entails accountable trade-offs. Hence A.

Q16. Answer: B | Difficulty: Difficult

The author accepts translator visibility when interventions are responsive to the structure of the original. Hence B.

Q17. Answer: B | Difficulty: Moderate

The paragraph contrasts routine efficiency with shock resilience and explains how removing slack can weaken the latter. Hence B.

Q18. Answer: C | Difficulty: Moderate

The core idea is that uncertainty conveys evidential strength and limits, improving honest decisions. Hence C.

Q19. Answer: B | Difficulty: Moderate

The paragraph describes induced demand: added capacity changes behaviour, so congestion relief can erode. Hence B.

Q20. Answer: A | Difficulty: Difficult

The argument broadens replication from numerical identity to testing whether a claim survives contextual variation. Hence A.

Q21. Answer: 3 | Difficulty: Moderate

Sentences 1,2,4,5 form a chain about coral reef vulnerability and consequences. Sentence 3 shifts to urban storm barriers. Answer 3.

Q22. Answer: 3 | Difficulty: Moderate

Sentences 1,2,4,5 concern archival selection and discoverability. Sentence 3 makes an unrelated and absolute claim about digital storage. Answer 3.

Q23. Answer: 2143 | Difficulty: Difficult

2 introduces standards and initial coordination; 1 refers to ‘these conventions’; 4 explains increasing switching costs; 3 states the path-dependence consequence. Sequence 2143.

Q24. Answer: 3241 | Difficulty: Moderate

3 introduces dispersed knowledge; 2 gives examples; 4 explains how decisions affect price; 1 states the resulting information aggregation. Sequence 3241.

 

DILR Solutions

Q25. Answer: C | Difficulty: Easy

Totals are A=440, B=430, C=450, D=430. C is highest.

Q26. Answer: 950 | Difficulty: Easy

Tuesday total = 120+90+110+100=420. Thursday total = 140+110+150+130=530. Combined = 950.

Q27. Answer: C | Difficulty: Moderate

Percentage increases: A=60/80=75%; B=10%; C=80/70≈114.3%; D=40/90≈44.4%. C is greatest.

Q28. Answer: 6120 | Difficulty: Moderate

Weekly profits: A 440×2=880; B 430×3=1290; C 450×4=1800; D 430×5=2150. Total=6120.

Q29. Answer: A | Difficulty: Moderate

Wednesday total=100+130+120+110=460; Monday total=340. Ratio 460:340=23:17.

Q30. Answer: 2 | Difficulty: Easy

The only valid schedules are P-U-Q-R-S-T and P-U-Q-T-R-S. U is therefore fixed in Slot 2, so the TITA answer is 2.

Q31. Answer: A | Difficulty: Moderate

Both valid schedules place Q in Slot 3. The other listed claims vary or fail.

Q32. Answer: C | Difficulty: Moderate

With T in Slot 4, the schedule is P-U-Q-T-R-S, so R is in Slot 5.

Q33. Answer: B | Difficulty: Moderate

Slot 4 is R in one valid schedule and T in the other. Hence R and T.

Q34. Answer: 2 | Difficulty: Difficult

Direct enumeration under the four conditions gives exactly 2 schedules.

Q35. Answer: 4 | Difficulty: Moderate

Valid selections are ABD, BDF, CEF and DEF: 4 in total.

Q36. Answer: A | Difficulty: Moderate

If A is chosen, the only valid selection is ABD. Hence B and D.

Q37. Answer: 2 | Difficulty: Difficult

D occurs in 3 valid portfolios and F also occurs in 3; every other project appears fewer times. Therefore 2 projects are tied for the highest frequency.

Q38. Answer: D | Difficulty: Moderate

The E-containing valid selections are CEF and DEF; F is common to both.

Q39. Answer: D | Difficulty: Easy

At Rs 96/litre: P uses 15 L => 1440+240=1680; Q 10 L=>960+300=1260; R 15 L=>1440+180=1620; S 10 L=>960+120=1080. S is cheapest.

Q40. Answer: 1260 | Difficulty: Moderate

Travel times are P=3 h, Q=3 h, R=3 h, S=4 h. Among the qualifying routes P,Q,R, the minimum cost is Rs 1260 (Route Q).

Q41. Answer: 600 | Difficulty: Moderate

P costs Rs 1680 and S costs Rs 1080. Difference=600.

Q42. Answer: 48 | Difficulty: Moderate

S originally takes 160/40=4 h. New speed=50 km/h, so time=160/50=3.2 h. Reduction=0.8 h=48 minutes.

Q43. Answer: C | Difficulty: Moderate

Using the stated results and final points, the unique completion has Z defeating W.

Q44. Answer: B | Difficulty: Moderate

The unique completion requires X-Y to be a draw.

Q45. Answer: 2 | Difficulty: Moderate

The draws are W-Y and X-Y, so there are 2 drawn matches.

Q46. Answer: 1 | Difficulty: Easy

Only Z records a win over W, so exactly 1 team defeats W.

QA Solutions

Q47. Answer: B | Difficulty: Moderate

Let cost price be 100. Marked price=140. Selling price=140×0.90×0.95=119.7. Profit=19.7%, so B.

Q48. Answer: 2 | Difficulty: Easy

(n-2)(n-5)<0, so 2<n<5. Integers are 3 and 4: 2 integers.

Q49. Answer: B | Difficulty: Moderate

Let x litres be 30%. Then 0.30x+0.50(20-x)=0.42×20. Solving gives x=8.

Q50. Answer: 96 | Difficulty: Moderate

n must be a multiple of lcm(8,12)=24. Write n=24k. Since 24k≡5 (mod 7), 3k≡5 (mod 7), giving k≡4 (mod 7). The least k is 4, so n=96.

Q51. Answer: C | Difficulty: Moderate

If sides are a,b, then a²+b²=169 and ab=60. Thus (a+b)²=289, so a+b=17 and perimeter=34.

Q52. Answer: B | Difficulty: Moderate

p/q+q/p=(p²+q²)/(pq)=5/2. Hence (p-q)²/(pq)=(p²+q²-2pq)/(pq)=5/2-2=1/2.

Q53. Answer: 9 | Difficulty: Moderate

Net rate with both open is 1/10-1/15=1/30 tank per hour. In 3 hours, 1/10 of the tank is filled, leaving 9/10. Pipe A alone fills at 1/10 per hour, so it needs 9 more hours.

Q54. Answer: B | Difficulty: Easy

Total score=9×64=576. Removing 88 leaves 488. Average of the remaining 8 is 488/8=61.

Q55. Answer: 15 | Difficulty: Difficult

Set a=x-2,b=y-3,c=z-1. Then a,b,c≥0 and a+b+c=4. Number=C(6,2)=15.

Q56. Answer: B | Difficulty: Moderate

log2[x(x-2)]=3, so x(x-2)=8. x²-2x-8=0 gives x=4 or -2; domain requires x>2, hence 4.

Q57. Answer: C | Difficulty: Moderate

Let incomes=5a,6a and expenditures=4b,5b. Equal savings gives 5a-4b=6a-5b, so a=b. A saves a out of 5a=20%.

Q58. Answer: 4 | Difficulty: Moderate

S10=230 and terms 11-20 sum to 630, so S20=860. Now S20=10(2a+19d)=860 and S10=5(2a+9d)=230. Thus 2a+19d=86 and 2a+9d=46; subtracting gives 10d=40, so d=4.

Q59. Answer: A | Difficulty: Moderate

Total pairs=C(9,2)=36. Same-colour pairs=C(2,2)+C(3,2)+C(4,2)=1+3+6=10. Probability=10/36=5/18.

Q60. Answer: B | Difficulty: Moderate

Equation: y-3=-2(x-2), so y=-2x+7. Setting y=0 gives x=7/2.

Q61. Answer: 105 | Difficulty: Difficult

Multiples of 8 up to 600: 75. Multiples of 15: 40. Multiples of both are multiples of 120: 5. Divisible by exactly one =75+40-2×5=105.

Q62. Answer: B | Difficulty: Moderate

For 2 years, CI-SI=P(r/100)^2. Thus 144=10000(r/100)^2=r², giving r=12%.

Q63. Answer: B | Difficulty: Moderate

x=log2(5) and y=log5(8). Hence xy=log2(5)×log5(8)=log2(8)=3.

Q64. Answer: 24 | Difficulty: Moderate

756=4×189=2²×3³×7. Therefore the number of positive divisors is (2+1)(3+1)(1+1)=3×4×2=24.

Q65. Answer: C | Difficulty: Easy

Volume=πr²h=π×9×8=72π.

Q66. Answer: 17 | Difficulty: Moderate

Let the legs be x and x+7. Area 60 gives x(x+7)/2=60, so x²+7x-120=0, yielding x=8. The legs are 8 and 15, so the hypotenuse is 17.

Q67. Answer: B | Difficulty: Easy

x²-4x+7=(x-2)²+3, so minimum is 3.

Q68. Answer: C | Difficulty: Moderate

If the last digit is 0: choose the first digit in 5 ways and arrange 3 of the remaining 4 digits in 4P3=24 ways, giving 120. If the last digit is 5: the first digit has 4 non-zero choices (1-4), and the next three positions have 4P3=24 arrangements, giving 96. Total=216, option C.