MBA4U.in – CAT Practice Mock Test 1

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 actual CAT interface.

 

Section I – VARC (24 Questions)

RC Passage 1 – Measuring What Matters

Passage difficulty: Moderate

When organisations discover that a desirable outcome is difficult to observe directly, they often replace it with a convenient metric. A school that wants students to learn may monitor test scores; a hospital that wants patients to recover may track average length of stay; a city that wants safer streets may count arrests. None of these substitutions is irrational. Measurement is indispensable to coordination. Yet a metric becomes dangerous when its administrative convenience is mistaken for conceptual completeness.

The problem is not merely that metrics are imperfect. Every representation is imperfect. The deeper problem is behavioural: once rewards and penalties are tied to a number, people begin to optimise the number. Teachers can narrow instruction to likely test items, hospitals can avoid difficult cases, and police departments can prioritise offences that are easy to record. The measured indicator may improve even as the underlying objective stagnates or deteriorates.

One response is to design more sophisticated indicators. But adding variables can create the illusion that complexity has been captured simply because a formula has become complicated. A dashboard with twenty indicators may still omit the dimensions that matter most, especially those that are qualitative, delayed, or context-dependent. Moreover, complex metrics are often difficult for outsiders to audit, which transfers power from citizens or frontline workers to specialists who understand the model.

This does not imply that institutions should abandon quantitative targets. Instead, metrics should be treated as provisional instruments whose meaning depends on surrounding judgement. A useful system combines numbers with periodic qualitative review, asks whether people have begun gaming the indicator, and is willing to revise or retire measures that have ceased to track the intended goal. The best metric, therefore, is not one that eliminates judgement but one that makes judgement more disciplined.

Q1. The central argument of the passage is that:

• metrics should be replaced by qualitative judgement in most institutions.
• metrics are useful only when they remain subordinate to the broader objective and open to revision.
• complex metrics are always less reliable than simple ones.
• people inevitably manipulate any numerical target, making measurement futile.

Q2. Which of the following best explains why a metric may improve while the underlying objective worsens?

• The metric may be based on too few variables.
• Institutions may lack enough historical data.
• People may optimise the indicator rather than the objective it is meant to represent.
• Qualitative outcomes are impossible to measure.

Q3. The author would most likely agree with which statement about a twenty-indicator dashboard?

• It necessarily captures reality better than a single metric.
• Its complexity can conceal important omissions and make scrutiny harder.
• It should be preferred whenever experts can explain it.
• It eliminates the need for qualitative review.

Q4. The examples of schools, hospitals and police departments primarily serve to:

• show that public institutions are uniquely vulnerable to corruption.
• demonstrate that measurement is impossible in service sectors.
• illustrate how proxies can reshape behaviour once linked to incentives.
• argue that all performance targets should be removed.

RC Passage 2 – The Ecology of Attention

Passage difficulty: Moderate-Difficult

Digital platforms are frequently described as competing for users’ attention, as though attention were a fixed commodity stored inside each individual. The metaphor is useful but incomplete. Attention is not merely extracted; it is also shaped. Habits of noticing are trained by environments. A commuter who repeatedly receives alerts during a journey may learn to experience pauses as invitations to check a screen. Over time, the platform is not simply consuming spare attention but helping define what counts as a pause and what one is expected to do with it.

This distinction matters because policy debates often focus on the quantity of screen time. Duration is visible and easy to regulate, but two hours spent composing music and two hours spent responding to intermittent notifications are not psychologically equivalent. The structure of attention – whether it is sustained, fragmented, self-directed or externally cued – may matter as much as the number of minutes involved.

Designers sometimes defend persuasive features by noting that users can disable notifications or set limits. Such tools can help, but this defence assumes that preferences are fully formed before users encounter the product. In reality, repeated interaction can alter preferences themselves. A person may begin by choosing a feature and later find that the feature has helped create the very impulse that now sustains its use.

Recognising this feedback loop does not require treating users as powerless. People retain agency, and many deliberately redesign their digital environments. But meaningful agency is easier when systems make their influence legible. The policy challenge, then, is not simply to reduce exposure. It is to create conditions in which users can understand how interfaces shape routines and can make choices without every moment of hesitation being converted into an opportunity for capture.

Q5. The passage challenges the idea that attention is merely a fixed commodity because:

• users can increase their total daily attention through practice.
• digital environments can alter habits about what deserves attention and when.
• screen-time statistics are usually inaccurate.
• attention cannot be measured in minutes.

Q6. Why does the author contrast composing music with responding to notifications?

• To show that productive screen use should be legally exempt from limits.
• To argue that creative activity always requires digital technology.
• To illustrate that equal durations of screen use can have different attentional structures.
• To show that notifications reduce musical ability.

Q7. The defence that users can disable persuasive features is criticised mainly because it:

• ignores the possibility that repeated use can reshape the preferences on which later choices are based.
• assumes that users understand technical settings.
• underestimates the cost of mobile data.
• treats all users as equally susceptible to distraction.

Q8. Which policy approach is most consistent with the passage?

• A universal daily screen-time cap for all adults.
• A ban on all notifications from commercial applications.
• Requirements that make persuasive design effects more visible and easier for users to control.
• No intervention, because users always retain full agency.

RC Passage 3 – History and Counterfactuals

Passage difficulty: Difficult

Historians are often suspicious of counterfactual questions: What if a treaty had failed? What if a ruler had lived longer? The suspicion is understandable. Counterfactuals can become games in which imagination outruns evidence. Yet avoiding them entirely is also problematic, because causal claims about the past quietly depend on comparisons with alternatives that did not occur. To say that a drought contributed to rebellion is to imply that, other things being sufficiently similar, rebellion would have been less likely without the drought.

The responsible use of counterfactuals therefore does not require writing elaborate alternative histories. It requires making causal assumptions explicit. A good counterfactual is constrained by what contemporaries could plausibly have done and by the structural conditions they faced. The farther a hypothetical moves from those constraints, the less useful it becomes for historical explanation.

Counterfactual reasoning also exposes a tension between contingency and structure. If every event is explained as the inevitable product of long-term forces, individual choices become decorative. If every outcome is attributed to a leader’s decision or a battlefield accident, structural pressures disappear. Counterfactuals can test the balance: if changing a single decision plausibly alters the outcome, contingency mattered; if the same broad outcome remains likely across several plausible alternatives, structural forces deserve greater weight.

None of this turns history into an experimental science. We cannot rerun the past under controlled conditions. Counterfactuals are therefore not proofs; they are disciplined probes. Their value lies less in telling us what would certainly have happened than in clarifying what our explanations commit us to believe about causes.

Q9. Why does the author say that causal claims about history “quietly depend” on counterfactuals?

• Because historians usually invent alternative narratives before writing factual ones.
• Because claiming that X caused Y implies a comparison with what might have happened without X.
• Because historical archives contain descriptions of unrealised plans.
• Because causal explanations are impossible without experiments.

Q10. According to the passage, a useful historical counterfactual should be:

• dramatic enough to reveal hidden possibilities.
• limited to events involving individual leaders.
• constrained by plausible choices and actual structural conditions.
• independent of contemporary evidence.

Q11. The discussion of contingency and structure suggests that counterfactuals can:

• prove that individual decisions are more important than institutions.
• help assess how sensitive an outcome is to plausible changes in particular decisions.
• eliminate uncertainty from historical explanation.
• show that long-term forces always dominate short-term events.

Q12. The phrase “disciplined probes” most nearly implies that counterfactuals are:

• controlled experiments conducted on historical data.
• speculative stories whose entertainment value is primary.
• structured tools for testing the implications of causal explanations without providing certainty.
• methods for predicting future political events.

RC Passage 4 – Repair, Innovation and Technology

Passage difficulty: Moderate

Innovation is commonly narrated as a sequence of new inventions, but technological systems survive through an enormous amount of repair. Roads are resurfaced, software libraries are patched, machines are recalibrated, and databases are cleaned. Because repair rarely produces a dramatic “before and after,” it is easily excluded from stories of progress. Yet a society that invents rapidly and maintains poorly may experience less reliable technology than one that introduces novelty slowly but sustains what it already has.

Repair also contains knowledge. A technician who repeatedly encounters a failed component may learn more about a system’s real operating conditions than the engineer who designed it under ideal assumptions. This practical knowledge is often local, tacit and difficult to encode in formal manuals. When organisations outsource maintenance solely to reduce costs, they may save money while losing feedback that could improve future design.

There is, however, a danger in romanticising repair. Maintaining every inherited system can lock societies into inefficient infrastructure and postpone necessary replacement. The question is not whether repair is inherently superior to innovation, but how institutions decide when to maintain, adapt or abandon. Such decisions depend on costs, risks, environmental consequences and the availability of alternatives.

A fuller account of technological progress would therefore treat invention and maintenance as complementary. New designs create possibilities; maintenance determines whether those possibilities remain usable in ordinary life. The shiny prototype and the unnoticed repair log belong to the same history of technology.

Q13. The primary purpose of the passage is to:

• argue that maintenance should always receive more funding than invention.
• show that repair is an essential but under-recognised component of technological progress.
• criticise engineers for ignoring real operating conditions.
• demonstrate that old infrastructure is environmentally superior.

Q14. What is the significance of the technician example?

• It shows that formal engineering knowledge is unnecessary.
• It illustrates how maintenance work can generate operational knowledge that feeds back into design.
• It proves that outsourcing is always economically inefficient.
• It suggests technicians should replace engineers in product development.

Q15. Why does the author warn against “romanticising repair”?

• Because repair work is usually invisible.
• Because maintenance may preserve inefficient systems when replacement would be better.
• Because repaired systems are less safe than new systems.
• Because technicians resist innovation.

Q16. Which statement best captures the relationship between invention and maintenance in the passage?

• They are competing strategies and institutions must choose one.
• Maintenance is useful only after innovation has failed.
• They are complementary processes that jointly determine technological usefulness over time.
• Innovation matters for firms while maintenance matters only for governments.

Verbal Ability

Q17. [Para Summary – Moderate] Cities often add trees to reduce summer heat. Yet the cooling effect is uneven: mature trees provide more shade than saplings, water availability affects survival, and planting concentrated in already-green neighbourhoods can widen environmental inequality. Urban greening is therefore not merely a question of how many trees are planted but of where, what kind and how they are maintained.

• Tree planting is ineffective unless every neighbourhood receives the same number of mature trees.
• Urban greening should be assessed through distribution, species/age choices and long-term maintenance, not planting counts alone.
• Cities should stop planting saplings because they provide little immediate cooling.
• Environmental inequality is caused mainly by differences in water availability.

Q18. [Para Summary – Difficult] Scientific models simplify reality, but simplification is not necessarily a weakness. A map that reproduced every physical detail of a territory would be unusable as a map. The important question is whether a model omits features irrelevant to its purpose or suppresses mechanisms essential to the conclusion being drawn.

• All scientific models are unreliable because they omit details.
• A model is useful only when it reproduces reality completely.
• The quality of a simplification depends on whether what is omitted matters for the model’s intended inference.
• Maps are more reliable than scientific models because their purpose is clearer.

Q19. [Para Completion – Moderate] A language can gain speakers while losing domains of use. Families may continue to speak it at home even as schools, offices and digital services shift to another language. ________. For this reason, language vitality cannot be inferred from speaker counts alone.

• This is why multilingualism always causes language decline.
• A language may therefore remain numerically large while becoming institutionally marginal.
• Speaker counts are usually impossible to estimate.
• Schools should never teach a second language.

Q20. [Para Completion – Moderate-Difficult] Forecasts are often judged after the event as simply right or wrong. But a forecast that assigns a 30% probability to rain is not disproved when it stays dry. ________. Evaluating probabilistic forecasts therefore requires many comparable predictions, not isolated outcomes.

• The forecast was correct because rain was unlikely.
• The relevant question is whether events assigned similar probabilities occur at roughly those frequencies over time.
• Weather models should avoid percentages and give categorical answers.
• A single dry day shows that the model is poorly calibrated.

Q21. [Odd Sentence Out – Moderate] Identify the odd sentence out. Enter the letter of the sentence that does not fit the coherent paragraph.

1. Coral reefs occupy a small fraction of the ocean floor.
2. They support a remarkably high diversity of marine species.
3. Reef organisms also contribute to coastal protection by reducing wave energy.
4. Deep-sea mining requires specialised equipment designed for high pressure.
5. Damage to reefs can therefore have ecological and economic consequences.

(TITA)

Q22. [Odd Sentence Out – Difficult] Identify the odd sentence out. Enter the letter of the sentence that does not fit the coherent paragraph.

1. Archival records are shaped by decisions about what institutions considered worth preserving.
2. Historians therefore study absences in archives as well as surviving documents.
3. Digitisation can improve access to records across geographical boundaries.
4. The silence of an archive may reflect exclusion rather than the absence of historical activity.
5. Reading an archive critically requires attention to the processes that produced it.

(TITA)

Q23. [Parajumble – Difficult] Identify the odd sentence out. Enter the letter of the sentence that does not fit the coherent paragraph.

1. Yet the apparent convenience of a standard can hide the negotiations through which it was created.
2. Standards make coordination possible by allowing different actors to rely on shared specifications.
3. Once widely adopted, those specifications can appear natural rather than historically contingent.
4. Examining the history of a standard therefore reveals both technical choices and distributions of power.

Arrange the four sentences in the correct order and enter the four-letter sequence. (TITA)

1. Yet the apparent convenience of a standard can hide the negotiations through which it was created.
2. Standards make coordination possible by allowing different actors to rely on shared specifications.
3. Once widely adopted, those specifications can appear natural rather than historically contingent.
4. Examining the history of a standard therefore reveals both technical choices and distributions of power.

Q24. [Parajumble – Moderate-Difficult] Identify the odd sentence out. Enter the letter of the sentence that does not fit the coherent paragraph.

1. As a result, organisms that are rare in one season may become abundant in another.
2. Ecological surveys often provide only a snapshot of a community at a particular time.
3. Repeated sampling is therefore necessary when researchers want to distinguish persistent patterns from temporary fluctuations.
4. But many populations vary sharply with rainfall, temperature or migration.

Arrange the four sentences in the correct order and enter the four-letter sequence. (TITA)

1. As a result, organisms that are rare in one season may become abundant in another.
2. Ecological surveys often provide only a snapshot of a community at a particular time.
3. Repeated sampling is therefore necessary when researchers want to distinguish persistent patterns from temporary fluctuations.
4. But many populations vary sharply with rainfall, temperature or migration.

Section II – DILR (22 Questions)

DILR Set 1 – Research Presentations

Set difficulty: Moderate-Difficult

Five researchers – A, B, C, D and E – present one paper each in five consecutive slots numbered 1 to 5, one researcher per slot. The schedule satisfies all the following conditions:

• A presents before D.
• B presents immediately after E.
• C is not in slot 1 or slot 5.
• Exactly one presentation is scheduled between A and E.

Q25. Which researcher must present in slot 5?

• A
• B
• C
• D

Q26. If A is in slot 1, who must be in slot 3?

• B
• C
• D
• E

Q27. If C is in slot 2, which researcher is in slot 4?

• A
• B
• D
• E

Q28. [TITA] How many valid schedules satisfy all the conditions?

Q29. Which pair can occupy slots 1 and 2 respectively?

• D and A
• A and C
• B and E
• C and D

DILR Set 2 – Regional Sales

Set difficulty: Moderate

A company sold four products P, Q, R and S in three regions. The table shows units sold.

Region North: P=120, Q=150, R=90, S=140

Region West: P=160, Q=110, R=130, S=100

Region South: P=140, Q=170, R=120, S=150

Profit per unit is Rs 20 for P, Rs 25 for Q, Rs 30 for R and Rs 15 for S.

Q30. Which region recorded the highest total units sold?

• North
• West
• South
• North and South tie

Q31. Which product generated the highest total profit across all three regions?

• P
• Q
• R
• S

Q32. [TITA] What is the difference between total units of Q and total units of R?

Q33. If South sales of P increase by 25% while all else remains unchanged, what is the new total P sales?

• 440
• 445
• 450
• 455

Q34. What percentage of West-region sales were contributed by P and R together?

• 52%
• 56%
• 58%
• 60%

DILR Set 3 – Library Footfall

Set difficulty: Moderate-Difficult

A university library records visitors in four time blocks on two days. Monday: 8-10=120, 10-12=180, 12-2=150, 2-4=210. Tuesday: 8-10=150, 10-12=165, 12-2=195, 2-4=240. Of the visitors in each block, the percentage using the digital-resource room was respectively 25%, 20%, 40%, 30% on Monday and 20%, 40%, 20%, 25% on Tuesday.

Q35. Across both days, which time block had the highest total footfall?

• 8-10
• 10-12
• 12-2
• 2-4

Q36. [TITA] How many visitors used the digital-resource room on Monday?

Q37. What percentage of Tuesday visitors used the digital-resource room?

• 24%
• 25%
• 26%
• 28%

Q38. The increase in total footfall from Monday to Tuesday is approximately:

• 10.0%
• 12.5%
• 13.6%
• 15.0%

DILR Set 4 – Project Staffing

Set difficulty: Moderate

A consulting firm has 160 employees assigned to exactly one of four projects A, B, C and D. Project A has 30 employees. Project B has 50% more employees than A. Project C has 15 fewer employees than B. The remaining employees are on Project D. Women constitute 40% of A, 40% of B, 60% of C and 40% of D.

Q39. How many employees are assigned to Project D?

• 50
• 52
• 55
• 58

Q40. [TITA] How many women are assigned across all four projects?

Q41. Which project has the largest number of men?

• A
• B
• C
• D

Q42. If 5 employees move from D to A, what is the new ratio A:D?

• 5:7
• 7:10
• 7:11
• 2:3

DILR Set 5 – Scholarship Selection

Set difficulty: Moderate-Difficult

Six applicants P, Q, R, S, T and U are considered for exactly three scholarships. The selected group must satisfy: P and Q cannot both be selected; if R is selected, S must also be selected; T can be selected only if Q is selected; and at least one of P or U must be selected.

Q43. Which of the following can be the selected group?

• P, Q, U
• R, T, U
• Q, T, U
• P, R, T

Q44. If R is selected, which applicant must also be selected?

• P
• Q
• S
• U

Q45. [TITA] How many valid groups of three are possible?

Q46. If the selected group contains both Q and U, which applicant can be the third member while preserving validity?

• P only
• R only
• S or T
• R or T

Section III – Quantitative Ability (22 Questions)

Q47. [Moderate] A retailer buys an item for Rs 840 after receiving a 30% trade discount on its list price. He sells it at the original list price. His profit percentage on cost is:

• 40%
• 42 6/7%
• 45%
• 50%

Q48. [Easy] [TITA] A class has 18 students with average marks 64 and 12 students with average marks 76. What is the average mark of the whole class?

Q49. [Moderate] A person spends 75% of income. Income rises by 20% while expenditure rises by 12%. By what percentage do savings increase?

• 36%
• 40%
• 44%
• 48%

Q50. [Moderate] For real x, the expression (x-3)^2 + (x-7)^2 has minimum value:

• 4
• 6
• 8
• 10

Q51. [Easy] [TITA] What is the least positive integer n such that 2^n is divisible by 64 and n is divisible by 3?

Q52. [Moderate] Three consecutive positive integers have product 336. What is their sum?

• 19
• 20
• 21
• 22

Q53. [Moderate] The coordinates of a triangle are (1,2), (7,2) and (4,8). Its area is:

• 15 sq units
• 18 sq units
• 21 sq units
• 24 sq units

Q54. [Moderate] [TITA] A number leaves remainder 5 when divided by 7 and remainder 3 when divided by 5. What is the least such positive number?

Q55. [Moderate] The ratio of present ages of A and B is 4:5. After 8 years it becomes 6:7. What is B’s present age?

• 20
• 24
• 28
• 32

Q56. [Easy] For positive x, if (x-2)/(x+2)=1/3, then x equals:

• 3
• 4
• 5
• 6

Q57. [Moderate] [TITA] How many three-digit numbers have digit sum 6?

Q58. [Moderate] Two taps fill a tank independently in 20 minutes and 30 minutes. A drain empties the full tank in 60 minutes. If all three are opened together, how long will the empty tank take to fill?

• 12 min
• 15 min
• 18 min
• 20 min

Q59. [Easy] The maximum value of -x^2 + 8x – 7 is:

• 7
• 8
• 9
• 10

Q60. [Easy] Points A(2,3) and B(8,11) are joined. The length AB is:

• 8
• 10
• 12
• 14

Q61. [Easy] [TITA] If 3^x = 27^(x-2), find x.

Q62. [Moderate] A sum amounts to Rs 13,310 in 2 years at 10% compound interest per annum. The principal was:

• Rs 10,000
• Rs 10,500
• Rs 11,000
• Rs 12,000

Q63. [Moderate] If a, b, c are positive and ab=12, bc=18, ca=24, then abc equals:

• 72
• 108
• 144
• 216

Q64. [Easy] The sum of the first n positive integers is 210. What is n?

• 19
• 20
• 21
• 22

Q65. [Moderate] [TITA] How many two-digit positive integers have their tens digit greater than their units digit?

Q66. [Moderate] A quadratic equation x^2 – px + 12 = 0 has integer roots differing by 1. What is p?

• 7
• 8
• 9
• 10

Q67. [Moderate] A cone and a cylinder have the same base radius and equal volumes. If the cylinder height is 8 cm, the cone height is:

• 8 cm
• 16 cm
• 20 cm
• 24 cm

Q68. [Easy] [TITA] The positive solution of |2x-5|=9 is:

 

 

Answer Key

Q	Ans	Q	Ans	Q	Ans	Q	Ans
1	B	18	C	35	D	52	C
2	C	19	B	36	189	53	B
3	B	20	B	37	C	54	33
4	C	21	D	38	C	55	A
5	B	22	C	39	C	56	B
6	C	23	BACD	40	70	57	21
7	A	24	BDAC	41	D	58	B
8	C	25	D	42	B	59	C
9	B	26	D	43	C	60	B
10	C	27	B	44	C	61	3
11	B	28	2	45	5	62	C
12	C	29	B	46	C	63	A
13	B	30	C	47	B	64	B
14	B	31	B	48	68.8	65	45
15	B	32	90	49	C	66	A
16	C	33	D	50	C	67	D
17	B	34	C	51	6	68	7

 

Detailed Solutions

RC Passage 1 – Measuring What Matters

Q1. Answer: B. The passage defends measurement but argues that metrics must remain provisional and interpreted with judgement.

Q2. Answer: C. The second paragraph explicitly describes optimisation of the measured number rather than the real goal.

Q3. Answer: B. The third paragraph warns that complexity can create false confidence and reduce auditability.

Q4. Answer: C. The examples demonstrate behavioural distortion caused by incentives tied to proxies.

RC Passage 2 – The Ecology of Attention

Q5. Answer: B. The author argues that platforms shape habits of noticing, not merely consume a fixed stock of attention.

Q6. Answer: C. The contrast supports the claim that quality and structure of attention matter, not only duration.

Q7. Answer: A. The third paragraph focuses on endogenous preferences shaped by repeated interaction.

Q8. Answer: C. The final paragraph argues for legibility and conditions that support meaningful agency.

RC Passage 3 – History and Counterfactuals

Q9. Answer: B. A causal claim implicitly contrasts the observed world with a plausible world in which the proposed cause is absent.

Q10. Answer: C. The second paragraph sets exactly these constraints.

Q11. Answer: B. Sensitivity to plausible changes helps weigh contingency versus structure.

Q12. Answer: C. The final paragraph explicitly distinguishes probes from proofs.

RC Passage 4 – Repair, Innovation and Technology

Q13. Answer: B. The passage broadens the standard innovation narrative by highlighting maintenance and repair.

Q14. Answer: B. The example shows repair as a source of local, practical knowledge.

Q15. Answer: B. The third paragraph explicitly notes lock-in and delayed replacement.

Q16. Answer: C. The conclusion describes them as complementary.

Verbal Ability Solutions

Q17. Answer: B. The paragraph argues for evaluating greening beyond raw planting counts, including distribution and maintenance.

Q18. Answer: C. The key distinction is between harmless simplification and omission of causally important features.

Q19. Answer: B. The missing sentence must connect home use with institutional decline and lead to the conclusion about speaker counts.

Q20. Answer: B. Calibration is assessed across repeated forecasts, matching predicted probabilities to observed frequencies.

Q21. Answer: D. A, B, C and E form a coherent paragraph about coral reefs; D shifts to deep-sea mining.

Q22. Answer: C. A, B, D and E concern archival silences and production; C concerns access via digitisation.

Q23. Answer: BACD. B introduces standards; A contrasts convenience with hidden negotiations; C follows adoption; D concludes with why history matters.

Q24. Answer: BDAC. B introduces snapshot surveys; D contrasts with seasonal variation; A gives the consequence; C concludes with repeated sampling.

DILR Solutions

DILR Set 1 – Research Presentations

Q25. Answer: D. Both feasible schedules place D in slot 5.

Q26. Answer: D. Exactly one slot lies between A and E, so E is in slot 3.

Q27. Answer: B. The only feasible schedule with C in slot 2 is A-C-E-B-D, so B is in slot 4.

Q28. Answer: 2. Direct enumeration gives two schedules: A-C-E-B-D and E-B-A-C-D.

Q29. Answer: B. A-C appears in one valid schedule; the other pairs do not.

DILR Set 2 – Regional Sales

Q30. Answer: C. Totals are North 500, West 500 and South 580.

Q31. Answer: B. Total profits are P=8400, Q=10750, R=10200 and S=5850. Therefore Q is highest.

Q32. Answer: 90. Q totals 430 and R totals 340; difference 90.

Q33. Answer: D. South P rises from 140 to 175. New total =120+160+175=455.

Q34. Answer: C. West total=500; P+R=290; percentage=58%.

DILR Set 3 – Library Footfall

Q35. Answer: D. Combined footfalls are 270, 345, 345 and 450 respectively, so 2-4 is highest.

Q36. Answer: 189. Monday digital users: 25% of 120=30, 20% of 180=36, 40% of 150=60, and 30% of 210=63; total=189.

Q37. Answer: C. Tuesday digital users=30+66+39+60=195. Total Tuesday footfall=750, so percentage=26%.

Q38. Answer: C. Monday total=660, Tuesday total=750; increase=90/660=13.64%.

DILR Set 4 – Project Staffing

Q39. Answer: C. B=45, C=30; D=160-105=55.

Q40. Answer: 70. Women: A12, B18, C18, D22; total 70.

Q41. Answer: D. Men: A18, B27, C12, D33; D is largest.

Q42. Answer: B. A=35, D=50, ratio 7:10.

DILR Set 5 – Scholarship Selection

Q43. Answer: C. Q-T-U satisfies all conditions; each other option violates at least one rule.

Q44. Answer: C. The rule explicitly requires S whenever R is selected.

Q45. Answer: 5. The valid groups are P-R-S, P-S-U, Q-S-U, Q-T-U and R-S-U: five in total.

Q46. Answer: C. With Q and U fixed, P is forbidden. R would require S as a fourth person. Either S or T can be the third member.

QA Solutions

Q47. Answer: B. The list price is 840/0.70 = Rs 1200. Profit=360, so profit percentage=360/840 x 100=42 6/7%.

Q48. Answer: 68.8. Combined average=(18×64+12×76)/30=2064/30=68.8.

Q49. Answer: C. Let income=100, expenditure=75, savings=25. New income=120, expenditure=84, savings=36. Savings rise by 11/25=44%.

Q50. Answer: C. The expression is minimized at the midpoint x=5, giving 2^2+(-2)^2=8.

Q51. Answer: 6. 2^n divisible by 64=2^6 requires n≥6; smallest multiple of 3 is 6.

Q52. Answer: C. 6x7x8=336, so the sum is 21.

Q53. Answer: B. The base from (1,2) to (7,2) is 6 and the perpendicular height is 6. Area=1/2 x 6 x 6=18.

Q54. Answer: 33. Numbers 5 mod 7: 5,12,19,26,33; 33 is 3 mod 5.

Q55. Answer: A. Let ages 4x,5x. (4x+8)/(5x+8)=6/7 =>28x+56=30x+48 =>x=4, B=20.

Q56. Answer: B. 3x-6=x+2, so 2x=8 and x=4.

Q57. Answer: 21. Count a+b+c=6 with a≥1. Put a’=a-1: a’+b+c=5. Unrestricted nonnegative count C(7,2)=21; upper bounds do not bind.

Q58. Answer: B. Net rate=1/20+1/30-1/60=1/15, so the tank fills in 15 minutes.

Q59. Answer: C. Complete square: -(x-4)^2+9, maximum 9.

Q60. Answer: B. Distance=sqrt((8-2)^2+(11-3)^2)=sqrt(100)=10.

Q61. Answer: 3. 27=3³, so x=3x-6 => x=3.

Q62. Answer: C. P x 1.1^2=13310, hence P=11000.

Q63. Answer: A. (abc)²=(ab)(bc)(ca)=12×18×24=5184, hence abc=72.

Q64. Answer: B. n(n+1)/2=210 => n²+n-420=0 => n=20.

Q65. Answer: 45. For tens digit a=1 to 9, the unit digit has a choices (0 to a-1). Total=1+2+…+9=45.

Q66. Answer: A. Factor pairs of 12 differing by 1 are 3 and 4; p=sum=7.

Q67. Answer: D. (1/3)pi r^2 h = pi r^2 x 8, so h=24 cm.

Q68. Answer: 7. 2x-5=9 gives x=7; the other solution is -2.