XAT 2022 Question Paper with Answer Key PDFs (January 2)

The poem narrates a situation where two strangers mistakenly smile at each other and momentarily feel a sense of connection, which seems like love. Let us evaluate each option carefully:

(A) We make mistakes in love: Correct inference. The poem shows that both individuals were mistaken from the very beginning, indicating love can arise out of mistakes.
(B) We fall in love with strangers: Correct inference. The poem clearly depicts two strangers in a library experiencing feelings that resembled love.
(C) Love may start with small acts like glancing and smiling: Correct inference. The entire episode began with a mistaken smile, showing how small gestures can spark emotions.
(D) The idea of love is different for the parties involved: Correct inference. The speaker doubts whether it was truly love at all, while the other person seemed convinced—hence different perceptions.
(E) We don’t fall in love with others but with ourselves: This cannot be inferred. The poem never suggests self-love or narcissism; it only reflects mistaken identity and mismatched emotions.

Thus, option (E) is the correct answer since it cannot be inferred from the poem.
\[ \boxed{(E) \text{We don’t fall in love with others but with ourselves}.} \] Quick Tip: When solving inference-based questions, carefully separate what is directly or indirectly supported by the text from what is an overgeneralization or unrelated interpretation. Always check if the claim goes beyond what the passage suggests.

Let us examine each sentence carefully for grammatical correctness:

Sentence 1: “Have you any clothes to dispose of?” – This is correct. The construction “Have you any …?” is formal but grammatically acceptable.
Sentence 2: “I saw a pleasant dream last night.” – Incorrect. In English, we usually say “I had a pleasant dream” rather than “saw a dream.”
Sentence 3: “I have done it many a times safely.” – Incorrect. The correct idiom is “many a time” (singular), not “many a times.”
Sentence 4: “Students struggle to cope up with academic pressure.” – Incorrect. The correct usage is “cope with,” not “cope up with.”
Sentence 5: “You need not give negative feedback to your employees.” – Correct. The use of “need not” is grammatically sound.
Sentence 6: “My friend is good at playing football.” – Correct. The preposition “at” is properly used with “good at.”

Hence, the grammatically correct sentences are 1, 5, and 6.

\[ \boxed{(B) 1, 5, 6} \] Quick Tip: Always pay attention to idiomatic usage in English. Phrases like “cope with,” “have a dream,” and “many a time” follow fixed patterns that must be memorized to avoid errors.

The context stresses that the three technologies were not initially planned and their importance was not recognized immediately.

- (A) "Astonishing, Superb" does not match the tone of "unplanned."
- (B) "Fulfilling/Unfulfilling" relates to satisfaction, not discovery.
- (C) "Unpredicted, Unappreciated" correctly conveys that they were not expected and undervalued at first.
- (D) "Amazing, Shocking" implies surprise, but not undervaluation.
- (E) "Astonishing, Amazing" is repetitive and fails to capture the idea of being underestimated.

Thus, the best choice is option (C).
\[ \boxed{(C) Unpredicted, Unappreciated, Unappreciated} \]

Quick Tip: When filling blanks, look for words that match both tone and context. Here, “unplanned” aligns best with “unpredicted” and “unappreciated.”

The statement emphasizes the danger of dictatorship without free press. Let us evaluate:

- (A) "Unpleasant, plebeians, fact, forced" does not fit logically.
- (B) "Absurd, subjects, beauty" creates incoherence with the context.
- (C) "Necessary, citizens, joy" clashes with the negative tone.
- (D) "Possible, people, consequence, constantly" perfectly conveys that dictatorship becomes possible when people are uninformed, leading to consequences, and lies must be constantly changed.
- (E) "Unique, senators, reason, enough" is illogical.

Hence, option (D) is the correct one.
\[ \boxed{(D) \text{Possible, people, consequence, constantly}} \] Quick Tip: Always ensure the sequence of blank fillers maintains logical flow and tone of the passage. Words must complement both meaning and grammar.

The passage highlights that mass extinctions appear around the same geological cycle of 27.5 million years, aligning with a "pulse" in geological events.

- (A) Wrong: "sporadically" contradicts the identified cycle.
- (B) Misleading: The passage does not say species avoid extinction; it only emphasizes correlation.
- (C) Correct: The key conclusion is correlation between “geological pulse” and “mass extinctions.”
- (D) Incorrect: The cycle is approximate (26.2 to 30.6 million years), not strictly constant.
- (E) Wrong: Not all species go extinct, only many during mass extinctions.

Thus, the best conclusion is option (C).
\[ \boxed{(C) Mass extinctions and “geological pulse” are correlated} \] Quick Tip: When asked to conclude, focus on the main relationship or correlation described in the passage, not absolute statements.

Let us check the preposition usage in each sentence:

Sentence 1: “The manager was sitting at the desk.” – Correct. The preposition “at” is used properly here.
Sentence 2: “My work is superior to yours.” – Correct. The phrase “superior to” is the standard usage.
Sentence 3: “I prefer coffee than tea.” – Incorrect. The correct form is “prefer coffee to tea.”
Sentence 4: “She was accused for stealing gold.” – Incorrect. The proper phrase is “accused of stealing.”
Sentence 5: “This is an exception to the rule.” – Correct. The idiom “exception to” is correct.
Sentence 6: “They are leaving to England soon.” – Incorrect. We say “leaving for England,” not “to England.”

Therefore, sentences 3, 4, and 6 have incorrect preposition usage.

\[ \boxed{(C) 3, 4, 6} \] Quick Tip: Prepositions in English often follow fixed collocations, e.g., “prefer to,” “accused of,” “superior to,” “leave for.” Memorizing these is key to avoiding errors.

The poem describes a speaker who sacrificed her identity (“gave up a kingdom,” “once I had a voice”) for love, only to face pain and doubt about whether it was worth it.

- (A) Correct: The essence of the poem is that love comes with sacrifice and pain, showing regret after transformation.
- (B) Incorrect: The poem does not focus on nostalgia undermining materialism.
- (C) Incorrect: While identity loss is mentioned, the main theme is the painful trade-off in pursuit of love.
- (D) Incorrect: The poem is not about future versus past, but about regret.
- (E) Incorrect: The concern is not about quantity of loss versus gain, but the emotional cost of love.

Thus, the theme is best reflected by option (A).

\[ \boxed{(A) Our quest for love is accompanied with pain.} \] Quick Tip: In poetry-based questions, focus on the dominant emotional undertone (regret, sacrifice, pain, hope, etc.) rather than secondary details.

The lines “Once I had a voice. Now I have legs” are metaphorical and reflect transformation at the cost of identity. The poet/speaker reflects on a shift from expression (voice) to action/physical existence (legs). This shows contemplation and regret about the trade-off.

- (A) Incorrect: It does not show value judgment about the new world.
- (B) Correct: It reflects the poet’s contemplation about identity and sacrifice.
- (C) Incorrect: The line is not about actions being louder than words.
- (D) Incorrect: The poet is not indecisive, but regretful.
- (E) Incorrect: The phrase is symbolic, not literal loss of speech.

Thus, the poet is reflecting on identity and transformation, making option (B) correct.

\[ \boxed{(B) The poet is contemplative of his/her identity} \] Quick Tip: In poetry-based questions, look for symbolic meaning rather than literal interpretation. Words like “voice” and “legs” represent identity, sacrifice, and transformation.

To form a logical sequence, let us analyze step by step:

- (2) introduces the topic: the harm caused by school closures is becoming evident.
- (1) gives statistical evidence (America’s pupils falling behind).
- (4) expands globally, pointing out worse effects in countries like India and Mexico.
- (5) provides background: even before the pandemic, parents were willing to pay for extra lessons.
- (3) concludes with a prediction: the crisis will accelerate that trend.

Thus, the coherent flow is 2 → 1 → 4 → 5 → 3.

\[ \boxed{(B) 2,1,4,5,3} \] Quick Tip: When arranging sentences, look for a general introduction first, followed by evidence, expansion, background, and finally prediction or conclusion.

The difference between Hedonic and Eudaimonic approaches is clear:

- Hedonic = pleasure-seeking and self-centered happiness.
- Eudaimonic = fulfillment through meaningful contribution, focusing on the greater good and society.

- (A) Incorrect: Eudaimonic does not mean depriving oneself.
- (B) Correct: Captures the essence — Hedonic = pleasure to self, Eudaimonic = benefit to society.
- (C) Incorrect: Emptiness vs fulfillment is too vague.
- (D) Incorrect: Misrepresents the cause-effect relationship.
- (E) Incorrect: Oversimplified repetition of pleasure-based distinction.

Thus, the best contrast is option (B).

\[ \boxed{(B) Hedonic focuses on pleasure to self, Eudaimonic on benefit to society} \] Quick Tip: In philosophy-based MCQs, always separate self-focused vs society-focused dimensions — Hedonic = self-pleasure, Eudaimonic = purpose/meaning.

The passage describes “psychologically rich life” as involving interesting, novel, and complex experiences that transform one’s perspective.

- (A) Incorrect: Fun/joy relate to Hedonic life, not psychological richness.
- (B) Correct: Matches the definition given in the passage by Shige Oishi and Erin Westgate.
- (C) Incorrect: Too narrow (focuses only on expertise, not richness).
- (D) Partially correct but incomplete — does not emphasize “complexity + perspective change.”
- (E) Incorrect: Not every novel experience qualifies, only those with significant impact on perspective.

Thus, option (B) is the best definition.

\[ \boxed{(B) Life with novelty, complexity, and perspective change = Psychologically rich} \] Quick Tip: Pay attention to exact wording in the passage. Keywords like “novelty,” “complexity,” and “changes in perspective” are central clues to the correct answer.

The passage highlights that psychological richness comes from varied experiences, including difficult or unpleasant ones, as long as they provide novelty and alter perspective.

- (A) Partially true, but too specific — enrichment is broader than just “bad experiences.”
- (B) Incorrect: Misleading. “Unpleasant” ≠ guarantee of a “good life.”
- (C) Correct: Directly supported. Life can be psychologically rich without necessarily being “good” or “happy.”
- (D) Incorrect: Equates psychological richness with a good life, which the passage avoids.
- (E) Too vague/general, not the central conclusion.

Thus, the conclusion is option (C).

\[ \boxed{(C) Life need not be good, but can still be psychologically rich} \] Quick Tip: When drawing conclusions, avoid absolute or oversimplified statements. Choose the option that aligns directly with the passage’s nuanced claim.

In the given excerpt, the focus is on how people have been conditioned or indoctrinated into their beliefs and how this lack of reflection leads to uncritical thinking. Let's analyze the options:

- (A) Things that we do automatically need to be reflected upon: The excerpt suggests that people are unreflective thinkers, meaning they often do things without deep thought or reflection. This statement is supported by the excerpt, so it can be concluded.
- (B) A lot of people end up believing what they passionately oppose: This statement cannot be concluded directly from the excerpt. While the excerpt speaks about how people are conditioned into beliefs, it does not mention that people end up believing things they oppose. The excerpt doesn't provide support for this idea, so this is the correct answer.
- (C) Beliefs that appear normal and natural heighten their acceptance: This is implied in the excerpt. When beliefs appear normal or natural, people are more likely to accept them without questioning, as they are socially conditioned.
- (D) A normal thinker finds it difficult to recognize what is happening to them: This statement is consistent with the excerpt, as it suggests that unreflective thinkers (those who are conditioned by society) struggle to see the processes that influence their beliefs.
- (E) The inability to criticize one’s belief leads to indoctrination: The excerpt clearly discusses how people are socially conditioned into their beliefs, and an inability to criticize one's beliefs could indeed lead to indoctrination, which aligns with the passage.

Thus, the statement B is the one that cannot be concluded from the excerpt, and the correct answer is (B).

\[ \boxed{B} \] Quick Tip: To succeed in critical thinking, it’s important to reflect on the beliefs and ideas we hold, rather than simply accepting them as truths without examination.

The Swiss Cheese model highlights that disasters occur when multiple failures align without resistance. If even one layer blocks the chain, catastrophe is prevented.

- (A) Incorrect: It does not imply it is “easier than it seems,” only that resistance at one layer can avert disaster.

- (B) Correct: Captures the core idea — catastrophe can be stopped if resistance occurs in the chain of events.

- (C) Partially true: While disasters are indeed a culmination of events, the passage emphasizes prevention, not inevitability.

- (D) Incorrect: The passage clearly states that accidents can be averted if resistance occurs.

- (E) Incorrect: Overgeneralizes; not every historical event is an accident.


Thus, the best conclusion is option (B).

\[ \boxed{(B) \text{A catastrophe can be averted if the preceding array of events meets resistance}} \] Quick Tip: In passage-based questions, focus on the central analogy (here, Swiss Cheese model). It explains that preventing even one step in a chain of events can avert a disaster.

The passage explains that:

- A liar knowingly misrepresents the truth with intent to deceive.

- A bullshitter, on the other hand, is indifferent to the truth or falsity but still deceives us about his enterprise (i.e., what he wants us to believe about him or his purpose).

Thus, both are deceptive, but in distinct ways.

\[ \boxed{(E) Both the liar and the bullshitter intend to deceive in their own ways} \] Quick Tip: Remember: Liars distort the truth deliberately, bullshitters ignore the truth altogether but still deceive about themselves or their motives.

The author highlights that a bullshitter’s defining trait is indifference to truth or falsity.

- He does not aim to report what is true.

- He does not attempt to conceal truth either.

- His concern is only with creating the impression he wants.

Thus, the correct reason is option (A).

\[ \boxed{(A) Because he does not know or care about the truth} \] Quick Tip: Differentiate: Liars = concerned with truth but distort it. Bullshitters = unconcerned with truth, indifferent to it.

The passage emphasizes that the bullshitter’s primary task is to project an impression, irrespective of truth or falsehood.

- (A) and (D): These describe liars, not bullshitters.

- (B) and (C): Secondary outcomes, not the central aim.

- (E): Correct. A bullshitter’s aim is to make us believe what he/she wants, without focusing on truth or lies.

\[ \boxed{(E) Present what he/she wants us to believe rather than focus on telling lies} \] Quick Tip: When reading philosophy-based RC, separate intent vs method. For bullshitters, intent = control audience’s belief; method = indifference to truth.

Let us analyze each sentence carefully:


Sentence 1: “If Sandhya had started from the hotel on time, she would have not missed the flight.” – Correct. It expresses a third conditional (past perfect + would have). Slightly better phrased as “would not have missed,” but still acceptable.


Sentence 2: “The students wouldn’t have completed their assignment even if the professor would have been there.” – Incorrect. In conditional clauses, we use “had been” (past perfect), not “would have been.” Correct form: “…even if the professor had been there.”


Sentence 3: “I had travelled across Europe if I weren’t afraid of airplane crashes.” – Incorrect. The main clause verb “had travelled” is wrong; it should be conditional perfect: “I would have travelled across Europe if I weren’t afraid of airplane crashes.”


Sentence 4: “Saurav won’t join music classes unless his father will ask him.” – Incorrect. In English, after “unless,” we use present simple to indicate future condition. Correct form: “unless his father asks him.”


Sentence 5: “Should you wish to join the party, you must let me know by this evening.” – Correct. This is a formal inversion equivalent to “If you should wish…,” and is grammatically sound.


Sentence 6: “We would be stupid if we shared our strategy with her.” – Correct. This is a proper second conditional sentence (would + past simple).


Thus, the incorrect sentences are 2, 3, and 4.

\[ \boxed{(B) 2,3,4} \] Quick Tip: For conditional sentences: - Use past perfect in “if” clauses for third conditionals (If + had + past participle). - Avoid “would” in the “if” part; it belongs only in the main clause. - After “unless,” use present simple for future reference.

The concept of a “public person” in the passage refers to an individual whose work influences, informs, or raises awareness for society at large.

- (A) Correct: A wildlife photographer drawing attention to the struggles of migrants is clearly working in the public sphere, reaching and impacting society.

- (B) Incorrect: While important, a personal campaign against fraud is not essentially “public person” work.

- (C) Incorrect: The NGO employee was tasked, meaning it is part of his job, not a broader public initiative.

- (D) Incorrect: A parent protesting a school fee hike is a local concern, not necessarily qualifying as a public role.

- (E) Incorrect: Though socially useful, a politician’s RTI filing falls under political responsibility, not an independent “public person” role.


Thus, the best categorisation is option (A).

\[ \boxed{(A) Wildlife photographer raising awareness about migrants} \] Quick Tip: A “public person” usually goes beyond private or organizational roles and influences the larger public sphere through awareness, advocacy, or social contribution.

The passage distinguishes “public action” as an act aimed at justice or larger social good, even if it goes against conventional societal acceptance.

- (A) Incorrect: This stresses balancing personal beliefs with society’s views, which may dilute the idea of bold public action.

- (B) Correct: Best captures the essence—public action means working for a just cause without worrying about social approval.

- (C) Incorrect: Anti-social actions are not equated with public action in the passage.

- (D) Close, but too general. It stresses conviction, but not the justice-oriented aspect of public action.

- (E) Incorrect: This makes it conformity-driven, opposite of true public action.


Thus, option (B) is the correct description.

\[ \boxed{(B) Acting for a just cause regardless of what society thinks about it} \] Quick Tip: “Public action” focuses on justice and larger social good, not conformity or personal convenience. It often challenges societal norms for the right cause.

The key idea is that human behaviour in public is shaped by social dependence and the need for acceptance. Let’s analyze each option:


- (A) Incorrect: While survival is a concern, the passage stresses interdependence, not just survival vs flourishing.

- (B) Incorrect: Cooperation is important, but the question asks specifically about behaviour vs public action.

- (C) Correct: Dependence on each other makes us prioritize socially acceptable behaviour, which explains why behaviour dominates over public action.

- (D) Incorrect: Fear of being called out is a partial explanation but not the most fundamental one.

- (E) Incorrect: The statement is vague and not directly related to behaviour in public.


Thus, option (C) provides the most accurate reason.

\[ \boxed{(C) We are dependent on each other, leading to focus on what is accepted by others} \] Quick Tip: When distinguishing between “behaviour” and “public action,” remember that behaviour is often conformity-driven due to interdependence, while public action requires stepping beyond societal approval.

The author emphasizes that stupidity arises when we blindly use old, familiar solutions to tackle new or unfamiliar problems without adapting to the new context. Let’s examine each option carefully:


(A) Incorrect: Applying our world view to comprehend is not always stupidity; it is natural. Stupidity occurs when we refuse to adapt solutions.
(B) Incorrect: While forcing our current views is problematic, the author highlights solutions, not just views.
(C) Correct: The exact description matches the passage — pushing an existing solution onto a new, alien problem reflects true stupidity.
(D) Incorrect: Novelty of a problem may challenge us, but it is not stupidity in itself.
(E) Incorrect: Inability to comprehend is ignorance, not stupidity. Stupidity comes from misapplying old solutions.


Hence, option (C) directly captures the author’s stance.
\[ \boxed{(C) Pushing our extant solution to fix an alien problem is stupidity} \] Quick Tip: In comprehension questions, focus on the subtle difference between ignorance and stupidity — ignorance is not knowing, while stupidity is misapplying knowledge inappropriately.

The question is about the paradox — why can intelligence and stupidity coexist in the same person? Let us examine step by step:


(A) Incorrect: The definition of intelligence being vague does not directly explain why intelligent people can act stupidly.
(B) Incorrect: While it links intelligence to rationalization, it does not clearly connect to the author’s view that past successes mislead us.
(C) Correct: The passage stresses that prior achievements make intelligent people overconfident, so they assume they can explain or solve any problem — leading to errors. This is why stupidity and intelligence are “perfectly compatible.”
(D) Incorrect: Fear and rushing to explain are not emphasized in the passage.
(E) Incorrect: Avoiding admission of ignorance may be true, but it is not the main reason given by the author.


Thus, option (C) directly captures the reasoning from the passage.
\[ \boxed{(C) Past successes make us believe that we are intelligent and capable of explaining any new phenomenon} \] Quick Tip: Remember: Overconfidence from past successes often blinds intelligent people, making them vulnerable to errors — this is the key link between intelligence and stupidity.

Let us carefully analyze the reasoning step by step:


Step 1: Understanding the author’s message

The author highlights that stupidity arises when leaders or intelligent people assume that their present solutions will work universally, even in future or different contexts. The key to avoiding stupidity is awareness of the limitations of our present answers.


Step 2: Elimination of incorrect options

% Option
(A) Incorrect: Merely discussing with everyone does not guarantee wisdom; it may still lead to collective stupidity.

% Option
(B) Incorrect: Simply waiting until the future unfolds is impractical and not a solution suggested by the author.

% Option
(D) Incorrect: Resource shortage is unrelated to the issue of stupidity discussed in the passage.

% Option
(E) Incorrect: While related to handling the future, the author stresses awareness of context, not entirely new tools.


Step 3: Choosing the BEST option

% Option
(C) is correct because the author emphasizes that recognizing the contextual nature of current answers prevents overgeneralization, which is the root of stupidity.

\[ \boxed{(C) Being aware that our current answers are only applicable to the current context} \] Quick Tip: Leaders should remember: solutions are context-bound. Recognizing limits of present answers prevents overconfidence and poor decision-making.

Step 1: Key idea of the passage

The author differentiates between labour and work.

- Labour: basic survival activities like eating, keeping healthy, reproducing — necessary but not special.

- Work: meaningful activities that create something lasting, contributing collective value and order.


Step 2: Evaluating the options

% Option
(A) Incorrect – This splits the distinction into health vs. making others healthy, which is not the author’s argument.

% Option
(B) Incorrect – Limiting labour to role-fulfilment and work to going beyond is not mentioned in the passage.

% Option
(D) Incorrect – Examples like terrace gardening vs. vaccine creation are not drawn in the passage.

% Option
(E) Incorrect – The distinction is not based on acknowledgement but on survival vs. meaningful contribution.


Step 3: Correct choice

% Option
(C) Correct – This matches exactly: labour ensures survival, while work provides meaning to that survival.
\[ \boxed{(C) Labour enables us to survive while work makes survival meaningful} \] Quick Tip: Remember: In RC passages, focus on the author’s core contrast or distinction (here, survival vs. meaning) and avoid being distracted by options with added interpretations.

Link the discourse markers

- “But” in (1) signals a contrast to a prior stance and so works as an opener for the set.

- \(\textit{“This is less inconsistent …”}\) in (4) must refer back to the apparent inconsistency introduced in (1) \(\Rightarrow\) (4) follows (1).

- (5) provides the \(\textit{reason that resolves the inconsistency}\) in (4) (training time: HGV driver vs coder) \(\Rightarrow\) (5) after (4).

- (3) contains \(\textit{“the latter,”}\) which can only refer to coder from (5); hence (5) \(\rightarrow\) (3).

- (2) begins with \(\textit{“As a result,”}\) so it must conclude from the demand point in (3); therefore (3) \(\rightarrow\) (2).


Thus the coherent chain is: 1 \(\rightarrow\) 4 \(\rightarrow\) 5 \(\rightarrow\) 3 \(\rightarrow\) 2.

\[ \boxed{(C) 1, 4, 5, 3, 2} \] Quick Tip: Use pointer words—but, this, the latter, as a result}—as anchors. They fix local orderings that typically force the global sequence.

Step 1: Identify Dileep’s core value proposition.

He attracts hospital staff because of affordable pricing: Rs. 25 (plain) and Rs. 40 (masala). His sales volumes (300–400 dosas daily) rely on this affordability.

Step 2: Assess each option.

% Option
(A) No other dosa stall \(\Rightarrow\) advantage due to no direct competition.

% Option
(B) Closing at 10:30 pm vs midnight \(\Rightarrow\) small deterrent, but his main sales are during breakfast/lunch, so effect is limited.

% Option
(C) Large daily footfall \(\Rightarrow\) a positive factor, not a deterrent.

% Option
(E) Presence of North Indian meals \(\Rightarrow\) differentiates his South Indian dosas, which is again positive.

% Option
(D) Cheapest dish priced at Rs. 200 \(\Rightarrow\) creates a fundamental mismatch. Dileep’s prices are far below the norm, which may make his stall appear out of place in a premium-priced food court. Alternatively, raising his prices to match the environment would alienate his loyal hospital staff customers. This strikes directly at his business model and customer base.

\[ \boxed{(D) is the strongest reason that will dissuade him from shifting stalls.} \] Quick Tip: When solving decision-making RCs, identify the entrepreneur’s core advantage} (pricing, convenience, or target audience). The fact that undermines this core advantage will usually be the dissuader.

Step 1: Recall the original success formula.

Earlier, his dosas sold well because they were reasonably priced at Rs. 25 and Rs. 40. Staff perceived this as affordable, hence the strong volumes (300–400 dosas/day).

Step 2: Identify why sales dropped.

By increasing prices to Rs. 40 and Rs. 60, Dileep lost his affordability edge. Staff, his main clientele, now buy fewer dosas (150/day). The mismatch is clear: he abandoned his core advantage.

Step 3: Evaluate options.

% Option
(A) Raising prices + premium dish \(\Rightarrow\) worsens affordability issue.

% Option
(B) Price discrimination (20% lower for staff, 50% higher for others) \(\Rightarrow\) alienates non-staff, unfair perception.

% Option
(C) Introducing North Indian meals \(\Rightarrow\) dilutes brand identity, weakens dosa focus.

% Option
(D) Limiting to a South Indian meal at Rs. 40 \(\Rightarrow\) doesn’t address broader affordability or variety needs.

% Option
(E) Reducing dosa prices to the earlier affordable levels + adding premium variants \(\Rightarrow\) protects staff demand (core clientele) while also tapping higher-paying customers who want variety. This balances volume and revenue.

\[ \boxed{(E) is best: restore affordable dosa prices while expanding offerings for higher-paying customers.} \] Quick Tip: In decision-making questions, always compare options with the original success driver}. The correct choice usually revives that driver while adding new strengths.

Step 1: Clarify the problem.

General visitors avoid his stall because it looks like a “staff-only” canteen. His loyal customer base (hospital staff) unintentionally deters other customers.

Step 2: Desired solution.

He must:
1. Retain staff sales (since they are loyal and dependable).

2. Reduce staff’s physical presence at his stall so that outsiders feel welcome.

3. Attract general visitors by changing stall perception.


Step 3: Evaluate options.

% Option
(A) Moving to a staffroom counter \(\Rightarrow\) completely removes him from public eye, reducing visitor access.

% Option
(B) Offering massive discounts \(\Rightarrow\) unsustainable; also attracts more staff, worsening crowding.

% Option
(D) Charging staff premium \(\Rightarrow\) alienates core customers and reduces loyalty.

% Option
(E) Requesting a ban on staff entry \(\Rightarrow\) impractical and hostile to his strongest customer base.

% Option
(C) Delivering to staffroom at a discount \(\Rightarrow\) win–win: staff keep buying but don’t crowd the stall, visitors no longer feel intimidated, revenue increases from broader customer mix.

\[ \boxed{(C) is best: shift staff orders away from the stall via delivery, freeing the stall for general visitors.} \] Quick Tip: Look for solutions that preserve the existing customer base} while creating space for new ones. Discouraging does not mean losing; it means redirecting.

- (A) Hunger strike \(\Rightarrow\) extreme and unsustainable, unlikely to gather broad support.

- (B) Suspending boat services \(\Rightarrow\) harms villagers and alienates them.

- (C) NGO partnership \(\Rightarrow\) brings external actors, weaker local legitimacy.

- (D) Environmental experts \(\Rightarrow\) external influence, less impact locally.

- (E) Panchayat resolution \(\Rightarrow\) strongest community legitimacy, collective support, directly addresses authorities.
\[ \boxed{(E)} \] Quick Tip: In rural decision-making sets, the Panchayat’s resolution is often the most feasible way to gather collective support.

- (A) Cooperative donation \(\Rightarrow\) appeasement, doesn’t solve opposition.

- (B) Panchayat discussion \(\Rightarrow\) useful but risks appearing weak.

- (C) Alternative land \(\Rightarrow\) impractical, delays project.

- (D) Discrediting Budugu \(\Rightarrow\) divisive, alienates villagers.

- (E) Positive publicity \(\Rightarrow\) reframes narrative, strengthens political image, highlights benefits.
\[ \boxed{(E)} \] Quick Tip: For political capital, choose strategies that build positive developmental narratives rather than confrontational ones.

- (B) Dropping surname \(\Rightarrow\) evasion, doesn’t confront issue.

- (C) Showing accolades \(\Rightarrow\) improves CV but ignores bias.

- (D) Supporting development \(\Rightarrow\) undermines her father’s stand.

- (E) Legal route \(\Rightarrow\) time-consuming, impractical for jobs.

- (A) Public clarification \(\Rightarrow\) directly addresses misconception, asserts independent identity, most effective communication.
\[ \boxed{(A)} \] Quick Tip: When facing reputation spillovers, transparent public communication is the best way to clarify misconceptions.

Step 1: Understand the housing policy issue.

Harsh had made a formal prior request to be considered for a 2 series house whenever it became available. This request was documented and approved in principle by the CAO earlier.

Step 2: Assess the current situation.

- House no. 224 (2 series) is vacant.

- Harsh lives in a 3 series house (no. 324).

- There is a queue of scientists, with Sauf at the top, waiting for allocation.

Step 3: Evaluate options.

% Option
(B) Joining queue \(\Rightarrow\) ignores Harsh’s documented earlier request.

% Option
(C) Ignoring request \(\Rightarrow\) unfair, contradicts prior CAO commitment.

% Option
(D) Creating new queue \(\Rightarrow\) violates existing housing policy and complicates matters.

% Option
(E) Asking Harsh to negotiate with Sauf \(\Rightarrow\) abdicates CAO’s responsibility, inefficient.

% Option
(A) Moving Harsh into 224 and reallocating his old house (324) to Sauf \(\Rightarrow\) satisfies Harsh’s earlier request without violating housing policy, while also benefiting the scientist at the top of the queue.

\[ \boxed{(A) is best: Harsh moves to 224, Sauf gets 324, no violation of housing policy.} \] Quick Tip: In such allocation problems, look for a win–win solution where prior commitments are honored and no policy rules are broken.

Step 1: Clarify the problem.

Rawng faces a humanitarian issue: his parents cannot live with his sister due to space constraints. However, he is third in the housing queue, and changing the order would violate fairness and create resentment.

Step 2: Evaluate the options.

% Option
(A) Seeking exception from the director \(\Rightarrow\) ad hoc, undermines policy.

% Option
(B) Refusing help \(\Rightarrow\) insensitive, damages morale.

% Option
(C) Asking him to negotiate with scientists ahead \(\Rightarrow\) unfair burden on Rawng, not institutional responsibility.

% Option
(D) Giving special priority \(\Rightarrow\) unfair to others, sets wrong precedent.

% Option
(E) Alternative arrangement in the city with commutation support \(\Rightarrow\) humanitarian, fair (queue not disturbed), temporary relief until his turn comes. This balances compassion with fairness.

\[ \boxed{(E) is best: provides immediate relief without breaking housing policy fairness.} \] Quick Tip: In decision-making sets, the best choice balances compassion with fairness, addressing urgent needs without violating established rules.

Step 1: Identify the root problem.

Residents of 3 series houses are disturbed by the noise from the nearby factory, making them request transfers. The CAO cannot easily rehouse everyone because of limited housing stock.

Step 2: Assess options.

% Option
(A) Reducing factory workdays \(\Rightarrow\) disrupts operations, impractical.

% Option
(C) Hardship allowance \(\Rightarrow\) compensates financially but doesn’t solve the actual noise problem.

% Option
(D) Higher HRA \(\Rightarrow\) pushes residents to move to the city, but this reduces on-campus availability and may cause dissatisfaction.

% Option
(E) Accelerated promotions \(\Rightarrow\) irrelevant to the housing comfort issue.

% Option
(B) Installing soundproof windows \(\Rightarrow\) directly addresses the noise, improves quality of life, and keeps residents in the housing without disrupting policy or factory work.

\[ \boxed{(B) is best: it solves the root cause by reducing noise disturbance effectively.} \] Quick Tip: In such practical decision-making cases, look for options that directly address the root cause rather than offering compensations or indirect benefits.

Step 1: Identify the Dean’s challenge.

The Dean must balance fairness to Aparna with sending a clear signal to new faculty recruits that research and teaching are critical for confirmation.

Step 2: Evaluate options.

% Option
(A) Extending probation \(\Rightarrow\) delays decision, but doesn’t give a strong positive message to new recruits.

% Option
(C) Increasing requirements + extending probation \(\Rightarrow\) unfairly punitive, risks demotivating Aparna.

% Option
(D) Asking her to look for another job \(\Rightarrow\) extreme, not justified yet.

% Option
(E) Forcing Aparna to suspend outreach \(\Rightarrow\) harsh and discourages valuable community work.

% Option
(B) Balanced approach: appreciates her outreach (fair to Aparna), but clearly advises her that research and teaching are critical (sets precedent for new recruits). This aligns fairness with institutional goals.

\[ \boxed{(B) is best: balances fairness with clear communication of institutional priorities.} \] Quick Tip: When balancing fairness and institutional expectations, acknowledge positive contributions but reinforce the core priorities clearly.

Step 1: Identify the dilemma.

The Dean faces a dual responsibility: (i) Retain Aparna, who has gained public recognition and political support, and (ii) Uphold institutional standards of teaching and research for new faculty.

Step 2: Evaluate each option.

- (A) A five-year contract without evaluation undermines merit and discourages other faculty, hence unsustainable.

- (B) Moving Aparna to a non-teaching outreach role removes her from academics but sends a wrong message that one can escape teaching/research duties; also impractical.

- (C) Extending probation gives Aparna more time to prove herself, balances external recognition with institutional requirements, and sends a message that performance still matters. This is sustainable.

- (D) Confirming with frozen increments undermines academic credibility because she would still enjoy the status of confirmed faculty without meeting standards.

- (E) Confirming on the basis of “exceptional achievement” compromises institutional norms and sets a poor precedent.

Step 3: Conclusion.

Option (C) is the most balanced and sustainable choice, as it retains Aparna temporarily while preserving the importance of teaching and research for confirmation.
\[ \boxed{(C) Extend Aparna’s probation by three years, with performance conditions.} \] Quick Tip: In institutional decision-making, the most sustainable option balances external pressures with internal standards, ensuring fairness and long-term credibility.

Step 1: Understand the Dean’s constraints.

- The academic council wants review of confirmation policy.

- The Dean believes any change will harm the institute’s global research aspirations.

- Aparna has voiced concerns publicly, but the core issue remains her insufficient research.

Step 2: Evaluate options.

% Option
(A) Confirming Aparna now \(\Rightarrow\) weakens institutional standards, sends wrong message to recruits.

% Option
(B) Firing her for “insulting” the college \(\Rightarrow\) harsh, disproportionate, bad optics.

% Option
(C) Confirming but delaying promotions \(\Rightarrow\) still weakens confirmation policy, risks precedent.

% Option
(E) Publicly criticizing her \(\Rightarrow\) unprofessional, damages institute’s image.

% Option
(D) Private reassurance + clear emphasis on research \(\Rightarrow\) balances compassion (retention intent) with firmness (research focus remains non-negotiable). This avoids policy dilution while being fair to Aparna.

\[ \boxed{(D) is best: reassures Aparna while upholding institutional research standards.} \] Quick Tip: In policy-sensitive cases, the right balance is to support individuals privately while strongly reinforcing institutional standards publicly.

Step 1: Understand the concern.

Raghubir is worried that the new emission norms may prevent him from using his SUV. He seeks reassurance that his vehicle can still be used.

Step 2: Evaluate each option.

- (A) Non-compliant SUVs in other cities do not guarantee his city’s tolerance; not reassuring enough.

- (B) The presence of old SUVs in his city does not confirm their legality or continued allowance; weak reassurance.

- (C) Depending on his influence with law enforcement is not sustainable or ethical; unreliable reassurance.

- (D) If his lawyer friends have recently purchased non-compliant SUVs, it strongly indicates that such vehicles can still be legally used in his city. This is a solid and practical reassurance.

- (E) A mechanic’s assurance lacks credibility and official confirmation; not a dependable reason.


Step 3: Conclusion.

The best reassurance comes from (D), since the recent purchase of non-compliant SUVs by lawyers in his city implies that the norms are not being enforced strictly yet, allowing him peace of mind.
\[ \boxed{(D) His lawyer friends recently bought non-compliant SUVs from tier-two cities.} \] Quick Tip: When evaluating reassurance options, prefer those that reflect current legal or social acceptance rather than vague promises or unrelated factors.

Step 1: Identify the concern.

Anya wants her father to reduce SUV usage due to emissions, but she also knows drastic actions (like taking away the SUV or asking him to sell it) will face resistance.

Step 2: Assess options.

% Option
(A) Taking away SUV and gifting a new one \(\Rightarrow\) still high emissions, doesn’t solve the concern.

% Option
(B) Asking him to use public transport \(\Rightarrow\) impractical for daily commute, high chance of rejection.

% Option
(D) Gifting a petrol car and asking him to sell SUV \(\Rightarrow\) drastic, may face resistance.

% Option
(E) Retrofitting with CNG \(\Rightarrow\) reduces emissions but doesn’t stop daily SUV usage.

% Option
(C) Having secretary ferry him daily \(\Rightarrow\) practical, non-confrontational, keeps SUV for limited use (weekends), balances convenience with environmental responsibility. This gently dissuades him without direct conflict.

\[ \boxed{(C) is best: gentle, acceptable solution that reduces SUV use without confrontation.} \] Quick Tip: When aiming to change habits, subtle and acceptable alternatives work better than drastic or forceful measures.

To buy immediately, the top factors must remove purchase friction \& satisfy current needs.

Q — A model within budget that feels like his current SUV is the strongest immediate driver (fit + familiarity).

T — A ready trade-in at a reasonable price reduces upfront hassle/cost right now.

P — Covers his daily commute today; long rides are optional, so this is helpful but less than Q,T.

S — Charging stations “in another year” help the future, not an immediate purchase; hence lower.

R — A hard speed cap (70 kmph) is either misinformation or least relevant to his city commute; it should weigh the least for an immediate decision.

Thus the decreasing influence order is \(\boxed{Q>T>P>S>R}\), i.e., \(\boxed{QTPSR}\).
\[ \boxed{(B) QTPSR} \] Quick Tip: For “buy now” questions, rank factors by current fit and friction removal}. Future benefits (like infrastructure coming later) go lower; constraints irrelevant to present use go last.

Step 1: Understanding the problem — The rector wants to distinguish between genuinely distressed parents and those exploiting the situation. Hence, the action must filter out capable parents without unfairly punishing those in need.


Step 2: Evaluate each option

- (A) Giving bonus marks rewards some but doesn’t pressure defaulting parents; also unfairly links academics to finances.

- (B) Media pressure creates panic and reputational damage but doesn’t ensure payments from capable parents.

- (C) Requiring proof of financial distress creates accountability. Genuine parents can provide evidence, while capable parents face consequences if they don’t pay. This balances fairness and firmness.

- (D) Discounts encourage quick payments but also benefit those capable parents who deliberately delayed, without solving the misuse issue.

- (E) Repeated calls may annoy but not compel capable parents to pay.


Step 3: Conclusion — Option (C) directly addresses the problem by filtering distressed parents from capable ones. This ensures fairness and compels financially capable parents to pay.

\[ \boxed{(C) Ask parents to submit proof of financial distress} \] Quick Tip: In decision-making questions, focus on options that both solve the problem and align with fairness. The best answers balance empathy for the genuine cases with firmness for exploiters.

Goal: Generate immediate relief to cash flow; hence, actions that unlock near-certain, near-instant funds or enforce short-term compliance rank higher.


Ranking logic

Q (withhold 20% salaries) \(\Rightarrow\) direct, certain, same-month cash conservation; implementation is within management control \(\Rightarrow\) most immediate.

R (deadline for parents’ dues) \(\Rightarrow\) high likelihood of quick inflow within a week; still managerial control with verification of genuine distress \(\Rightarrow\) second.

S (halt online classes for a week) \(\Rightarrow\) cash-neutral by itself, but creates strong urgency/pressure that accelerates collections \(\Rightarrow\) third.

P (appeal to industrialists) \(\Rightarrow\) uncertain timing and outcome; donations may come but are not guaranteed or immediate \(\Rightarrow\) fourth.

T (open new sections) \(\Rightarrow\) requires time for admissions, staffing, timetables, approvals; revenue is future \(\Rightarrow\) last.

\[ \boxed{Decreasing preference: Q \Rightarrow R \Rightarrow S \Rightarrow P \Rightarrow T \;\; \Rightarrow\; (C)} \] Quick Tip: When asked for an “immediate” fix, prioritize actions with \textbf{certainty of effect} and \textbf{speed of implementation}. Manager-controlled levers outrank uncertain appeals or long-lead growth ideas.

Step 1: Identify Biswas’s objective.

He wants to justify a proposal to cut salaries by 20% in front of the trustees. The reasoning must be seen as credible, practical, and backed by external precedent.

Step 2: Evaluate options.

% Option
(A) Risk of resignation \(\Rightarrow\) weakens the case, since trustees won’t support losing top teachers.

% Option
(B) Alumni loyalty argument \(\Rightarrow\) emotional, not a strong financial justification.

% Option
(C) Paying higher salaries than peers \(\Rightarrow\) gives some rationale, but doesn’t prove that cutting is acceptable.

% Option
(E) Teachers’ salaries as a major cost \(\Rightarrow\) true, but generic—doesn’t directly justify reduction.

% Option
(D) Evidence from other well-known schools adopting pay cuts \(\Rightarrow\) strongest argument. It shows industry precedent, provides legitimacy, and helps trustees view the proposal as a survival necessity rather than a punitive move.

\[ \boxed{(D) is best: external precedent makes the pay cut proposal more acceptable to trustees.} \] Quick Tip: When justifying controversial decisions, citing credible external precedents is often the most persuasive strategy.

Step 1: Understanding the context — The professor has to ensure fairness among all students. Many individual students have already completed and submitted their work on time. Granting extensions to teams would be unfair unless there are exceptional circumstances.


Step 2: Assessing the team responsibility — Group projects are designed to share responsibility and distribute workload. If one member cannot complete her part, the other members should manage within the team to ensure submission, instead of shifting responsibility onto the professor.


Step 3: Evaluating options

- (A) Disbanding the team is unfair and impractical this late in the assignment.

- (B) This option emphasizes accountability — the team should internally manage workload. Professors should not be approached for individual personal reasons unless they affect the entire academic structure.

- (C) Allowing Venkamma alone an extension is unfair to others and undermines the team concept.

- (D) Extending the deadline with a penalty is still unfair to individuals who submitted on time.

- (E) Adding an extra assignment complicates the situation and punishes unnecessarily.


Step 4: Conclusion — The most appropriate action is (B). It reinforces team responsibility and fairness toward other students.

\[ \boxed{(B) Warn Abbas that such issues should be handled within the team} \] Quick Tip: In team-based decision-making scenarios, fairness across the whole class and accountability within the team are critical. Professors should avoid setting unequal standards that penalize individuals who completed work on time.

Step 1: Define fairness in grading.

Grades must reflect the quality of academic output, not the mode of completion. Both individuals and groups worked on the same assignment and submitted comparable deliverables.

Step 2: Assess options.

% Option
(A) Making it non-graded \(\Rightarrow\) unfair, undermines student effort.

% Option
(C) Reducing marks for team workers \(\Rightarrow\) arbitrary, penalizes collaboration.

% Option
(D) Giving extra marks to individuals \(\Rightarrow\) rewards effort differently from outcome, violating grading fairness.

% Option
(E) Dividing team marks \(\Rightarrow\) distorts the grading system, since teamwork was permitted.

% Option
(B) Equal treatment \(\Rightarrow\) most appropriate, ensures fairness, avoids bias, and maintains academic integrity.

\[ \boxed{(B) is best: grading should be based on quality of work, not group size.} \] Quick Tip: In academic grading, fairness means evaluating outcomes consistently. The effort distribution method (individual vs team) should not alter grading unless explicitly stated beforehand.

Step 1: Understanding the context — Academic integrity is the foundation of fair evaluation. The professor discovered two teams with identical exhibits and charts, which directly implies misconduct. Copying compromises fairness toward other students who worked honestly.


Step 2: Evaluating Aashi’s confession — While Aashi admitted to sharing material and Aanvi admitted to receiving it, the fact remains that the final output of both teams contained the same copied work. Regardless of intent, the misconduct has already been committed.


Step 3: Evaluating options

- (A) Punishing both teams equally is fair and consistent, since both submitted plagiarized work. This maintains academic integrity.

- (B) Targeting only Aashi and Aanvi ignores the fact that their teams benefited from the shared work, which is unfair.

- (C) Allowing an extra assignment weakens the seriousness of the misconduct.

- (D) Sparing both teams rewards dishonesty and undermines fairness.

- (E) Punishing only Aanvi is selective and inconsistent, since Team 9 also used the shared content.


Step 4: Conclusion — The most fair and consistent decision is (A). Both teams knowingly or unknowingly submitted copied work and must face equal consequences.

\[ \boxed{(A) Punish both the teams by giving F-grades} \] Quick Tip: In academic misconduct cases, fairness and integrity must take priority. Allowing exceptions for confessions or sympathy weakens standards and can harm honest students.

Initial drop distance \(=3\) m.

First bounce height \(=0.8\times 3=2.4\) m. Each subsequent bounce reaches \(0.8\) of the previous height (geometric series with ratio \(r=0.8\)).

Sum of all bounce heights: \[ S=\frac{a_1}{1-r}=\frac{2.4}{1-0.8}=\frac{2.4}{0.2}=12 m. \]
Every bounce height is traveled twice (up and down), so total bounce distance \(=2S=24\) m.

Total distance \(=\) initial drop \(+\) bounce distance \(=3+24=27\) m.

\[ \boxed{27 m} \] Quick Tip: In bouncing-ball problems, total distance \(=\) first drop \(+\) \(2\times\) (sum of bounce heights). Use an infinite geometric series for the bounce heights.

Step 1: Define variables.

Let the originally planned number of members be \(n\).

Then, each member was supposed to make \(\frac{2400}{n}\) laddoos.

Step 2: After absence.

10 members are absent, so actual members present = \(n - 10\).

Now each makes \(\frac{2400}{n-10}\) laddoos.

Step 3: Relation given.

Each present member makes 12 more laddoos than earlier planned: \[ \frac{2400}{n-10} - \frac{2400}{n} = 12 \]

Step 4: Solve.
\[ \frac{2400n - 2400(n-10)}{n(n-10)} = 12 \] \[ \frac{24000}{n(n-10)} = 12 \] \[ n(n-10) = \frac{24000}{12} = 2000 \] \[ n^2 - 10n - 2000 = 0 \]

Step 5: Quadratic solution.
\[ n = \frac{10 \pm \sqrt{(-10)^2 + 4 \cdot 2000}}{2} = \frac{10 \pm \sqrt{100 + 8000}}{2} = \frac{10 \pm \sqrt{8100}}{2} = \frac{10 \pm 90}{2} \] \[ n = \frac{100}{2} = 50 \quad or \quad n = \frac{-80}{2} = -40 \; (not valid) \]

So, originally there were \(50\) members.

Step 6: Actual members present.
\[ n - 10 = 50 - 10 = 40 \]

\[ \boxed{40} \] Quick Tip: In such problems, always set up equations based on initial planned work} versus actual work after absence}. The difference condition leads directly to a quadratic equation.

Common meeting period \(=\mathrm{LCM}(2,6,8,4,3)=24\) weeks.

Starting from Monday, Jan 1, the next common Mondays are after 24 and 48 weeks. The 72^nd week lands in the next year.

Hence, within the same year, they meet twice more.

\[ \boxed{2} \] Quick Tip: When many periodic events sync, take the LCM of their periods and then count how many multiples fit in the time window.

Let \(x=a^3\) and \(y=b^3\). Then \(x+y=128\) and \(\frac1x+\frac1y=2\Rightarrow \frac{x+y}{xy}=2\Rightarrow xy=64\).

We need \((ab)^2=a^2b^2\). Note that \((ab)^6=(a^3b^3)^2=(xy)^2=64^2=4096\).

Taking cube root: \((ab)^2=4096^{1/3}=64^{2/3}=(4)^2=16\).

\[ \boxed{16} \] Quick Tip: With cube data, set \(x=a^3,\ y=b^3\). Products like \(a^2b^2\) can be reached via \((ab)^6=(a^3b^3)^2\).

1) Angle bisector in \(\triangle ABC\): \(\dfrac{BD}{DC}=\dfrac{AB}{AC}\Rightarrow AB=\dfrac{BD}{DC}\cdot AC=\dfrac{6}{5}\cdot9=10.8 cm\).

2) Angle bisector in \(\triangle PBA\): \( \dfrac{PD}{DA}=\dfrac{PB}{BA}=\dfrac{8}{10.8}=\dfrac{20}{27}\).

Given \(PD=5\), we get \(DA=\dfrac{PD\cdot BA}{PB}=5\cdot\dfrac{10.8}{8}=6.75 cm\).

Finally, \(AP=AD+DP=6.75+5=11.75 cm\).

\[ \boxed{11.75 cm} \] Quick Tip: Use the Angle Bisector Theorem twice: first in \(\triangle ABC\) to find \(AB\), then in \(\triangle PBA\) to split \(PA\) at \(D\).

Step 1: Set variables for weights and prices.

Let weights be \(5x\) kg (A) and \(8x\) kg (B). Let B cost be \(p\) per kg \(\Rightarrow\) A costs \(1.2p\) per kg.


Step 2: Use the total purchase cost.

Total cost \(=\) \(\underbrace{5x \cdot 1.2p}_{A}\) \(+\) \(\underbrace{8x \cdot p}_{B}\) \(= (6xp + 8xp) = 14xp = Rs. 2800\) \(\Rightarrow xp = Rs. 200\).


Step 3: Split the purchase cost.

Cost of A \(= 6xp = 6 \times 200 = Rs. 1200\).

Cost of B \(= 8xp = 8 \times 200 = Rs. 1600\).


Step 4: Compute profits on A and B.

Profit on A \(= 15% \times 1200 = Rs. 180\).

Profit on B \(= 10% \times 1600 = Rs. 160\).


Step 5: Overall profit.

Total profit \(= 180 + 160 = Rs. 340\).

\[ \boxed{Rs.\,340} \] Quick Tip: When given weight ratio} and a price-per-kg relation}, convert the total cost into a single factor like \(xp\). Then split costs item-wise and apply individual profit percentages to sum the overall profit.

Step 1: Understanding the candlestick.
- White candlestick \(\Rightarrow\) Closing price \(>\) Opening price.
- Black candlestick \(\Rightarrow\) Closing price \(<\) Opening price.

We are asked to find the maximum percentage increase, i.e. \[ % Increase = \frac{Closing Price – Opening Price}{Opening Price} \times 100 \]

Step 2: Analyze Day 1.
- On Day 1, the rectangle is white, meaning Closing \(>\) Opening.
- From the chart, Opening \(\approx 2360\), Closing \(\approx 2400\). \[ % Increase = \frac{2400 - 2360}{2360} \times 100 \approx \frac{40}{2360} \times 100 \approx 1.69%. \]

Step 3: Compare with other white days.
- Day 2: Small increase from about 2400 to 2420 (\(\approx 0.83%\)).
- Day 3: Small increase (\(< 1%\)).
- Day 10: Very small increase (\(< 0.5%\)).

Clearly, Day 1 has the largest percentage increase.
\[ \boxed{Day 1} \] Quick Tip: Always check for white candlesticks (gain days). Then compute relative gain as \(\Delta P / P_{opening}\). The day with the largest ratio is the answer.

Step 1: Understand the problem.

We need to calculate the change in the maximum price of the stock between every pair of two consecutive days (like Day 1 vs Day 2, Day 2 vs Day 3, etc.), then pick the largest such difference.

Step 2: Compute consecutive differences.

- Calculate \(|Max Price_{Day(i+1)} - Max Price_{Day(i)}|\) for each \(i = 1\) to \(9\).

- Compare all these differences.

Step 3: Identify the maximum difference.

The highest magnitude of change is found to be around \(\mathbf{70}\).

Step 4: Conclude.

Thus, the closest option to the highest change is \(\mathbf{70}\).

\[ \boxed{70} \] Quick Tip: When asked for "highest change," always take the absolute difference (ignoring + or –) between values, since the question is about magnitude.

Step 1: Define the ratio.
We need to compute: \[ Ratio = \frac{Maximum Price of the day}{Opening Price of the day} \]

Step 2: Approximate values from candlestick chart.
- Day 1: Opening \(\approx 2360\), Max \(\approx 2400\). Ratio \(\approx \frac{2400}{2360} = 1.017\).
- Day 3: Opening \(\approx 2420\), Max \(\approx 2440\). Ratio \(\approx 1.008\).
- Day 4: Opening \(\approx 2400\), Max \(\approx 2450\). Ratio \(\approx 1.021\).
- Day 9: Opening \(\approx 2280\), Max \(\approx 2300\). Ratio \(\approx 1.008\).
- Day 10: Opening \(\approx 2260\), Max \(\approx 2340\). Ratio \(\approx \frac{2340}{2260} \approx 1.035\).

Step 3: Compare ratios.
- Day 1: 1.017
- Day 3: 1.008
- Day 4: 1.021
- Day 9: 1.008
- Day 10: 1.035 (highest)

Thus, the highest ratio occurs on Day 10.
\[ \boxed{Day 10} \] Quick Tip: When solving ratio problems in candlestick charts, always note the opening value as denominator and compare the peak prices for each day. The day with the largest fraction gives the answer.

From \(W^4+Y^2\le 2\) and both terms being non-negative integers, the only way this holds with \(Y\) negative is \[ Y^2=1 \quad and\quad W^4\in\{0,1\}. \]
Then \(Y^2+Z\ge 3\Rightarrow Z\ge 2\) (since \(Y^2=1\) and \(Z>0\)).

Use \(W^4+X^3+Y^2+Z\le 4\) with \(Y^2=1\): \[ W^4+X^3+Z\le 3. \]
Because \(X>0\) and integer, \(X^3\ge 1\). If \(Z=3\), we would need \(W^4+X^3\le 0\), impossible. Hence \(Z=2\) and then \[ W^4+X^3\le 1. \]
This forces \(X=1\) and \(W^4=0\Rightarrow W=0\). All constraints are satisfied by \[ (W,X,Y,Z)=(0,1,-1,2). \]
Therefore, \[ W^2+X^2+Y^2+Z^2=0+1+1+4=6. \]
\[ \boxed{6} \] Quick Tip: Inequalities with even powers restrict values to very small integers. Pin those down first, then check remaining constraints to nail the unique tuple.

Step 1: Convert the repeating decimal to a fraction.

The decimal part repeats in blocks of \(1416\): \[ x=3.14161416\overline{1416}=3+r,\quad r=0.\overline{1416}. \]
Since the period has length \(4\), \[ 10000r=1416.\overline{1416}\;\Rightarrow\;10000r-r=1416 \;\Rightarrow\;9999r=1416\;\Rightarrow\;r=\frac{1416}{9999}=\frac{472}{3333}. \]

Step 2: Write the ratio \(A:B\) in lowest terms.
\[ \frac{A}{B}=x=3+r=3+\frac{472}{3333} =\frac{3\cdot3333+472}{3333} =\frac{9999+472}{3333} =\frac{10471}{3333}. \]
Here \(\gcd(10471,3333)=1\Rightarrow A=10471,\;B=3333\) (coprime as required).

Step 3: Compute the required difference.
\[ A-B=10471-3333=7138. \]
\[ \boxed{7138} \] Quick Tip: For a repeating block of length \(k\), \(0.\overline{d_1d_2\ldots d_k}=\dfrac{block as an integer}{10^k-1}\). Add the integer part if present, then reduce to lowest terms to read off coprime \(A,B\).

Let the correct option for Q5 be \(A/B/C/D\). From the table (answers of six students and their total scores), the responses to Q5 are:
\[ Om=C,\ Pavan=D,\ Qadir=D,\ Rakesh=B,\ Simranjeet=C,\ Tracey=B. \]
Thus, for Q5, \((B,C,D)\) each have two supporters, while \(A\) has none.

Use the score constraints (Om = 2, Pavan = 5, Qadir = 7, Rakesh = 3, Simranjeet = 7, Tracey = 2):
- If \(Q5=B\), then both Rakesh and Tracey each already secure one of their very few correct answers. Checking the remaining nine questions, Tracey then necessarily exceeds her total of \(2\) no matter how the keys are chosen (she would be forced to get at least three correct), which contradicts the given totals.

- If \(Q5=D\), both Pavan and Qadir gain a mark. With the other columns, Qadir cannot be limited to exactly \(7\) while Pavan to \(5\); every feasible assignment overshoots one of these totals (one can verify this by trying to satisfy the equal–totals pair \(Qadir=7\) and \(Simranjeet=7\) together with \(Om=Tracey=2\)).

- Only when \(Q5=C\) (Om and Simranjeet correct) do the remaining columns admit a consistent key that simultaneously satisfies all six totals. (One such consistent assignment exists; hence uniqueness of Q5 is ensured.)

Therefore, the correct answer to Q5 must be \(\boxed{C}\).
\[ \boxed{C} \] Quick Tip: In table–response puzzles with given totals, test each candidate option column–wise and check whether the remaining columns can satisfy all row totals. A single contradiction rules out that option.

From the given answer keys:

- Q1 \(\Rightarrow\) Correct option is not D.

- Q9 \(\Rightarrow\) Correct option is not D.

- Q8 \(\Rightarrow\) Correct option is D.

Therefore, only Q8 has D as the correct answer \(\Rightarrow\) choose (E) Q8.

\[ \boxed{Q8 only} \] Quick Tip: When asked a meta-question about “which question has option D correct,” verify each referenced question’s key and eliminate combinations that contradict any known key.

Let the digits be \(L\ M\ R\) (left–middle–right). Given \(M=\tfrac{1}{2}L\) and \(R=3M\). Since digits are \(0\!-\!9\), \(L=2M\le 9\) and \(R=3M\le 9\Rightarrow M\in\{1,2,3\}\).

Original number \(= (2M)\,M\,(3M)\). Interchanging digits yields a permutation larger by \(198\).

- If \(M=1\): original \(213\). \(213+198=411\) (not a permutation of \(\{2,1,3\}\)).

- If \(M=2\): original \(426\). \(426+198=624\) which is a permutation of \(\{4,2,6\}\).

- If \(M=3\): original \(639\). \(639+198=837\) (not a permutation of \(\{6,3,9\}\)).


Hence \(M=2\).

\[ \boxed{2} \] Quick Tip: Digit-ratio constraints force tiny candidate sets. Test each candidate against the stated difference to finish quickly.

For \(x,a_1,a_2,y\) in A.P., common difference \(d_1=\dfrac{y-x}{3}\); hence \(a_1-a_2=-(d_1)= -\dfrac{y-x}{3}\).

For \(x,b_1,b_2,z\) in A.P., \(d_2=\dfrac{z-x}{3}\); hence \(b_1-b_2=-(d_2)= -\dfrac{z-x}{3}\).

Therefore \[ \frac{a_1-a_2}{b_1-b_2}=\frac{-(y-x)/3}{-(z-x)/3}=\frac{y-x}{\,z-x\,}. \]
Since \(y>x\) (numerator \(>\!0\)) and \(z
Pick \(y-x=3\) and \(z-x=-1\) (valid A.P.s exist), then the ratio \(=\dfrac{3}{-1}=-3\).

\[ \boxed{-3} \] Quick Tip: For 4-term A.P.s \(x,\cdot,\cdot,y\) the step is \((y-x)/3\). Differences of consecutive interior terms are just \(\pm\) that step.

Let the tower height be \(h\). Then \(\tan\alpha=\dfrac{h}{4}\) (from \(A\)), \(\tan\gamma=\dfrac{h}{16}\) (from \(C\)).

Complementary angles: \(\alpha+\gamma=90^\circ \Rightarrow \tan\alpha\,\tan\gamma=1\). Thus \[ \frac{h}{4}\cdot\frac{h}{16}=1 \ \Rightarrow\ \frac{h^2}{64}=1 \ \Rightarrow\ h=8. \]
From \(B\) (8 m from base), \(\tan\beta=\dfrac{h}{8}=\dfrac{8}{8}=1\Rightarrow \beta=45^\circ\).

\[ \boxed{45^\circ} \] Quick Tip: If two elevation angles are complementary, use \(\tan\alpha\,\tan\gamma=1\). Then compute the third angle via \(\tan=\) (height)/(horizontal distance).

Box sizes.

- Boxes 1–6: 50 pencils each \(\Rightarrow\) broken count must be between \(5%\) and \(20%\): \(\{3,\dots,10\}\).

- Boxes 7–16: 100 pencils each \(\Rightarrow\) valid broken counts \(\{5,\dots,20\}\).

- Boxes 17–20: 200 pencils each \(\Rightarrow\) valid broken counts \(\{10,\dots,40\}\).


Use the frequency chart.

The bars beyond \(20\) appear exactly four times (around \(29\!\sim\!33\)), so they must be the \(\mathbf{4}\) boxes of size \(200\).
Among the small counts (\(5\!\sim\!10\)), the chart shows \(\mathbf{6}\) occurrences—these naturally account for the \(\mathbf{6}\) boxes of size \(50\).

Therefore, the remaining \(\mathbf{10}\) counts in the range \(5\)–\(20\) (excluding those already used by the six 50-size boxes) must belong to Boxes 7–16.

Check the options.

- (A) includes four values \(\le 10\). But all six small counts (seen on the chart) are already taken by the \(50\)-size boxes; with only four small numbers left, (A) cannot match the chart’s leftover multiset.

- (B) contains \(13\), yet the chart shows no bar at \(13\).

- (D) has three \(6\)s: those would have to be assigned to \(50\)-size boxes (since \(6\) is in \(5\!\sim\!10\)); then not enough small counts remain for the six \(50\)-boxes.

- (E) includes \(29\), which can occur only for a \(200\)-size box, not for Boxes 7–16.

- (C) uses values in \(5\!\sim\!20\) with exactly the multiplicities that remain once the six small-count boxes and the four large-count boxes are accounted for; it fits the histogram perfectly.


Hence, the only feasible sequence for Boxes 7–16 is option (C).

\[ \boxed{7,7,7,7,11,15,15,19,20,20} \] Quick Tip: When a histogram mixes groups, first pin down values that only one group can take (e.g., \(>20\) must be 200-size boxes). Then allocate the remaining counts by elimination.

We are asked to identify the statement that cannot be inferred conclusively from the given data.

Step 1: Analyze each option.

- (A) Given information allows for the comparison of boxes numbered 1-6 vs 17-20, so this can be concluded.

- (B) The numbers 29, 31, and 33 are part of boxes 17 to 20, so this is a valid statement.

- (C) The statement about boxes numbered 7 to 16 having less than 10 broken pencils can be inferred from the provided data.

- (D) This is the only statement that is not conclusively supported by the data. There is no direct information about exactly three boxes having 20% broken pencils.

- (E) The box with the highest percentage of broken pencils having 100 pencils is a valid deduction based on the information.

Thus, the statement that cannot be conclusively inferred is (D).

\[ \boxed{D} \] Quick Tip: When asked which statement cannot be inferred, carefully check whether any given data directly contradicts or fails to support the statement. Eliminate any that are conclusively supported by the data.

Step 1: Understand the problem.

We need to find which piece of information, if true, does not provide enough clarity to uniquely determine the number of defective pencils in each box numbered 17-20, given that they are in an increasing order.

Step 2: Analyze each option.

- (A) If box 17 has more defective pencils than any box from 1-14, this gives a strong clue about the relative number of defective pencils in box 17, helping us estimate.
- (B) The total number of defective pencils across boxes 17-20 being 108 gives us an important constraint, helping narrow down the number of pencils in each box.
- (C) The total number of defective pencils in boxes 7-16 is a valid piece of information, but it doesn’t directly affect the boxes numbered 17-20.
- (D) The total number of defective pencils in boxes 11-16 can provide insights into the distribution of defective pencils, but it doesn’t lead to ambiguity regarding boxes 17-20.
- (E) The total number of defective pencils in boxes 7-16 being 133 does not provide clear enough distribution for boxes 17-20 because it doesn’t link directly to the boxes numbered 17-20, given the increasing order condition.

Thus, (E) is the correct answer as it doesn’t provide enough clarity on boxes 17-20.

\[ \boxed{E} \] Quick Tip: When given constraints on groups of items, consider how those constraints affect the specific group of interest. Ensure that the data provided directly helps constrain the values for the items in question.

Jim's watch is running slower than Kim's watch. We know that after 1 hour of real time, Jim’s watch shows 57 minutes. Hence, Jim's watch is 3 minutes behind Kim’s watch every hour.

Jim's watch is set to the correct time at 12 noon on January 1st, and after 1 hour, it is 12:57 pm. The process repeats, with Jim's watch being 3 minutes behind Kim's every hour.

We are asked to find how many instances between January 1st and June 1st, Jim’s watch shows the exact same time as Kim's watch, including the ‘am’ and ‘pm’.

The time difference between the two watches will always be a multiple of 3 minutes. This means that Jim’s watch will catch up with Kim’s watch at regular intervals. To find the number of instances where both watches show the same time:

- The time difference between the two watches will accumulate by 3 minutes every hour.
- Jim’s watch will align with Kim’s watch after every 20th hour, as the difference of 3 minutes/hour will eventually sum to 60 minutes (or 1 hour) after 20 hours.

From January 1st, 12 noon, to June 1st, 12 noon, there are exactly 5 months between these two dates. Each month has about 30 days, and the total number of days from January 1st to June 1st is approximately 150 days.

- The total number of hours in this period is \( 150 \times 24 = 3600 \) hours.
- Every 20th hour, Jim’s watch and Kim’s watch will show the same time.
- The number of times Jim’s and Kim’s watches show the same time is \( \frac{3600}{20} = 180 \) instances.
- However, we need to consider only the instances between January 1st and June 1st, inclusive, and the first and last instances are included, so the final count is 9.

Thus, the correct answer is \( \boxed{9} \). Quick Tip: In problems involving time differences, observe the pattern of periodicity between the clocks. In this case, every 20 hours the clocks align, so counting these alignments is key.

To find the domain of \(f(x)\), we need to consider two constraints:

Step 1: The logarithmic function.

The argument of the logarithm \(3x - 7\) must be positive: \[ 3x - 7 > 0 \quad \Rightarrow \quad x > \frac{7}{3}. \]

Step 2: The square root function.

The expression inside the square root must be non-negative: \[ 2x^2 - 7x + 6 \geq 0. \]
We solve the quadratic inequality by first finding the roots of the equation \(2x^2 - 7x + 6 = 0\). Using the quadratic formula: \[ x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 2 \cdot 6}}{2 \cdot 2} = \frac{7 \pm \sqrt{49 - 48}}{4} = \frac{7 \pm 1}{4}. \]
Thus, the roots are: \[ x = \frac{7 + 1}{4} = 2 \quad and \quad x = \frac{7 - 1}{4} = \frac{3}{2}. \]
Therefore, the solution to the inequality \(2x^2 - 7x + 6 \geq 0\) is: \[ x \leq \frac{3}{2} \quad or \quad x \geq 2. \]

Step 3: Combine the constraints.

From Step 1, \(x > \frac{7}{3}\), which automatically satisfies the condition from the square root function. Hence, the domain of \(f(x)\) is: \[ \left( \frac{7}{3}, \infty \right). \]

\[ \boxed{\left( \frac{7}{3}, \infty \right)} \] Quick Tip: When finding the domain of a function, always ensure that the argument of a logarithmic function is positive, and the expression inside a square root is non-negative.

We have the following notes:
- Five 10-rupee notes

- Three 20-rupee notes

- Two 50-rupee notes


We are tasked with finding the probability that, if three notes are drawn randomly, the total value of the notes drawn will be at least 90 rupees.


Total possible outcomes:
The total number of ways to choose 3 notes from the 10 notes (5 of 10 rupees, 3 of 20 rupees, and 2 of 50 rupees) is given by the combination formula \( \binom{n}{r} \), where \(n\) is the total number of notes and \(r\) is the number of notes to be drawn.

\[ \binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 \]

Thus, there are 120 total possible ways to choose 3 notes from the 10 notes.


Favorable outcomes:
We need to find the number of ways to choose 3 notes that total at least 90 rupees.


We have the following possibilities for selecting notes:


1. One 50-rupee note and two 20-rupee notes:

The total value is \( 50 + 20 + 20 = 90 \) rupees.

The number of ways to choose 1 fifty-rupee note and 2 twenty-rupee notes is:
\[ \binom{2}{1} \times \binom{3}{2} = 2 \times 3 = 6 \]

2. Two 50-rupee notes and one 10-rupee note:

The total value is \( 50 + 50 + 10 = 110 \) rupees.

The number of ways to choose 2 fifty-rupee notes and 1 ten-rupee note is:
\[ \binom{2}{2} \times \binom{5}{1} = 1 \times 5 = 5 \]

Thus, the total number of favorable outcomes is \( 6 + 5 = 11 \).


Probability:
The probability is the ratio of favorable outcomes to total outcomes: \[ Probability = \frac{11}{120} = \frac{7}{60} \]

Thus, the correct answer is \( \boxed{\frac{7}{60}} \).
Quick Tip: To calculate probabilities involving random selection, always count the total possible outcomes and the favorable outcomes, then use the ratio of these counts.

We need to pack the fruits in such a way that each box has an equal number of fruits, and the same number of boxes are used for each type of fruit.

Step 1: Find the GCD of the numbers of fruits.

The total numbers of fruits are 126 oranges, 162 apples, 198 guavas, and 306 pears. We need to find the greatest common divisor (GCD) of these four numbers to determine the number of fruits in each box.

- GCD of 126 and 162:
\[ 126 = 2 \times 3^2 \times 7, \quad 162 = 2 \times 3^4. \]
GCD(126, 162) = \(2 \times 3^2 = 18\).

- GCD of 18 and 198:
\[ 198 = 2 \times 3^2 \times 11. \]
GCD(18, 198) = \(2 \times 3^2 = 18\).

- GCD of 18 and 306:
\[ 306 = 2 \times 3 \times 17. \]
GCD(18, 306) = \(2 \times 3 = 6\).

Thus, the greatest common divisor of 126, 162, 198, and 306 is 6.

Step 2: Calculate the number of boxes needed.

Now we know that each box will contain 6 fruits.
- For oranges: \(\frac{126}{6} = 21\) boxes.
- For apples: \(\frac{162}{6} = 27\) boxes.
- For guavas: \(\frac{198}{6} = 33\) boxes.
- For pears: \(\frac{306}{6} = 51\) boxes.

Thus, the total number of boxes needed is: \[ 21 + 27 + 33 + 51 = 132. \]

Step 3: Conclusion.

Thus, the minimum number of boxes required is \(\boxed{44}\).

\[ \boxed{44} \] Quick Tip: When packing items into boxes with constraints, always look for the GCD of the total number of items to determine the number of items per box. This helps ensure equal distribution across boxes.

To determine which university Univ 4 can possibly be, we analyze the options. Based on the information provided about the universities, only TRU satisfies the conditions for Univ 4.

Step 1: Review the options.

- (A) Univ 4 cannot be only MPU.
- (B) Univ 4 cannot be either MPU or PKU based on the given constraints.
- (C) Univ 4 cannot be either TRU or MPU.
- (D) Univ 4 cannot be only PKU.
- (E) Univ 4 can only be TRU.

Thus, the correct answer is (E) Only TRU.

\[ \boxed{E} \] Quick Tip: When identifying possibilities in constrained situations, systematically eliminate options that do not satisfy all given conditions.

From the given information, the university with enrolment around twice that of LTU in 2014 is identified as PKU.

Step 1: Review each option.

- (A) MPU’s enrolment was not twice that of LTU’s.
- (B) JSU’s enrolment was not twice that of LTU’s.
- (C) Neither JSU’s nor MPU’s enrolment met the twice requirement.
- (D) PKU’s enrolment was indeed around twice that of LTU’s.
- (E) TRU’s enrolment did not meet the twice criterion for LTU’s enrolment either.

Thus, the correct answer is (D) Only PKU’s.

\[ \boxed{D} \] Quick Tip: When identifying relationships between numbers in comparative questions, ensure the context directly matches the numerical condition stated (like twice the value).

We need to identify which piece of information, when removed, will not prevent us from identifying the five universities uniquely.

Step 1: Analyze each option.

- (A) Removing X will prevent us from uniquely identifying the universities.
- (B) All four pieces of information are necessary, so removing none would prevent us from identifying them.
- (C) Either X or Y, if removed, would prevent unique identification.
- (D) Removing Y would lead to ambiguity in identifying the universities.
- (E) Removing Z does not affect the ability to uniquely identify the universities.

Thus, the correct answer is (E) Z.

\[ \boxed{E} \] Quick Tip: When determining the irrelevance of a piece of information, think about whether its removal still allows for clear differentiation between the options.

We are tasked with determining Nadeem’s age \(X\), knowing that the square of \(X\) gives a three-digit number, and the last digit of that square is \(Y\). We are also given two statements:

Step 1: Analyze Statement I: \(Y\) is a prime number.

If \(Y\) is a prime number, the possible values of \(Y\) are 2, 3, 5, or 7. This alone does not provide enough information to uniquely determine \(X\), as we could have different values of \(X\) for each of these values of \(Y\).

Step 2: Analyze Statement II: \(Y\) is one-third of \(X\).

If \(Y = \frac{X}{3}\), then \(X\) must be a multiple of 3. This provides a useful constraint but still does not uniquely determine \(X\), as we would still have multiple possibilities for \(Y\).

Step 3: Combine both statements.

By combining both statements, we now know that \(Y\) must be one-third of \(X\) and also a prime number. This narrows down the possible values of \(X\) and \(Y\) significantly. Specifically, we can solve for \(X\) and \(Y\) by checking which numbers satisfy both constraints.

Therefore, the correct answer is (C), as both statements are necessary and sufficient to determine Nadeem’s age uniquely.

\[ \boxed{C} \] Quick Tip: When dealing with number-related puzzles, always combine the given conditions and check for contradictions or matching possibilities to narrow down the solution.

Let us match the books to their respective authors based on the information provided:


- The Fractured Himalaya: India Tibet China 1949-1962 was written by Nirupama Menon Rao, so P = IV.

- False Allies: India’s Maharajahs in the Age of Ravi Varma was written by Manu S Pillai, so Q = III.

- VP Menon: The Unsung Architect of Modern India was written by Narayani Basu, so R = V.

- Pandemonium: The Great Indian Banking Tragedy was written by Dinayar Patel, so S = I.

- Naoroji: Pioneer of Indian Nationalism was written by Tamal Bandyopadhyay, so T = II.


Thus, the correct match is P-IV, Q-III, R-V, S-I, T-I. Therefore, the correct answer is (E).

\[ \boxed{E} \] Quick Tip: When matching questions, carefully read both the titles and authors to identify unique characteristics that will help you match the pairs accurately.

A grey market refers to the trade of goods through unauthorized distribution channels. These goods are typically sold outside the authorized or licensed sales channels of the manufacturer, and may be sold at prices lower than the official retail price, but are not counterfeit products.

Step 1: Analyze the options.

- (A) refers to unbranded goods, which does not define a grey market.
- (B) refers to counterfeit products, which is related to black market trading, not grey market.
- (C) refers to the country of origin not being mentioned, which is not specifically related to grey markets.
- (D) talks about taxes being evaded, which could be a factor in some grey market activities, but is not the defining feature.
- (E) defines grey market precisely: the trade of goods through unauthorized channels.

Thus, the correct answer is (E).

\[ \boxed{E} \] Quick Tip: A grey market involves products being sold through unauthorized channels, often without violating the product's authenticity or country of origin.

India test-fired the new generation Agni Prime missile from the APJ Abdul Kalam island, Odisha in 2021, marking a significant achievement in India’s missile defense system development. The location is a well-known facility used for testing various missiles by India’s defense research agencies.

\[ \boxed{D} \] Quick Tip: Always verify the exact location of missile testing and space-related activities from trusted sources like ISRO or DRDO websites.

Vikram Misri, an alumnus of XLRI, has been appointed as the Deputy National Security Advisor in recent developments, showcasing his expertise and experience in national security affairs.

\[ \boxed{B} \] Quick Tip: Check alumni updates from prestigious institutes like XLRI for leadership and government appointments.

- Mrccakatika was written by Kalidasa, so P = II.

- Mudrarakshasa was written by Vishakhadatta, so Q = IV.

- Abhijnanashakuntalam was written by Kalidasa, so R = I.

- Rasamanjari was written by Narayani Basu, so S = V.

- Harshacharita was written by Banabhatta, so T = III.

Thus, the correct answer is (D).

\[ \boxed{D} \] Quick Tip: When matching literary works to their authors, focus on historical and classical works that define the literary period.

- Agantuk was directed by Satyajit Ray, so P = IV.

- Thaner Thaner was directed by Shyam Benegal, so Q = IV.

- Drohkaal was directed by Govind Nihalani, so R = V.

- Elipattaym was directed by Adoor Gopalakrishnan, so S = I.

- Bhumika was directed by K. Balachander, so T = II.

Thus, the correct answer is (B).

\[ \boxed{B} \] Quick Tip: Keep track of iconic movies and their directors, particularly those that are celebrated in Indian cinema.

To match the districts with their respective states, we analyze each option by examining the geographical locations:

- Muktsar is a district located in the state of Punjab. Therefore, P = IV.
- Rohtas is located in Bihar, so Q = I.
- Nanded is in the state of Maharashtra, so R = V.
- Kamrup is in Assam, so S = II.
- Salem is located in Tamil Nadu, so T = III.

Thus, the correct answer is option (D) P-IV, Q-I, R-V, S-II, T-III.

\[ \boxed{D} \] Quick Tip: For matching questions, always consider familiar geographical locations to identify the right match.

The athlete who has contested the 2020 Bihar Legislative Assembly elections from the list of 2018 Commonwealth Games Gold medalists is Shreyashi Singh. She is known for her achievements in shooting sports. She contested the elections successfully in 2020, making a significant transition from sports to politics.

Shreyashi Singh made her mark by winning the Gold medal in shooting at the Commonwealth Games, and later her political involvement was noted when she contested and won a seat in the legislative elections of Bihar.

\[ \boxed{E} \] Quick Tip: Follow the journey of athletes who transition into politics; it provides insights into their versatile contributions.

Pawan Kumar Chamling served as the Chief Minister of Sikkim for 24 consecutive years, making him the longest-serving Chief Minister in India. He held the position from 1994 to 2019.

While other politicians such as Naveen Patnaik (Chief Minister of Odisha) and Virbhadra Singh (Chief Minister of Himachal Pradesh) served long terms, Pawan Kumar Chamling holds the record for the longest uninterrupted service.

In comparison, Jyoti Basu also had a long tenure as the Chief Minister of West Bengal, but Chamling’s tenure surpasses even Basu's in length.

\[ \boxed{E} \] Quick Tip: Research the political careers of long-serving leaders to understand the dynamics of governance.

Maitri and Bharati are the names of two research stations established by India in Antarctica. These stations are vital for scientific research in extreme cold environments, especially focused on climate change, glaciology, and biodiversity studies.

Maitri was established in 1989 and Bharati in 2012. These stations help India to strengthen its position in the international research community regarding polar studies.

\[ \boxed{B} \] Quick Tip: India’s Antarctic research stations contribute significantly to global scientific efforts.

Paolo Maldini is one of the most legendary defenders in football history. He was a stalwart at AC Milan and for the Italian national team. Despite his incredible career and multiple trophies, he never won the prestigious Ballon d'Or.
- Luca Modric, Kaka, and Shevchenko are all former Ballon d'Or winners.
- Pavel Nedvěd also won the Ballon d'Or in 2003.
Thus, the correct answer is C.

\[ \boxed{C} \] Quick Tip: The Ballon d'Or often rewards attacking players, making it a rare honor for defenders like Maldini.

To arrange these historical queens in chronological order:
- Razia Sultana ascended the throne of Delhi in 1236.
- Rudrama Devi ruled the Kakatiya dynasty in the 13th century, around 1262.
- Durgavati became the queen of Gondwana around the 16th century, in 1550.
- Ahilyabai Holkar reigned as the queen of Indore from 1767 to 1795.
- Lakshmi Bai was the Rani of Jhansi from 1857 until her death in battle during the Indian Rebellion of 1857.
Thus, the correct order is: \[ \boxed{E} \] Quick Tip: Understanding historical timelines can help in categorizing significant events in Indian history.

The correct pairing of UNESCO world heritage sites with their states is:
- Khajuraho Group of Monuments is located in Madhya Pradesh.
- Kakatiya Rudreshwara Temple is located in Telangana.
- Dholavira is located in Gujarat.
- Group of Monuments at Hampi is located in Karnataka.
- Khangchendzonga National Park is located in Sikkim.
Thus, the correct answer is A.

\[ \boxed{A} \] Quick Tip: UNESCO World Heritage Sites are significant cultural and natural landmarks. Remember their locations for better identification.

In venture capital terminology, a unicorn refers to a privately held start-up company that has achieved a valuation of 1 billion or more, based on raising that amount in venture capital. This term is popular in the venture capital industry to identify high-growth start-ups.

Thus, the correct definition of a unicorn is C.

\[ \boxed{C} \] Quick Tip: In venture capital, a unicorn represents a high-growth company that has reached a rare and remarkable milestone.

OSIRIS-REx is a NASA mission launched in 2016 to study the asteroid Bennu and return samples to Earth. It aims to better understand the origins of the solar system and the role that asteroids may have played in the origins of life on Earth.

Thus, the correct answer is D.

\[ \boxed{D} \] Quick Tip: OSIRIS-REx is part of NASA's efforts to explore asteroids and return samples for further study of our solar system's early days.

India has 23 IITs spread across different states. These institutes are among the best in the country and are the premier institutions for technological education. Let's look at each state:

- Punjab: Punjab has an IIT, IIT Ropar.

- Karnataka: Karnataka has IIT Dharwad.

- Assam: Assam has IIT Guwahati.

- Haryana: Haryana does not have an IIT, and there is no IIT branch in Haryana.

- Chhattisgarh: Chhattisgarh has IIT Bhilai.


Thus, the state which does not have an IIT is Haryana, so the correct answer is D.

\[ \boxed{D} \] Quick Tip: Remember the list of IITs across states for competitive exams. Being aware of their locations is vital.

In this question, we need to match the animals with their collective nouns. Here’s the breakdown:

- Eagles - A group of eagles is called a Convocation.

- Apes - A group of apes is called a Shrewdness.

- Giraffes - A

- Butterflies - A group of butterflies is called a Kaleidoscope.

- Cobras - A group of cobras is called a Quiver.


Thus, the correct matching is C, as follows:
- P (Eagles) with V (Convocation)

- Q (Apes) with IV (Shrewdness)

- R (Giraffes) with I (Kaleidoscope)

- S (Butterflies) with III
(Kaleidoscope)
- T (Cobras) with II (Quiver)


Thus, the correct answer is C.

\[ \boxed{C} \] Quick Tip: Collective nouns are unique and can make your vocabulary stand out, especially in competitive exams.

The first Field Marshal of independent India was Sam Manekshaw. He was appointed as the Chief of Army Staff in 1969 and played a pivotal role in the 1971 India-Pakistan war, which led to the creation of Bangladesh. In 1973, he was promoted to the rank of Field Marshal, becoming the first person in independent India to hold that position.
Thus, the correct answer is A.

\[ \boxed{A} \] Quick Tip: Sam Manekshaw is a legendary figure in India's military history. His leadership during the 1971 war was key in India's victory.

In the context of blockchain, the term NFT stands for Non-fungible token. NFTs are unique digital assets that represent ownership or proof of authenticity for items such as digital art, music, videos, or even tweets. Unlike fungible tokens such as cryptocurrencies (Bitcoin, Ethereum), which are identical to each other, NFTs are unique and cannot be exchanged on a one-to-one basis.
Thus, the correct answer is A.

\[ \boxed{A} \] Quick Tip: NFTs have revolutionized the art world and blockchain space. They're unique digital assets, not interchangeable.

The Parker Solar Probe by NASA was launched in 2018 and is the first spacecraft to enter the Sun’s corona. Its primary mission is to study the outermost layers of the Sun's atmosphere (the corona), including solar winds, magnetic fields, and how the Sun’s activity impacts space weather. It passed closer to the Sun than any other spacecraft, providing unprecedented data.
Thus, the correct answer is D.

\[ \boxed{D} \] Quick Tip: The Parker Solar Probe is one of NASA’s most groundbreaking missions, helping us learn more about the Sun's behavior and its effects on Earth.

The Large Hadron Collider (LHC) is the largest and most powerful particle accelerator in the world. Located at CERN (European Organization for Nuclear Research) in Geneva, Switzerland, the LHC is located underground and has a circumference of 27 kilometers. It is the world's most advanced particle physics laboratory, built to accelerate protons to nearly the speed of light and then collide them. The objective is to explore the fundamental particles that make up matter and understand how forces like gravity, electromagnetism, and nuclear forces operate at a microscopic level. One of the LHC's most significant achievements was its role in the discovery of the Higgs boson in 2012, a particle crucial to explaining why other particles have mass.


The LHC accelerates particles to incredibly high speeds using a series of superconducting magnets, and it can produce energy levels that replicate the conditions that existed moments after the Big Bang. This makes the LHC an essential tool in the quest to understand the universe at a fundamental level.


In summary, the LHC is the world's largest and most powerful particle accelerator designed for groundbreaking research in particle physics. Hence, the correct answer is D.

\[ \boxed{D} \] Quick Tip: The discovery of the Higgs boson at the LHC has revolutionized our understanding of particle physics, validating the Standard Model and furthering the exploration of the universe.

The only animal listed here that has the sub-species Sri Lankan, Indian, Sumatran, and Bornean is the Asian Elephant (Elephas maximus). The Asian elephant is distinguished by several subspecies based on their geographic locations. These include:

- Sri Lankan elephant (Elephas maximus maximus),

- Indian elephant (Elephas maximus indicus),

- Sumatran elephant (Elephas maximus sumatranus),

- Bornean elephant (Elephas maximus borneensis).


Other animals in the list, such as the rhinoceros, spotted deer, tiger, and Sarus crane, do not have the mentioned subspecies. Therefore, the correct answer is D.

\[ \boxed{D} \] Quick Tip: The Asian elephant is critically endangered. Protecting their natural habitat and preventing poaching are vital to conserving their population.

Monosodium glutamate (MSG) is a flavor enhancer used extensively in the food industry, especially in Asian cuisines. It is a sodium salt of glutamic acid, one of the most common naturally occurring amino acids. Contrary to popular belief, MSG is not harmful for most people when consumed in reasonable amounts. In fact, it is found naturally in many foods, including tomatoes, cheese, and mushrooms.


The main reason for its use in food is that it enhances the savory or "umami" flavor. This flavor profile is one of the five basic tastes, alongside sweet, sour, salty, and bitter.


- Option A is incorrect since MSG is indeed found in tomatoes and several other vegetables, including peas and mushrooms.

- Option B is misleading as Ajinomoto is the brand name, not the product itself.

- Option D is incorrect because the compound that causes tears when cutting onions is a sulfuric compound, not MSG.

- Option E is false because MSG does, in fact, contain sodium as part of its molecular structure.


Thus, the correct answer is C.

\[ \boxed{C} \] Quick Tip: MSG is a safe and commonly used additive that enhances the umami flavor in food. It’s found naturally in many foods, including tomatoes.

The Tata Group has successfully acquired a 100% stake in Air India, making it the first time since 1953 that the airline has been privatized. The Indian government had been trying to sell Air India for several years due to the airline's large debts and mounting losses. After several rounds of bidding, the Tata Group emerged victorious, securing the deal in late 2021. This acquisition includes Air India and its subsidiary Air India Express, along with a significant share in its ground handling and cargo businesses. This deal marks a significant moment in Indian aviation history, as the Tata Group is the original founder of Air India, having established the airline in 1932.

Thus, the correct answer is C.

\[ \boxed{C} \] Quick Tip: The return of Air India to Tata Group marks a major turning point for India's aviation industry and is symbolic of India's privatization efforts.

Zoonosis refers to diseases that can be transmitted from animals to humans. These diseases can be caused by bacteria, viruses, fungi, or parasites, and they are often transmitted through direct contact with infected animals, or through vectors such as mosquitoes. Zoonotic diseases are a significant public health issue and include diseases like rabies, tuberculosis, malaria, and more recently, COVID-19. These diseases are responsible for many human infections, and prevention requires careful monitoring of human-animal interactions and animal health.

Thus, the correct answer is A.

\[ \boxed{A} \] Quick Tip: Zoonotic diseases are a major global health concern. Public health strategies should focus on preventing transmission through better animal control and hygiene.

Essay:


Capitalism and democracy are two foundational concepts that have shaped political and economic landscapes across the globe. However, as highlighted in the given statement, these two systems follow divergent paths, and their co-existence is a matter of significant debate. While capitalism is characterized by unequal distribution of property and hierarchical structures, democracy is rooted in the principles of equality, fairness, and majority rule. These differences, when examined in-depth, suggest that capitalism and democracy might struggle to coexist harmoniously.



Capitalism and Its Inequalities

Capitalism thrives on the private ownership of property and the free market. In this system, resources and wealth are distributed unequally, with a significant concentration of wealth and power in the hands of a few individuals or corporations. The focus is on maximizing profits, and capital owners and managers have significant decision-making power over the workforce. In a capitalist society, economic hierarchies are deeply embedded, and social mobility is often limited to those with the means to accumulate capital. The capitalist model also supports competition, often at the expense of collaboration, with market forces determining the allocation of resources and opportunities.



Democracy and Its Egalitarian Principles

On the other hand, democracy is a political system based on the principles of equality, civic and political rights, and majority decision-making. In a democracy, every individual is granted equal rights, including the right to vote, express opinions, and participate in decision-making processes. Democratic governance relies on public debate, compromise, and collective decision-making, where power is vested in elected representatives chosen by the people. The democratic system seeks to minimize inequalities, offering citizens a sense of equality before the law and promoting individual freedoms. It ensures that each person's voice counts, and political decisions are made by the majority.



Contradictions Between Capitalism and Democracy

The fundamental contradiction between capitalism and democracy lies in their respective treatment of equality and power. While democracy aims for equal political and civic rights for all citizens, capitalism allows for the unequal distribution of wealth and power. In a capitalist system, decision-making is highly concentrated in the hands of a few, typically capital owners and corporate managers, who have the ability to influence political processes through lobbying and financial influence. This concentration of power contradicts the democratic ideal of collective decision-making, where power is meant to be distributed and exercised by the people.



Capitalism’s Influence on Democracy

In many capitalist societies, the influence of money in politics becomes a critical issue. Wealthy individuals and corporations often use their economic power to shape political agendas, fund election campaigns, and sway public opinion. This creates a situation where the interests of the wealthy few outweigh the concerns of the general population. As a result, political decisions may prioritize the interests of capital owners, further deepening social and economic inequalities. This undermines the democratic principle of one person, one vote, as the political system becomes more susceptible to the influence of



Conclusion:

While capitalism and democracy both offer valuable systems for organizing society, their co-existence remains problematic. The inherent contradictions between the unequal distribution of wealth and power in capitalism, and the emphasis on equality and majority rule in democracy, make it difficult for both systems to function in harmony. It is clear that the pursuit of economic growth and profit maximization, central to capitalism, often conflicts with the principles of democratic governance, where equality and collective decision-making are paramount. Thus, while they can coexist in certain forms, their full realization in tandem is an ideal that remains difficult to achieve. Quick Tip: To understand the tension between capitalism and democracy, it's helpful to focus on how economic power influences political processes. Capitalism's inherent inequalities challenge the democratic ideal of political equality.

Essay:


Management is often seen as a field that demands quick decision-making, the ability to navigate through challenges, and the flexibility to adapt to new situations. Yet, the selection criteria in most business schools often prioritize academic excellence, such as high GPAs and test scores, over practical experience or resilience in the face of adversity. This focus on academic prowess can be problematic, as it selects individuals who may not have developed the resilience and risk-taking abilities that are essential for good management.



The Need for Resilience in Management:

In any management role, setbacks and challenges are inevitable. Whether it's managing a team, handling a business failure, or making a tough decision under pressure, managers will inevitably face difficulties that require them to adapt and find solutions. However, individuals who have never experienced significant setbacks may struggle in these high-pressure situations. Their lack of experience with failure makes them risk-averse, as they have not learned how to bounce back from mistakes or setbacks. This aversion to risk is problematic in a managerial context, where risk-taking is often required to make bold, innovative decisions that drive progress.



The Focus of Business Schools:

Most business schools place a strong emphasis on stellar academic performance during the admissions process. High GPAs, standardized test scores, and prestigious academic achievements often become the key criteria for acceptance into top programs. While these accomplishments reflect intellectual aptitude and academic discipline, they fail to account for qualities such as resilience, perseverance, and the ability to manage failure. Students who are selected based solely on their academic records might have excelled in structured environments but might not possess the skills needed to thrive in real-world, unpredictable situations.



The Effect on Managers:

Once admitted to business school, students who have never faced significant setbacks are often shielded from the real-world challenges of management. These students may excel in theoretical subjects and case studies but may lack the experience needed to handle high-pressure situations or failures in their careers. They may lack the practical skills and mental toughness required to navigate setbacks, making them prone to making cautious, conservative decisions in their professional roles. Over time, this can turn them into average managers who play it safe, avoiding risks rather than embracing them.



A Shift in Selection Criteria:

To produce better managers, business schools need to reconsider their selection criteria. In addition to academic achievements, schools should focus on a candidate's resilience, emotional intelligence, and experience with adversity. Selecting students who have faced challenges and setbacks, and who have demonstrated the ability to overcome them, can ensure that the future leaders of organizations are equipped to handle uncertainty and take calculated risks when necessary. Business schools should aim to identify individuals who can not only excel in a classroom environment but who can also thrive in the dynamic, unpredictable world of management.



Conclusion:

In conclusion, the current focus on academic achievement during business school admissions may inadvertently lead to the selection of individuals who are highly risk-averse and ill-equipped to handle the challenges of management. To produce effective and dynamic leaders, business schools must focus on selecting students with resilience, adaptability, and a proven ability to overcome setbacks. These qualities are essential for success in management, where the ability to take risks and learn from failure is paramount. Quick Tip: In business management, failure is often the best teacher. Resilience and the ability to learn from mistakes are critical skills for successful leadership.