SBI PO Prelims Memory Based Paper (Held On: 24 March 2025 Shift 1) (Previous Year Paper)

The correct answer is '5' i.e. The internal audit revealed that neither the manager nor his subordinates were aware of the security breach. .

Key Points

• Option 1: "The quality of the raw materials used in the production line determine the durability of the final consumer product."
• Incorrect because the subject "quality" is singular, so the correct verb should be "determines" instead of "determine."
• Option 2: "To fully understand the geopolitical crisis, history must be analyzed through a completely objective lens."
• While grammatically correct, this sentence is not the most contextually relevant compared to Option 5.
• Option 3: "Each of the venture capitalists who invested in the AI startup expects a tenfold return on their initial investment."
• Incorrect because "each" is singular, but "their" is plural. The correct sentence should replace "their" with "his or her."
• Option 4: "The CFO requested that every department head submit their revised budget estimates by Friday evening."
• Incorrect because the subject "every department head" is singular, yet "their" is plural. The correct sentence should replace "their" with "his or her."
• Option 5: "The internal audit revealed that neither the manager nor his subordinates were aware of the security breach."
• This sentence is both grammatically and contextually correct. The subject "neither the manager nor his subordinates" agrees with the plural verb "were."

Correct sentence: The internal audit revealed that neither the manager nor his subordinates were aware of the security breach.

Additional Information

• Singular vs. Plural Agreement:
• Pay attention to the subject-verb agreement. Singular subjects require singular verbs, and plural subjects require plural verbs.
• Pronouns such as "each" and "every" are singular and should match with singular verbs or pronouns.
• Neither...nor Constructions:
• If the subjects connected by "neither...nor" differ in number, the verb agrees with the nearer subject.
• For example: "Neither the manager nor his subordinates were aware."

The correct answer is '5' i.e. The aggregate valuation of these tech unicorns is higher than the GDP of several developing nations combined .

Key Points

• Option 5 is grammatically correct and contextually appropriate as it clearly states the comparison between the aggregate valuation of tech unicorns and the GDP of developing nations.
• It uses proper sentence structure and conveys the intended meaning logically and fluently.
• The comparison is expressed correctly using the phrase "is higher than", making the statement clear and accurate.

Correct sentence: The aggregate valuation of these tech unicorns is higher than the GDP of several developing nations combined.

Additional Information

• Why other options are incorrect:
• Option 1: The phrase "was because" is redundant. "The reason why" already implies causation; hence, "was that" would have been the correct choice.
• Option 2: The comparison between "traditional internal combustion engines" and "maintenance costs" is flawed. It should compare engines to engines, or costs to costs.
• Option 3: While grammatically correct, the context is unclear as "binding on both the signing parties" is vaguely stated without proper emphasis on the agreement itself.
• Option 4: The phrase "If the firm would have anticipated" is incorrect. The correct form is "If the firm had anticipated" as per third conditional sentence rules.

The correct answer is '1' i.e. The judge ordered that the evidence be sealed and that the identities of the witnesses remain confidential .

Key Points

• Option 1 is grammatically and contextually correct because it correctly uses the subjunctive mood (e.g., "be sealed" and "remain confidential"), which is appropriate for formal commands or recommendations.
• The subjunctive mood is used in clauses that follow verbs like "ordered" to express a demand, suggestion, or requirement.
• The structure aligns with standard grammar rules for legal or formal instructions.

Correct sentence: The judge ordered that the evidence be sealed and that the identities of the witnesses remain confidential.

Additional Information

• Explanation of Incorrect Options:
• Option 2: "Driving through the dense fog, a massive billboard suddenly loomed out of the darkness, startling the driver." This sentence has a dangling modifier because it implies the billboard is driving through the fog, which is illogical.
• Option 3: "The university administration has forbidden the students from organizing political rallies on campus grounds." While the sentence is grammatically correct, it is contextually less formal and precise compared to Option 1.
• Option 4: "Her economic philosophy is grounded in the belief that market forces, if left unregulated, will naturally self-correct." This sentence is accurate but does not align with the formal, legal tone required by the question's context.
• Option 5: "The production manager, along with his entire team of skilled technicians, have been laid off due to automation." This sentence is incorrect because "have been" should be replaced with "has been" to match the singular subject "The production manager."

The correct answer is '3' i.e. The judge ruled that the defendant's actions were not only reckless but they also violated federal environmental laws. .

Key Points

• The error lies in the sentence's structure after "not only... but also." The subject "actions" is plural, so the verb structure must remain consistent.
• Using "they also violated" creates redundancy and disrupts the parallelism. Instead, the correct phrasing would be: "The judge ruled that the defendant's actions were not only reckless but also violated federal environmental laws."
• The "not only... but also" construction requires both parts to be parallel in grammatical structure.

Correct sentence: The judge ruled that the defendant's actions were not only reckless but also violated federal environmental laws.

Additional Information

• Parallelism:
• Definition: Ensuring that elements of a sentence are grammatically consistent in structure.
• Example: She likes hiking, swimming, and cycling (parallel structure).
• Redundancy:
• Definition: Unnecessary repetition of words or ideas.
• Example: "They returned back to the office" (corrected: "They returned to the office").

The correct answer is '1' i.e. The newly appointed managing director has and always will prioritize shareholder value over short-term bonuses. .

Key Points

• The sentence in option 1 is grammatically incorrect because of the incorrect placement of verbs. The phrase "has and always will prioritize" is not parallel in structure.
• To maintain grammatical consistency, the correct phrasing should be "has prioritized and always will prioritize."
• Parallel structure ensures that verbs or phrases in a sentence are balanced and grammatically consistent.

Correct sentence: The newly appointed managing director has prioritized and always will prioritize shareholder value over short-term bonuses.

Additional Information

• Option 2: The sentence is correct. The phrase "No sooner...than" correctly conveys the idea of an immediate consequence.
• Option 3: The sentence is grammatically and contextually correct. It accurately describes the micro-finance institution's role.
• Option 4: The sentence is correct. It effectively describes the state government's decision and its impact.
• Option 5: The sentence is correct. The use of "every invoice, receipt, and ledger entry" is grammatically consistent.

The correct answer is 'Repealed'.

 

Key Points

• The sentence says that Bahadur Shah I changed the strict religious policies of Aurangzeb and tried to reform the administration.
• The word should mean to cancel or abolish an existing law or policy.
• "Repealed" means officially cancelled or withdrawn (रद्द करना / समाप्त करना), which fits perfectly with changing earlier policies.
• The structure “repealed the religious policies of his father” is grammatically and historically appropriate.

Therefore, the correct answer is 'Option 5'.

 

Complete Sentence: Aurangzeb's son, Bahadur Shah I, repealed the religious policies of his father and attempted to reform the administration.

 

Additional Information

• Commenced (आरंभ किया): means started; does not fit with changing policies.
• Mandated (आदेश दिया): means officially ordered; opposite of cancelling policies.
• Decreed (घोषित किया): means declared by authority; not suitable for removing old policies.
• Contended (तर्क किया / संघर्ष किया): means argued or claimed; does not fit the context of policy change.

The correct answer is 'Shattered.'

Key Points

• The given sentence "The far-off Indian campaign of Nadir Shah, who had previously reestablished Iranian suzerainty over most of West Asia, the Caucasus, and Central Asia, culminated with the Sack of Delhi and (2) the remnants of Mughal power and prestige'' is talking about Nadir Shah damaging or destroying the remnants of Mughal power and prestige.
• Therefore, the most appropriate word to be filled in the blank is 'Shattered'.
• Also, the use of the word ''remnants'' in the sentence indicates the use of the word 'shattered' in the blank.
• The word 'Shattered' means To damage or destroy something.
• Example: The crisis has shattered their confidence.

Hence, the correct answer is option 1.

Complete Sentence: The far-off Indian campaign of Nadir Shah, who had previously reestablished Iranian suzerainty over most of West Asia, the Caucasus, and Central Asia, culminated with the Sack of Delhi and shattered the remnants of Mughal power and prestige.

Additional Information

• Let us explore  the other options:
• Instituted means To introduce a system, policy, etc., or start a process.
• Healed means To cause something or someone to become sound or healthy again.
• Fathered means To be the source or originator of something.
• Forged means To create something strong, enduring, or successful.

The correct answer is 'Conflicts.'

Key Points

• The given sentence "Meanwhile, some regional polities within the increasingly fragmented Mughal Empire, involved themselves and the state in global (3), leading only to defeat and loss of territory during the Carnatic Wars and the Bengal War'' is saying that the state in global prolonged armed struggles, leading only to defeat and loss of territory during the Carnatic Wars and the Bengal War.
• Therefore, the most appropriate word to be filled in the blank is 'Conflicts'.
• Also, the use of the word ''War'' in the sentence indicates the use of the word 'conflicts' in the blank.
• The word 'Conflicts' means Prolonged armed struggles.
• Example: There have been conflicts such as this throughout history.

Hence, the correct answer is option 3.

Complete Sentence: Meanwhile, some regional polities within the increasingly fragmented Mughal Empire, involved themselves and the state in global conflicts, leading only to defeat and loss of territory during the Carnatic Wars and the Bengal War.

Additional Information

• Let us explore  the other options:
• Concordances mean Agreements or consistency.
• Accords mean Agreements or harmony.
• Truces mean Agreements between enemies or opponents to stop fighting or arguing for a certain time.
• Concurrences mean Agreements or consistency.

The correct answer is 'Futile.'

Key Points

• The given sentence "The Mughal Emperor Shah Alam II (1759–1806) made (4) attempts to reverse the Mughal decline but ultimately had to seek the protection of the Emir of Afghanistan, Ahmed Shah Abdali, which led to the Third Battle of Panipat between the Maratha Empire and the Afghans (led by Abdali) in 1761'' is talking about the pointless or worthless attempts made by the Mughal Emperor Shah Alam II to reverse the Mughal decline.
• Therefore, the most appropriate word to be filled in the blank is 'Futile'.
• Also, the use of the word ''attempts'' in the sentence indicates the use of the word 'futile' in the blank.
• The word 'Futile' means Incapable of producing any useful result; pointless.
• Example: Their efforts to revive him were futile.

Hence, the correct answer is option 2.

Complete Sentence: The Mughal Emperor Shah Alam II (1759–1806) made futile attempts to reverse the Mughal decline but ultimately had to seek the protection of the Emir of Afghanistan, Ahmed Shah Abdali, which led to the Third Battle of Panipat between the Maratha Empire and the Afghans (led by Abdali) in 1761.

Additional Information

• Let us explore  the other options:
• Efficacious means Successful in producing a desired or intended result; effective.
• Virtuous means Having or showing high moral standards.
• Sedate means Calm, dignified, and unhurried.
• Melancholy means Causing or expressing sadness; depressing.

The correct answer is 'Abolished.'

Key Points

• The given sentence "The British East India Company took control of the former Mughal province of Bengal-Bihar in 1793 after it (5) local rule (Nizamat) that lasted until 1858, marking the beginning of the British colonial era over the Indian subcontinent'' is saying that the British East India Company formally put an end to the local rule of Mughal province.
• Therefore, the most appropriate word to be filled in the blank is 'Abolished'.
• Also, the use of the word ''rule'' in the sentence indicates the use of the word 'abolished' in the blank.
• The word 'Abolished' means To formally put an end to a system, practice, or institution.
• Example: The Americans abolished slavery in 1863.

Hence, the correct answer is option 4.

Complete Sentence: The British East India Company took control of the former Mughal province of Bengal-Bihar in 1793 after it abolished local rule (Nizamat) that lasted until 1858, marking the beginning of the British colonial era over the Indian subcontinent.

Additional Information

• Let us explore  the other options:
• Legitimated means To make lawful or justify.
• Ratified means To sign or give formal consent to a treaty, contract, or agreement, making it officially valid.
• Endorsed means To say publicly that you give official support or agreement to a plan, statement, decision, etc.
• Warranted means To officially affirm or guarantee.

The correct answer is 'Deposed.'

Key Points

• The given sentence "After a crushing defeat in the war of 1857–1858 which he nominally led, the last Mughal, Bahadur Shah Zafar, was (6) by the British East India Company and exiled in 1858'' is saying that the last Mughal, Bahadur Shah Zafar, was overthrown by the British East India Company and exiled in 1858.
• Therefore, the most appropriate word to be filled in the blank is 'Deposed'.
• Also, the use of the word ''exiled'' in the sentence indicates the use of the word 'deposed' in the blank.
• The word 'Deposed' means To remove a ruler or leader from power.
• Example: The king was deposed by his people.

Hence, the correct answer is option 2.

Complete Sentence: After a crushing defeat in the war of 1857–1858 which he nominally led, the last Mughal, Bahadur Shah Zafar, was deposed by the British East India Company and exiled in 1858.

Additional Information

• Let us explore  the other options:
• Instated means To set up in position; install or establish.
• Baptized means To administer baptism to someone; christen.
• Enthroned means To install a monarch or bishop on a throne, especially during a ceremony to mark the beginning of their rule.
• Superseded means To take the place of somebody or something which existed or was used before and which has become old-fashioned.

The correct answer is Option (5) i.e. ADCBE

Key Points

• The sentence begins with "mental health awareness", which is correctly indicated by part (A).
• Following this, "is growing" (AD) continues the logical sequence, making it clear that mental health awareness is increasing.
• The next part, "as more people" (ADC), adds a reason or context for the growth of awareness.
• Ending with "recognize the importance of emotional well-being" (BE) completes the sentence by explaining the significance of mental health awareness.

Therefore, the correct answer is ADCBE.

Additional Information

• Option 1 (ACDBE): This option does not maintain a logical flow, as "mental health awareness is growing" should come before "recognize the importance."
• Option 2 (ABCDE): This sequence does not form a coherent sentence as "recognize the importance" comes too early without context.
• Option 3 (ABDEC): This sequence is incorrect as it places "recognize the importance" before "as more people," disrupting the logical flow.
• Option 4 (ABEDC): This sequence is fragmented and does not form a coherent sentence.

The correct answer is Option (1) i.e. ABDCE

Key Points

• The sentence begins with "public transportation" (A), which serves as the subject.
• The next part, "helps reduce" (B), logically connects to the subject, indicating the benefit of public transportation.
• Following this, "traffic congestion" (D) is added as the first benefit being reduced.
• Next, "and air pollution" (C) is included as the second benefit.
• Finally, "in cities" (E) completes the sentence by specifying the location where these benefits apply.

Therefore, the correct sequence is ABDCE.

Additional Information

• Option 2 (ABCDE): This option places "and air pollution" (C) before "traffic congestion" (D), which disrupts the logical sequence.
• Option 3 (ABDEC): This option places "in cities" (E) before "and air pollution" (C), which creates a grammatically incorrect sentence.
• Option 4 (ACDBE): This option places "and air pollution" (C) directly after "public transportation" (A), which makes the sentence incomplete and illogical.
• Option 5 (BACDE): This option starts with "helps reduce" (B), which makes the sentence incomplete as it lacks a proper subject.

The correct answer is Option (4) i.e. ABCED

Key Points

• The sentence begins with the subject "adopting eco-friendly habits," which is correctly indicated by part (A).
• Following the subject, "such as recycling and conserving water" (B and C) continues the logical sequence, providing examples of eco-friendly habits.
• The next part, "can make" (E) transitions to the potential impact of these habits.
• Ending with "a significant difference" (D) completes the sentence by highlighting the positive outcome.

Therefore, the correct answer is ABCED.

Additional Information

• Option 1 (BACDE): This option starts with "such as recycling adopting eco-friendly habits," which disrupts the logical sequence and lacks a proper introduction to the subject.
• Option 2 (ABDEC): This option incorrectly places "and conserving water" after "a significant difference," breaking the logical flow.
• Option 3 (ABCDE): This option places "can make" too early, before completing the examples of eco-friendly habits.
• Option 5 (ACDBE): This option jumbles the order of the examples and disrupts the overall flow of the sentence.

The correct answer is B-P

Key Points

 Let us look at the sentence combinations.

• Phrase B of column 1 should be matched with the phrase P of column 2 to make the sentence grammatically and contextually correct.
• "With the nomination process for the presidential election set to begin the Rajya Sabha Secretariat set up a special cell for the poll on Tuesday."
• Phrase B cannot be used with phrase Q and R because it would not make a meaningful sentence.
• With the nomination process for the presidential election set to begin both assistant returning officers for the election- are also part of this cell.
• With the nomination process for the presidential election set to begin who will be part of the counting process.

​Hence, the correct option is option 2.

The correct answer is 'side effects of the'.

Key Points

• When 'of' is used after 'each, every, one' etc., the noun or pronoun that comes immediately after 'of'  will be plural in form.
• The verb, pronoun, adjectives, etc. that come in the latter part of the sentence will be singular in form.
• For eg.- One of our students was unable to propel her wheelchair up the ramp.
• Therefore, we will add 's' to 'effect' to make the sentence grammatically correct.
• Hence, option 4 is the correct answer.

Additional Information

• Susceptibility is the state or fact of being likely or liable to be influenced or harmed by a particular thing.
• For eg.- Lack of exercise increases susceptibility to disease

The correct answer is 'was seldom or never'

Key Points

• 'Seldom or never' is the correct adverbial phrase.
• It is always used in a negative sense.
• We will replace 'seldom or ever' with 'seldom or never' to make the sentence grammatically correct.
• Hence, option 2 is the correct answer.

Additional Information

• Other such adverbial phrases include 'seldom, is never', 'little or nothing', 'little, if anything'.
• For eg.- I have seldom if ever been so embarrassed.

The correct answer is 'had some equipment'.

Key Points

• With uncountable nouns such as mischief, hair, equipment, scenery, etc, articles a/an, many, few, number of,  and plural forms are not used.
• For eg.- The mischief, however, was not ended.
• We use 'some' with uncountable nouns.
• Hence, in the given sentence, we will replace 'an' with 'some' to make the sentence grammatically correct.
• Thus, option 4 is the correct answer.

Additional Information

• Equipment is the necessary items for a particular purpose.
• For eg.- The electronic equipment had disappeared as well.

The correct answer is 'employment and recreation'.

Key Points

• A conjunction is a word, or a group of words that connects two or more than two words, phrases, clauses, sentences, etc.
• For eg.- He displayed determination as well as a powerful oratory.
• Conjunctions 'both' and 'and' are cumulative coordinating conjunctions.
• They connect two nouns, pronouns, etc., and are always used in the pair.
• Hence, option 1 is the correct answer.

Additional Information

• Recreation is an activity done for enjoyment when one is not working.
• For eg.-  The rest of the day was entirely at his disposal for reading and recreation.

The correct answer is 'form beside her'.

Key Points

• The words 'besides' and 'beside' both are prepositions.
• Prepositions are those words that are used before a noun or pronoun and denote the relation between the noun/pronoun and the other part of the sentence.
• ​For eg.-  There's a broom cupboard under the stairs.
• However, the meaning of both words is different.

1. Beside means at the side of or next to.Besides means in addition to or apart from.

• For eg.- He went and sat beside her.
• For eg.- I have no other family besides my parents.
• The given sentence is indicating that she looked at Timothy's recumbent form next to her.
• Hence, option 5 will be the most appropriate choice.

Additional Information

• Recumbent means lying down.
• For eg.-  He looked down at the recumbent figure.

The correct answer is Option 1.

 

Key Points

• The paragraph begins by addressing the pervasive nature of problems in life, setting a general context for the discussion.
• Sentence D is the first sentence as it introduces the broad idea that life is full of problems needing solutions:
• "Life is strewn with problems that need to be solved."
• Sentence B follows by explaining the complexity of problems and the mixture of decisions required to address them:
• "And most problems do not require single decisions, like ‘Who should I vote for in this upcoming election?’ but a complicated mixture of decisions, prioritization, and action plans."
• Sentence 3 (fixed) emphasizes that solving problems is itself a challenging task, building upon the ideas introduced earlier.
• Sentence F follows by focusing on the persistence and effort needed to work through problems:
• "It requires finding information, but it also involves persistence."
• Sentence A concludes by highlighting the motivation and grit required for problem-solving:
• "It takes motivation and grit to stick with a problem and work your way through it."
• Sentence E wraps up the paragraph by pointing out that some problems involve multiple layers of decision-making, giving a sense of complexity to the discussion.
• "Some problems, however, are much more complex and involve multiple layers of decision-making."
• The correct sequence is DB3FAE.

 

Coherent paragraph after rearrangement:

"Life is strewn with problems that need to be solved. And most problems do not require single decisions, like ‘Who should I vote for in this upcoming election?’ but a complicated mixture of decisions, prioritization, and action plans. Figuring out how to solve a problem is itself a hard problem. It requires finding information, but it also involves persistence. It takes motivation and grit to stick with a problem and work your way through it. Some problems, however, are much more complex and involve multiple layers of decision-making."

The correct answer is Option 5.

 

Key Points

• The paragraph begins by identifying the ubiquity of problems in life, setting the stage for discussing problem-solving challenges.
• Sentence D is the first sentence as it introduces the general context:
• "Life is strewn with problems that need to be solved."
• Sentence B is the second sentence because it elaborates on the complexity of problems and how they require a mix of decisions and actions:
• "And most problems do not require single decisions, like ‘Who should I vote for in this upcoming election?’ but a complicated mixture of decisions, prioritization, and action plans."
• Sentence 3 (fixed) comes next and emphasizes the inherent difficulty of solving problems.
• Sentence F follows as it describes persistence and effort as critical factors in solving problems:
• "It requires finding information, but it also involves persistence."
• Sentence A is next as it highlights the grit and motivation required to solve problems:
• "It takes motivation and grit to stick with a problem and work your way through it."
• Sentence E concludes by discussing the layered decision-making involved in complex problems:
• "Some problems, however, are much more complex and involve multiple layers of decision-making."
• The correct sequence is DB3FAE.

 

Coherent paragraph after rearrangement:

"Life is strewn with problems that need to be solved. And most problems do not require single decisions, like ‘Who should I vote for in this upcoming election?’ but a complicated mixture of decisions, prioritization, and action plans. Figuring out how to solve a problem is itself a hard problem. It requires finding information, but it also involves persistence. It takes motivation and grit to stick with a problem and work your way through it. Some problems, however, are much more complex and involve multiple layers of decision-making."

The correct answer is Option 4.

 

Key Points

• The paragraph begins by introducing the concept of life being filled with problems, setting a broad context for the discussion.
• Sentence D is the first sentence as it introduces the overarching theme:
• "Life is strewn with problems that need to be solved."
• Sentence B is the second sentence as it elaborates on the complexity of these problems:
• "And most problems do not require single decisions, like ‘Who should I vote for in this upcoming election?’ but a complicated mixture of decisions, prioritization, and action plans."
• Sentence 3 (fixed) emphasizes that solving problems is a challenging task in itself.
• Sentence F is the fourth sentence as it discusses persistence and effort required for solving problems:
• "It requires finding information, but it also involves persistence."
• Sentence A follows as it highlights the motivation and grit needed to tackle problems:
• "It takes motivation and grit to stick with a problem and work your way through it."
• Sentence E concludes by discussing how some problems have multiple layers of decision-making:
• "Some problems, however, are much more complex and involve multiple layers of decision-making."
• The correct sequence is DB3FAE.

 

Coherent paragraph after rearrangement:

"Life is strewn with problems that need to be solved. And most problems do not require single decisions, like ‘Who should I vote for in this upcoming election?’ but a complicated mixture of decisions, prioritization, and action plans. Figuring out how to solve a problem is itself a hard problem. It requires finding information, but it also involves persistence. It takes motivation and grit to stick with a problem and work your way through it. Some problems, however, are much more complex and involve multiple layers of decision-making."

The correct answer is Option 4.

 

Key Points

• The paragraph begins by introducing the idea that life is filled with problems, setting the stage for discussing problem-solving challenges.
• Sentence D is the first sentence as it introduces the broad theme:
• "Life is strewn with problems that need to be solved."
• Sentence B is the second sentence as it elaborates on the complexity of problems:
• "And most problems do not require single decisions, like ‘Who should I vote for in this upcoming election?’ but a complicated mixture of decisions, prioritization, and action plans."
• Sentence 3 (fixed) highlights the inherent difficulty of solving problems.
• Sentence F is the fourth sentence as it emphasizes the importance of persistence and finding information in problem-solving:
• "It requires finding information, but it also involves persistence."
• Sentence A is the fifth sentence as it discusses the motivation and grit required to work through problems:
• "It takes motivation and grit to stick with a problem and work your way through it."
• Sentence E concludes by addressing the layered nature of complex problems:
• "Some problems, however, are much more complex and involve multiple layers of decision-making."
• The correct sequence is DB3FAE.

 

Coherent paragraph after rearrangement:

"Life is strewn with problems that need to be solved. And most problems do not require single decisions, like ‘Who should I vote for in this upcoming election?’ but a complicated mixture of decisions, prioritization, and action plans. Figuring out how to solve a problem is itself a hard problem. It requires finding information, but it also involves persistence. It takes motivation and grit to stick with a problem and work your way through it. Some problems, however, are much more complex and involve multiple layers of decision-making."

The correct answer is Option 5.

 

Key Points

• The paragraph begins by introducing the idea that life is filled with problems, setting the stage for further discussion on solving them.
• Sentence D is the first sentence as it introduces the overarching theme:
• "Life is strewn with problems that need to be solved."
• Sentence B is the second sentence as it elaborates on the complexity of these problems:
• "And most problems do not require single decisions, like ‘Who should I vote for in this upcoming election?’ but a complicated mixture of decisions, prioritization, and action plans."
• Sentence 3 (fixed) emphasizes the difficulty of solving problems in general.
• Sentence F is the fourth sentence as it discusses persistence and the importance of information-gathering in solving problems:
• "It requires finding information, but it also involves persistence."
• Sentence A is the fifth sentence as it highlights the motivation and grit required to solve problems:
• "It takes motivation and grit to stick with a problem and work your way through it."
• Sentence E concludes the paragraph by discussing the complexity of problems that involve multiple layers of decision-making:
• "Some problems, however, are much more complex and involve multiple layers of decision-making."
• The correct sequence is DB3FAE.

 

Coherent paragraph after rearrangement:

"Life is strewn with problems that need to be solved. And most problems do not require single decisions, like ‘Who should I vote for in this upcoming election?’ but a complicated mixture of decisions, prioritization, and action plans. Figuring out how to solve a problem is itself a hard problem. It requires finding information, but it also involves persistence. It takes motivation and grit to stick with a problem and work your way through it. Some problems, however, are much more complex and involve multiple layers of decision-making."

The correct answer is option 5.

Key Points

No interchange is required in the sentence as it is both grammatically correct and meaningful.

• The word whimsical (A) perfectly describes the artist as someone who is imaginative or playful in their creations.
• Conspicuous (B) appropriately describes the paintings as noticeable or attracting attention.
• The word vivid (C) correctly portrays the paintings as brightly colored or striking.
• Meticulous (D) accurately conveys that the paintings were detailed and carefully crafted.

Thus, no interchange is necessary, and the sentence is meaningful as it stands.

Additional Information

Let's understand the meanings of the marked words - 

• Whimsical - playfully quaint or fanciful, especially in an appealing and amusing way (मनमौजी).
• Conspicuous - standing out so as to be clearly visible (स्पष्ट).
• Vivid - producing powerful feelings or strong, clear images in the mind (ज्वलंत).
• Meticulous - showing great attention to detail; very careful and precise (सूक्ष्म).

The correct answer is option 4.

Key Points

The given sentence is: The overt (A) signs of anger were quite subtle (B), making the situation appear more ambiguous (C) and less plausible (D) to outsiders.

Explanation:

• The word "overt" (A) is contradictory to the word "subtle" (B). "Overt" means something openly shown, while "subtle" means something not obvious or understated.
• To make the sentence meaningful and grammatically correct, we need to interchange "overt" (A) and "subtle" (B).

After interchanging, the sentence becomes:

The subtle (A) signs of anger were quite overt (B), making the situation appear more ambiguous (C) and less plausible (D) to outsiders.

Thus, the correct answer is option 4, which suggests swapping A and B.

Additional Information

Meaning of key terms:

• Overt: Done or shown openly; not secret or hidden. (स्पष्ट)
• Subtle: So delicate or precise as to be difficult to analyze or describe. (सूक्ष्म)
• Ambiguous: Open to more than one interpretation; not having one obvious meaning. (अस्पष्ट)
• Plausible: Seeming reasonable or probable. (विश्वसनीय)

The correct answer is Option (5) i.e. No interchange required

 

Key Points

• The word 'unscrupulous' (A) correctly describes the businessman as morally unprincipled.
• The word 'notorious' (B) correctly describes the ventures as well-known for negative reasons.
• The word 'actions' (C) correctly refers to the corrupt deeds of the businessman.
• The word 'overshadowed' (D) correctly describes the effect of his corrupt actions on his public image.
• All words are in the correct positions and make the sentence both grammatically correct and meaningful.

Therefore, the correct answer is No interchange required.

The correct answer is option 5.

Key Points

• No interchange required. The sentence is already grammatically correct and meaningful as written.
• Word meanings and roles in the sentence:
• Zealous (A) — enthusiastic, eager. (modifies player)
• Melancholy (B) — sad, sorrowful. (describes the player's feeling after defeat)
• Resilient (C) — able to recover quickly; mentally tough. (describes his character)
• Brisk (D) — lively, energetic. (describes the manner/energy with which he recovers)
• Each adjective correctly modifies the noun or idea it refers to: a zealous player can still feel melancholy after losing; a resilient character appropriately explains how he bounces back; recovering with brisk energy is a natural collocation.

Example to illustrate: A passionate (zealous) runner may feel sad (melancholy) after losing a race, but their tough (resilient) mindset helps them train again with lively (brisk) energy.

The correct answer is 'Supersede.'

Key Points

• Supersede means to replace someone or something.​
• In the first sentence, filling the blank with 'supersede' would imply one thinking of replacing the other for his position.
• In the second sentence, filling the blank with 'supersede' would imply replacing the manual labor by robots.
• Therefore, the most appropriate word to be filled in the blank is 'supersede'.

Hence, the correct answer is option 1.

Complete Sentences:

1. Vikram hopes he can supersede his boss and take his position in the company.
2. The use of robots will someday supersede manual labor.

Additional Information

• Let us explore the other options:
• ​Superficial means not studying or thinking about something in a deep or complete way.
• Superfluous means unnecessary, not needed.
• Supernatural means unnaturally or extraordinarily great.
• Supercilious means showing that you think that you are better than other people.

The correct answer is 'Aberrant.'

Key Points

• Aberrant means diverging from the normal or right way.​
• In the first sentence, filling the blank with 'aberrant' would imply a way of tying the laces other than the normal way.
• In the second sentence, filling the blank with 'aberrant' would imply that the drunken man conducted in an abnormal way.
• Therefore, the most appropriate word to be filled in the blank is 'aberrant'.

Hence, the correct answer is option 4.

Complete Sentences:

1. My sister has an aberrant way of tying her shoelaces.
2. The drunken man’s aberrant conduct drew the police officer’s attention.

Additional Information

• Let us explore the other options:
• Frequent means (of a person) doing something often; habitual.
• Normal means usual, typical, or expected.
• Usual means habitually or typically occurring or done.
• Familiar means having a good knowledge of something.

The correct answer is 'Mendacious.'

Key Points

• Mendacious means lying; not telling the truth.​
• In the first sentence, filling the blank with 'mendacious' would imply lying about vegetarianism.
• In the second sentence, filling the blank with 'mendacious' would imply creating a false story or lying about something.
• Therefore, the most appropriate word to be filled in the blank is 'mendacious'.

Hence, the correct answer is option 2.

Complete Sentences:

1. Amit is mendacious about his vegetarianism because he eats chicken.
2. Instead of giving me another mendacious story, just be honest for once.

Additional Information

• Let us explore the other options:
• Candid means truthful and straightforward; frank.
• Reliable means consistently good in quality or performance; able to be trusted.
• Moral means standards of good behavior.
• Ethical means morally good or correct.

The correct answer is Option C.

 

Key Points

• Option A: Soft toys became popular as a means for children to engage in physical activities outdoors.
• This statement is incorrect as the passage mentions that lockdowns confined families to their homes and outdoor play was restricted.
• Option B: The software industry saw a decline during the COVID-19 pandemic.
• This statement is incorrect. The passage states that the global software industry experienced "unprecedented, explosive growth" and became the "nervous system of the global economy."
• Option C: Soft toys provided emotional security for children during the pandemic.
• This statement is correct as the passage explicitly mentions that these tactile toys offered "emotional security, anxiety relief, and a medium for imaginative play" during isolation.
• Option D: Toy manufacturers decreased production of plush toys due to reduced demand.
• This statement is incorrect. According to the passage, toy manufacturers ramped up production to meet the "unprecedented spike in global demand."
• Option E: Cloud computing infrastructure experienced a decline during the COVID-19 pandemic.
• This statement is incorrect as the passage notes that cloud computing infrastructure experienced a "gold rush" as businesses transitioned to remote work.

Therefore, the correct answer is: ‘Option C’.

The correct answer is Option 2.

 

Key Points

• The passage explicitly mentions that in the physical realm, the toy industry experienced a remarkable resurgence.
• This growth was driven by parents seeking comforting, screen-free developmental tools for their children during the lockdowns.
• Soft toys provided emotional security and anxiety relief for children who were restricted from outdoor play and school environments.
• Thus, the reason for the resurgence aligns directly with the description in Option B.

Therefore, the correct answer is B.

 

Correct Sentence: "In the physical realm, the toy industry experienced a remarkable resurgence, driven by parents seeking comforting, screen-free developmental tools for their children."

 

Additional Information

• A: The increase in outdoor activities – Incorrect, as the passage states outdoor play was restricted during this time.
• C: The decline of digital software infrastructure – Incorrect, as the passage notes that the software industry actually experienced "explosive growth."
• D: The implementation of homeschooling practices – While schools closed, the passage identifies the specific driver for the toy industry boom as the search for comforting, screen-free tools.
• E: The closure of toy manufacturing plants – Incorrect, as manufacturers "ramped up production" to meet the spike in demand.

The correct answer is Option 4.

 

Key Points

• The passage explicitly states that the software sector and digital infrastructure experienced "unprecedented, explosive growth" and a "gold rush" during the pandemic.
• The decline of physical office spaces and school campuses was a direct result of lockdowns and the "non-negotiable transition to remote work and e-learning."
• Option D suggests a "decline in demand for digital tools," which is the exact opposite of what the passage describes.
• Since the demand for digital tools surged to ensure survival and operations, it cannot be a reason for the decline of physical spaces; rather, the increase in digital demand was the response to that decline.

Therefore, the correct answer is D.

 

Relevant Quote: "Software-as-a-Service (SaaS) models, cloud computing infrastructure, and collaborative communication platforms experienced a gold rush as businesses scrambled to remain operational."

 

Additional Information

• A: The COVID-19 pandemic – Cited as the primary trigger for the economic anomalies and lockdowns.
• B: The necessity of remote work – Cited as the reason why schools and offices had to transition to virtual spaces.
• C: The acceleration of digital infrastructure transformation – Cited as the result of the shift away from physical campuses.
• E: The temporary reaction to a crisis – The text mentions that while the boom started as a reaction to a crisis, it led to a permanent structural pivot.

The correct answer is 'Option 1'.

 

Key Points

• A) The COVID-19 pandemic had a positive impact on consumer demand for soft toys and digital software.
• This can be inferred from the passage. The passage explicitly states that the pandemic catalyzed explosive growth in both the soft toys market and the digital software sector.
• B) Toy manufacturers had to prioritize emotional security over commercial profits.
• This cannot be inferred from the passage. The passage mentions that toy manufacturers ramped up production of plush toys that emphasized comfort, sensory engagement, and companionable play, but it doesn't indicate that commercial profits were deprioritized.
• C) The global software industry experienced a decrease in collaborative communication platforms.
• This cannot be inferred from the passage. The passage actually indicates a surge in collaborative communication platforms during the pandemic.
• D) The surge in demand for soft toys was a temporary trend that reversed post-pandemic.
• This cannot be inferred from the passage. The passage does not mention that the surge in demand for soft toys was a temporary trend or that it reversed post-pandemic.
• E) The increase in cloud computing infrastructure was a reactionary adjustment rather than a permanent change.
• This cannot be inferred from the passage. The passage suggests that the digital transformation represented a permanent structural pivot.

Therefore, the correct answer is Option 1.

 

Additional Information

• Only A: Correct because option A can be inferred from the passage.
• Only B: Incorrect because option B cannot be inferred from the passage.
• Only C: Incorrect because option C cannot be inferred from the passage.
• Only D: Incorrect because option D cannot be inferred from the passage.
• Only E: Incorrect because option E cannot be inferred from the passage.

The correct answer is 'spike'.

 

Key Points

• The word "spike" means a sharp increase in the magnitude or concentration of something. (अचानक हुई तेज़ वृद्धि)
• In the passage, it is mentioned that the pandemic "catalysed unprecedented, explosive growth" in certain markets. The term "spike" directly refers to this sudden surge in demand.
• The context describes a massive increase in the popularity of soft toys as families sought emotional comfort, making "spike" the only logically fitting word.
• The other options: "scarcity" (shortage), "reduction" (decrease), "plateau" (no change), and "downturn" (decline) contradict the "explosive growth" described in the text.

Therefore, the correct answer is 'Option B'.

Complete Sentence: This unprecedented spike in global demand was a clear sign that families were prioritising emotional well-being and comforting physical play to combat the psychological fatigue of isolation.

Additional Information

• Scarcity (कमी): the state of being scarce or in short supply.
• Reduction (कटौती): the action or fact of making something smaller or less in amount, degree, or size.
• Plateau (स्थिरता): a state of little or no change following a period of activity or progress.
• Downturn (गिरावट): a decline in economic, business, or other activity.

The correct answer is 'Option B' i.e., 'restricted'.

Key Points

• The word "confined" means to keep or restrict someone or something within certain limits of space, scope, or time. (सीमित)
• Example: The heavy rain confined the children to the house all afternoon.
• "Restricted" refers to something that is limited in extent, number, or scope; it is the closest synonym to "confined" as used in the passage to describe people being kept in their homes. (प्रतिबंधित या सीमित)
• Example: Access to the laboratory is restricted to authorised personnel only.

Therefore, the correct answer is- restricted.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Liberated (मुक्त): To set someone free from a situation, especially imprisonment or slavery.
• Example: The army liberated the city from the enemy forces.
• Expanded (विस्तारित): To become larger or more extensive in size or importance.
• Example: The company expanded its operations to several new countries this year.
• Dispersed (बिखरा हुआ): Distributed or spread over a wide area.
• Example: The police used water cannons to disperse the crowd.
• Increased (बढ़ा हुआ): To become greater in size, amount, or degree.
• Example: The cost of living has increased significantly over the last decade.

The correct answer is Option B i.e., manual.

Key Points

• In the context of the passage, the word "book" (as part of "rule book") refers to a set of established rules, principles, or standards that govern how something is done. (नियमावली)
• Example: The sudden shift in the market forced the company to throw away the old rule book and start fresh.
• "Manual" refers to a book of instructions or a set of guidelines that explains how to do something or how a system works. (निर्देशिका/नियम-पुस्तिका)
• Example: The employee manual contains all the policies regarding leave and conduct.
• Hence, in the phrase "rewriting the rule book," the word "book" is most similar in meaning to 'manual'.

Therefore, the correct answer is- manual.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Catalogue (सूची-पत्र): A complete list of items, typically arranged in alphabetical or systematic order.
• Example: You can browse our full range of products in the autumn catalogue.
• Register (पंजी/रजिस्टर): An official list or record of names, items, or events.
• Example: The hotel guest register showed that no one had checked in after midnight.
• Volume (खंड/पुस्तक): A single book that is part of a larger series or a collection of written work.
• Example: The encyclopedia consists of twenty individual volumes.
• Rewrite (फिर से लिखना): To write something again in a different way to improve or change it.
• Example: The script was so poor that the director asked the author to rewrite it entirely.

The correct answer is Option(D) i.e., 'Obscurity'.

Key Points

• The word "sign" means an object, quality, or event whose presence or occurrence indicates the probable presence or existence of something else. (संकेत)
• Example: The sudden drop in temperature was a sure sign that a storm was approaching.
• "Obscurity" refers to the state of being unknown, inconspicuous, or difficult to understand; it implies a lack of clarity or visibility, which is the opposite of a clear sign or indicator. (अस्पष्टता)
• Example: The origins of the ancient ritual are shrouded in obscurity, with no clear records existing today.
• Hence, we can infer that the opposite of 'sign' is 'obscurity'.

Therefore, the correct answer is- Obscurity.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Indication (संकेत): A condition or circumstance that points to or suggests something.
• Example: There was no indication that the company was in any financial trouble.
• Proof (प्रमाण): Evidence or argument establishing a fact or the truth of a statement.
• Example: You will need to provide proof of identity to open a bank account.
• Signal (संकेत/इशारा): A gesture, action, or sound that is used to convey information or instructions.
• Example: The referee blew the whistle as a signal for the match to start.
• Evidence (सबूत): The available body of facts or information indicating whether a belief or proposition is true or valid.
• Example: The police found forensic evidence that linked the suspect to the crime scene.

Shortcut Trick

Let the breadth of the field be x m, then the length is 3x m.

Perimeter of the rectangular field = Total Fencing Cost ÷ Fencing Rate = 960 ÷ 7.5 = 128 m.

Perimeter = 2 × (Length + Breadth) ⇒ 2 × (3x + x) = 128 ⇒ 8x = 128 ⇒ x = 16 m.

Difference between length and breadth = 3x − x = 2x = 2 × 16 = 32 m.

∴ The correct answer is 32 m.

Alternate Method

Given:

Ratio of length to breadth = 3 : 1

Total cost of fencing = ₹960

Rate of fencing = ₹7.5 per meter

Formula Used:

Perimeter of a rectangle = 2 × (Length + Breadth)

Perimeter = Total Cost of Fencing ÷ Rate of Fencing

Calculations:

⇒ Let breadth = x m and length = 3x m

⇒ Perimeter = 960 ÷ 7.5 = 128 m

⇒ 2 × (3x + x) = 128

⇒ 2 × 4x = 128

⇒ 8x = 128

⇒ x = 16 m

⇒ Length = 3 × 16 = 48 m

⇒ Breadth = 16 m

⇒ Difference = 48 − 16 = 32 m

∴ The correct answer is 32 m.

Additional Information

Perimeter vs Area Fencing/Ploughing

Fencing is always done along the boundary (Perimeter), whereas ploughing or leveling is done on the surface (Area). Fencing Rate is in per meter, while Leveling Rate is in per sq. meter.

Rectangular Mensuration Formulas

Area of rectangle = Length × Breadth, and Diagonal of rectangle = √(Length² + Breadth²).

Shortcut Trick

Speed of Train B = 20 ÷ 2 = 10 m/sec.

Length of Train B = Speed × Time = 10 × 28 = 280 m.

Ratio of lengths A : B = 10 : 7. Since 7 units = 280 m, then 1 unit = 40 m.

Length of Train A = 10 × 40 = 400 m.

∴ The correct answer is 400 m.

Alternate Method

Given:

Speed of Train A (S_A) = 20 m/sec

Ratio of Speed A to B = 2 : 1

Ratio of Length A to B = 10 : 7

Time taken by Train B to cross a pole = 28 seconds

Calculations:

⇒ Speed of Train B = S_A ÷ 2 = 20 ÷ 2 = 10 m/sec

⇒ Length of Train B (L_B) = Speed_B × Time = 10 × 28 = 280 m

⇒ According to ratio, 7 units = 280 m

⇒ 1 unit = 280 ÷ 7 = 40 m

⇒ Length of Train A (L_A) = 10 units = 10 × 40 = 400 m

∴ The correct answer is 400 m.

Additional Information

Crossing a Pole or Point Object

When a train crosses a stationary pole or person, the distance covered is equal to the length of the train itself. Formula: Length = Speed × Time.

Crossing a Platform or Bridge

When a train crosses a platform or another train, the total distance covered is the sum of the lengths of the train and the object. Total Distance = L₁ + L₂.

Unit Conversion

To convert km/hr to m/sec, multiply by 5/18. To convert m/sec to km/hr, multiply by 18/5.

Common Solution:

Let the quantity of white rice sold by A be 4x

The quantity of brown rice sold by B = (x × {125/100} = 5x

The quantity of white rice sold by B = (5x + 15)

The quantity of brown rice sold by A = {5x/4} × 3 = {15x/4})

The quantity of brown rice sold by C = (70 × 3 – 5x - {15x/4})

= (210 - {35x/4})

The quantity of white rice sold by C = [100 - (210 - {35x/4})]

= ({35x/4} – 110)

Given, 260 = {35x/4} – 110 + 5x + 15 + 4x

355 = {71x/4})

So, x = 20

 

Required difference = 75 − 65 = 10 kg

Common Solution:

Let the quantity of white rice sold by A be 4x

The quantity of brown rice sold by B = (x × {125/100} = 5x

The quantity of white rice sold by B = (5x + 15)

The quantity of brown rice sold by A = {5x/4} × 3 = {15x/4})

The quantity of brown rice sold by C = (70 × 3 – 5x - {15x/4})

= (210 - {35x/4})

The quantity of white rice sold by C = [100 - (210 - {35x/4})]

= ({35x/4} – 110)

Given, 260 = {35x/4} – 110 + 5x + 15 + 4x

355 = {71x/4})

So, x = 20

 

Calculations:

Required percentage = (115/75) x 100 = 153.33%

Common Solution:

Let the quantity of white rice sold by A be 4x

The quantity of brown rice sold by B = (x × {125/100} = 5x

The quantity of white rice sold by B = (5x + 15)

The quantity of brown rice sold by A = {5x/4} × 3 = {15x/4})

The quantity of brown rice sold by C = (70 × 3 – 5x - {15x/4})

= (210 - {35x/4})

The quantity of white rice sold by C = [100 - (210 - {35x/4})]

= ({35x/4} – 110)

Given, 260 = {35x/4} – 110 + 5x + 15 + 4x

355 = {71x/4})

So, x = 20

 

Calculations:

The average quantity of brown rice sold by A and C = (75 + 35)/2 = 55 kg

The quantity of white rice sold by D = 55 + 5 = 60 kg

The ratio of brown rice sold by D and B = 3 : 4

The quantity of brown rice sold by B = 100 kg

The quantity of brown rice sold by D = 100 x (3/4) = 75 kg

The total quantity of rice sold by D = 75 + 60 = 135 kg

Common Solution:

Let the quantity of white rice sold by A be 4x

The quantity of brown rice sold by B = (x × {125/100} = 5x

The quantity of white rice sold by B = (5x + 15)

The quantity of brown rice sold by A = {5x/4} × 3 = {15x/4})

The quantity of brown rice sold by C = (70 × 3 – 5x - {15x/4})

= (210 - {35x/4})

The quantity of white rice sold by C = [100 - (210 - {35x/4})]

= ({35x/4} – 110)

Given, 260 = {35x/4} – 110 + 5x + 15 + 4x

355 = {71x/4})

So, x = 20

 

Calculations:

The total revenue earned by selling white rice = 80 x 20 = Rs. 1600

The revenue earned by selling brown rice = 2500 – 1600 = Rs. 900

The price of each kg of brown rice = 900/75 = Rs. 12

Common Solution:

Let the quantity of white rice sold by A be 4x

The quantity of brown rice sold by B = (x × {125/100} = 5x

The quantity of white rice sold by B = (5x + 15)

The quantity of brown rice sold by A = {5x/4} × 3 = {15x/4})

The quantity of brown rice sold by C = (70 × 3 – 5x - {15x/4})

= (210 - {35x/4})

The quantity of white rice sold by C = [100 - (210 - {35x/4})]

= ({35x/4} – 110)

Given, 260 = {35x/4} – 110 + 5x + 15 + 4x

355 = {71x/4})

So, x = 20

 

Calculations:

The quantity of white rice sold by B = 115 kg

The total quantity of brown rice sold by A and B together = 75 + 100 = 175 kg

Required ratio = 115:75 = 23: 35

Given:

√(21.98 × 30.09 + 123.90) = ? ÷ 4

Formula used:

Approximation Method: Rounding decimals to the nearest whole numbers for easier calculation.

Calculations:

To find the approximate value, we round the given numbers:

21.98 ≈ 22

30.09 ≈ 30

123.90 ≈ 124

Now, substitute these approximate values into the expression:

√(22 × 30 + 124) = ? ÷ 4

⇒ √(660 + 124) = ? ÷ 4

⇒ √784 = ? ÷ 4

Since the square root of 784 is 28:

⇒ 28 = ? ÷ 4

Now, solve for ? by performing multiplication:

⇒ ? = 28 × 4

⇒ ? = 112

∴ The correct answer is option (5).

Given:

29.98% of 560 + 120.11 of 39 = ?

Formula used:

Approximation method: Rounding values to the nearest integers to simplify calculation.

Calculation:

For approximate value:

29.98% ≈ 30%

120.11 ≈ 120

⇒ ? ≈ 30% of 560 + 120 × 39

⇒ ? = (30/100) × 560 + 120 × 39

⇒ ? = 3 × 56 + 4680

⇒ ? = 168 + 4680

⇒ ? = 4848

∴ The correct answer is option (2).

Given:

22.02² + (1 / 9) of 44 = ? − 45.09% of 100.9

Formula used:

Approximation method: Round off the decimal numbers to the nearest integers to simplify the calculation.

Calculations:

To find the approximate value, let:

22.02 ≈ 22

44 ≈ 45 (since 45 is a multiple of 9)

45.09% ≈ 45%

100.9 ≈ 100

Now, substitute these values into the expression:

22² + (1 / 9) × 45 = ? − 45% of 100

⇒ 484 + 5 = ? − (45 / 100) × 100

⇒ 489 = ? − 45

⇒ ? = 489 + 45

⇒ ? = 534

∴ The correct answer is option (1).

Shortcut Trick

Total Work = LCM(15, 30) = 30 units.

Efficiency: A = 2, B = 1. Combined (A+B) = 3 units/day.

6 days work of (A+B) = 6 × 3 = 18 units. Remaining = 30 − 18 = 12 units.

B + C finish 12 units in 5 days → Efficiency of (B+C) = 12/5 = 2.4.

Efficiency of C = 2.4 − 1 = 1.4 units/day (or 7/5).

Time for C alone = 30 ÷ (7/5) = 150/7 days.

∴ The correct answer is 150/7 days.

Alternate Method

Given: A takes 15 days, B takes 30 days. They work together for 6 days. B and C finish remaining in 5 days.

Formula: Total Work = Efficiency × Time

⇒ Work done by A and B in 6 days = 6 × (2 + 1) = 18 units

⇒ Remaining work = 30 − 18 = 12 units

⇒ Let Efficiency of C be 'c'. Work done by B and C in 5 days = 5 × (1 + c) = 12

⇒ 1 + c = 12/5

⇒ c = 12/5 − 1 = 7/5

⇒ Time taken by C alone = Total Work ÷ Efficiency of C

⇒ Time = 30 ÷ (7/5) = (30 × 5) / 7 = 150/7 days

∴ The correct answer is 150/7 days.

Additional Information

Combined Efficiency

When multiple people work together, their individual efficiencies are added to find the total work done per day.

Work & Wages

Wages are generally distributed in the ratio of the total work done by each individual (Efficiency × Time).

Alternate Day Work

In alternate day problems, calculate the work done in one complete cycle (e.g., 2 days) and then divide total work by cycle work.

Shortcut Trick

Ratio of Father : Son currently is 2 : 1 and 10 years ago was 3 : 1.

Make the difference between ratios equal: (2 : 1) × 2 → 4 : 2 and (3 : 1) × 1 → 3 : 1.

Difference of 1 unit (4 − 3 or 2 − 1) corresponds to 10 years.

Father age = 4 × 10 = 40 years; Son age = 2 × 10 = 20 years.

Mother : Father = 9 : 8 ⇒ Since 8 units = 40, then 9 units (Mother) = 45 years.

Difference = 45 − 20 = 25 years.

∴ The correct answer is 25 years.

Alternate Method

Given: Present age Father (F) = 2 × Son (S); Ratio Mother (M) : Father (F) = 9 : 8.

⇒ Let Son's present age be x. Then Father's present age = 2x.

⇒ 10 years ago: (2x − 10) = 3 × (x − 10)

⇒ 2x − 10 = 3x − 30

⇒ x = 20 (Son's present age)

⇒ Father's present age = 2 × 20 = 40 years.

⇒ Mother's age = (9/8) × 40 = 45 years.

⇒ Difference = 45 − 20 = 25 years.

∴ The correct answer is 25 years.

Additional Information

Age Difference Constant

The numerical difference between the ages of two persons remains the same throughout their lives, regardless of the number of years passed.

Ratio Balancing Method

To equate parts in age ratios, multiply the ratios such that the difference between the ratio terms of the two individuals becomes equal.

Cross Multiplication Method

For problems involving two different time periods, use (Initial Ratio) → (Change) → (Final Ratio) to solve for units directly.

Shortcut Trick

Total investment ≈ ₹45000.

Ratio of interest is SI_A : SI_B = 15 : 8.

Since SI = P × R × T, then P ∝ SI ÷ (R × T). For equal time T = 2 years, P_A : P_B = (15 ÷ 7.5) : (8 ÷ 8) = 2 : 1.

Investment in Scheme B = 1 ÷ (2 + 1) × ₹45000 = ₹15000.

∴ The correct answer is ₹15000.

Alternate Method

Given:

Total investment (P) ≈ ₹45000

Rate of interest for Scheme A (R_A) = 7.5% p.a.

Rate of interest for Scheme B (R_B) = 8% p.a.

Time (T) = 2 years

Ratio of interest received = SI_A : SI_B = 15 : 8

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

Let the amount invested in Scheme A be P_A and in Scheme B be P_B.

⇒ SI_A = (P_A × 7.5 × 2) ÷ 100 = 15P_A ÷ 100

⇒ SI_B = (P_B × 8 × 2) ÷ 100 = 16P_B ÷ 100

Given that SI_A : SI_B = 15 : 8

⇒ (15P_A ÷ 100) ÷ (16P_B ÷ 100) = 15 ÷ 8

⇒ 15P_A ÷ 16P_B = 15 ÷ 8

⇒ P_A ÷ P_B = 16 ÷ 8

⇒ P_A ÷ P_B = 2 ÷ 1

⇒ Ratio of investment P_A : P_B = 2 : 1

⇒ Total investment ratio parts = 2 + 1 = 3 parts

⇒ 3 parts = ₹45000

⇒ 1 part = ₹15000

⇒ Investment in Scheme B (P_B) = 1 part = ₹15000

∴ The correct answer is ₹15000.

Additional Information

Simple Interest Principle

Simple Interest is calculated only on the principal amount, hence the annual interest remains constant every year.

Ratio of Principals in Simple Interest

When the ratio of interest is given, the ratio of the principal amounts is directly proportional to the interest and inversely proportional to the product of rate and time: P₁ : P₂ = (I₁ ÷ R₁T₁) : (I₂ ÷ R₂T₂).

Common solution:

Total profit earned by all the cinema halls = (200 $\times 30 =$ Rs\ 6000)

For cinema hall A

Total tickets sold = 200 x {25/100} = 50

Total profit earned = 6000 x {20/100} = Rs 1200

Similarly,

 

Calculation:

Profit earned on each ticket sold by A and B together = {1200+960}/{50+40}

= {2160/90} = Rs 24

Profit earned on each ticket sold by D and E together = {1500 + 900}/{20 + 60}

= {2400/80} = Rs 30

Required difference = 30 – 24 = Rs 6

Common solution:

Total profit earned by all the cinema halls = (200 $\times 30 =$ Rs\ 6000)

For cinema hall A

Total tickets sold = 200 x {25/100} = 50

Total profit earned = 6000 x {20/100} = Rs 1200

Similarly,

 

Calculation:

Total number of tickets sold by E and C together = 60 + 30 = 90

Total number of tickets sold by B = 40

Required percentage = (90 – 40)/40 x 100 = 125%

Common solution:

Total profit earned by all the cinema halls = (200 $\times 30 =$ Rs\ 6000)

For cinema hall A

Total tickets sold = 200 x {25/100} = 50

Total profit earned = 6000 x {20/100} = Rs 1200

Similarly,

 

Calculation:

Total number of tickets sold by X = 50 x (3/5) = 30

Profit earned on each ticket sold by D = 1500/20 = Rs 75

Profit earned on each ticket sold by X = 75 x 120% = Rs 90

Therefore, total profit earned by X = 30 x 90 = Rs. 2700

Common solution:

Total profit earned by all the cinema halls = (200 $\times 30 =$ Rs\ 6000)

For cinema hall A

Total tickets sold = 200 x {25/100} = 50

Total profit earned = 6000 x {20/100} = Rs 1200

Similarly,

 

Calculation:

Average number of tickets sold by B and D together = (40 + 20)/2 = 30

Average number of tickets sold by A and E together = (50 + 60)/2 = 55

Required difference = 55 – 30 = 25

Common solution:

Total profit earned by all the cinema halls = (200 $\times 30 =$ Rs\ 6000)

For cinema hall A

Total tickets sold = 200 x {25/100} = 50

Total profit earned = 6000 x {20/100} = Rs 1200

Similarly,

 

Calculation:

Total profit earned by F = 1200 x (4/3) = Rs 1600

Total tickets sold by C = 30

Let the total number of tickets sold by F be x

30 = 37.5% of x

So, x = 30 x (100/37.5) = 80

Profit earned on each ticket sold by F = 1600/80 = Rs. 20

Shortcut Trick

Approximate Investment: A = 8000, B = 5000. Ratio = 8 : 5.

Approximate Total Profit = 22000, B profit = 6000 ∴ A profit = 16000.

Profit Ratio A : B = 16000 : 6000 = 8 : 3.

Using Profit = Investment × Time: (8 × 365) ÷ (5 × Days_B) = 8 ÷ 3.

365 ÷ (5 × Days_B) = 1 ÷ 3 ⇒ Days_B = (365 × 3) ÷ 5 = 73 × 3 = 219 days.

Given Days_B = T + 2 ⇒ T = 219 − 2 = 217.

∴ The correct answer is 217.

Alternate Method

Given → Investment A ≈ 8000, Investment B ≈ 5000. Total Profit ≈ 22000, Profit B ≈ 6000. Formulas: Profit Ratio = (I₁ × T₁) : (I₂ × T₂) | Profit_A = Total Profit − Profit_B

⇒ Profit share of A = 22000 − 6000 = 16000. ⇒ Ratio of profits (A : B) = 16000 : 6000 = 16 : 6 = 8 : 3. ⇒ Ratio of (Investment × Time) = (8000 × 365) : (5000 × (T + 2)). ⇒ (8000 × 365) ÷ (5000 × (T + 2)) = 8 ÷ 3. ⇒ (8 × 365) ÷ (5 × (T + 2)) = 8 ÷ 3. ⇒ 365 ÷ (T + 2) = 5 ÷ 3. ⇒ T + 2 = (365 × 3) ÷ 5 = 73 × 3 = 219. ⇒ T = 219 − 2 = 217.

∴ The correct answer is 217.

Additional Information

Partnership Principles

When investments are for different time periods, the profit is distributed in the ratio of the product of Investment and Time.

Approximation in Exams

Values like 7999.99 should be rounded to the nearest integer (8000) to simplify calculations without affecting accuracy significantly.

Shortcut Trick

Assume Total Income = 100 units.

Rent = 30% of 100 = 30 units → Remaining = 70 units.

Groceries = 25% of 70 = 17.5 units → New Remaining = 52.5 units.

Entertainment share = 52.5 × (2 ÷ 5) = 21 units.

∴ The correct answer is 21%.

Alternate Method

Given: Rent = 30%, Groceries = 25% of remaining, Ent : Savings = 2 : 3.

⇒ Let Total Income = I

⇒ After Rent, Remaining = I × (100 − 30)/100 = 0.70I

⇒ After Groceries, Remaining = 0.70I × (100 − 25)/100 = 0.70I × 0.75 = 0.525I

⇒ Entertainment Expenditure = 0.525I × [2 ÷ (2 + 3)]

⇒ Entertainment = 0.525I × (2 ÷ 5) = 0.525I × 0.4 = 0.21I

⇒ Percentage = (0.21I ÷ I) × 100 = 21%

∴ The correct answer is 21%.

Additional Information

Successive Percentage Change

When values are calculated on the remaining balance, use the multiplying factor: Final = Initial × (1 − r₁/100) × (1 − r₂/100).

Ratio Distribution

To find a specific part in a ratio a:b, multiply the total by a/(a+b) or b/(a+b).

Base Value Importance

Always identify if the percentage is of the Total Income or the Remaining Amount to avoid calculation errors.

Shortcut Trick

Initial total volume ≈ 150 liters, Soda = 50 liters → Juice = 100 liters (Ratio of Juice to Soda = 2 : 1).

Removing 30 liters of mixture keeps the ratio 2 : 1, so remaining is 120 liters → Juice = 80 liters, Soda = 40 liters.

Adding 10 liters of pure juice makes Juice = 90 liters and Soda = 40 liters.

Resultant ratio of Juice to Soda = 90 : 40 = 9 : 4.

Wait, let us check option values: 150 liters, 50 soda → 100 juice. Take out 30 liters → remaining mixture = 120 liters. Since ratio is 2:1, remaining Juice = 80, Soda = 40. Add 10 liters juice → Juice = 90, Soda = 40. Ratio = 9:4 (which is Option 5). Let's check the corrected value.

∴ The correct answer is 9:4.

Alternate Method

Given:

Total volume of mixture ≈ 150 liters

Volume of soda ≈ 50 liters

Volume of juice = 150 − 50 = 100 liters

Mixture taken out ≈ 30 liters

Pure juice added ≈ 10 liters

Calculations:

⇒ Initial Ratio of Juice : Soda = 100 : 50 = 2 : 1

⇒ In 30 liters of mixture taken out:

⇒ Juice removed = (2 ÷ 3) × 30 = 20 liters

⇒ Soda removed = (1 ÷ 3) × 30 = 10 liters

⇒ Remaining Juice = 100 − 20 = 80 liters

⇒ Remaining Soda = 50 − 10 = 40 liters

⇒ After adding 10 liters of pure juice:

⇒ New Juice volume = 80 + 10 = 90 liters

⇒ New Soda volume = 40 liters

⇒ Resultant Ratio = 90 : 40 = 9 : 4

∴ The correct answer is 9:4.

Additional Information

Mixture Withdrawal Rule

When a portion of a mixture is removed, the remaining ingredients stay in the same ratio as the original mixture.

Replacement Formula

If y liters are removed from x liters of mixture and replaced with pure component, the remaining quantity of the other component is given by Initial Quantity × (1 − y/x).

Shortcut Trick

Average of 2^nd lowest and 10^th number is 32 ⇒ Sum = 64.

Let 1^st number be x. Then (x + 1) + (x + 9) = 64 ⇒ 2x + 10 = 64 ⇒ x = 27.

Set A: 27, 28, 29, 30, 31, 32, 33, 34, 35, 36. Second highest = 35.

Set B starts at 35 (5 consecutive odd numbers). Average is the middle (3^rd) term.

Set B: 35, 37, 39, 41, 43. Middle term = 39.

∴ The correct answer is 39.

Alternate Method

Given: Set A has 10 consecutive numbers. Average of 2^nd and 10^th is 32.

Formula: Average = Sum of observations ÷ Number of observations.

⇒ Let numbers in Set A be n, n+1, ..., n+9.

⇒ [(n + 1) + (n + 9)] ÷ 2 = 32

⇒ 2n + 10 = 64 ⇒ 2n = 54 ⇒ n = 27.

⇒ Second highest number of Set A = n + 8 = 27 + 8 = 35.

⇒ Lowest number of Set B = 35.

⇒ Set B (5 consecutive odd): 35, 37, 39, 41, 43.

⇒ Average of Set B = (35 + 43) ÷ 2 = 39.

∴ The correct answer is 39.

Additional Information

Average of Arithmetic Progression

For any series in AP, the average is simply (First term + Last term) ÷ 2 or the middle term if the number of terms is odd.

Consecutive Odd/Even Numbers

Consecutive odd or even numbers always have a common difference of 2. The average of n terms is the (n+1)/2 term.

Common solution:

Let the total vehicles (Petrol, EV and Diesel) manufactured by D be 100a

Petrol vehicles manufactured = 100a × {25/100} = 25a

Diesel vehicles manufactured = 25a × {60/100} = 15a

Given,

100a – 25a – 15a = 240

60a = 240

so, a = 4

The total vehicles (Petrol, EV and Diesel) manufactured = 100a = 400

Petrol vehicles manufactured =100

Diesel vehicles manufactured = 60

Similarly,

 

Calculation:

Total number of vehicles manufactured by A = 90 + 90 + 36 = 216

Total number of diesel vehicles manufactured by C, D and B together = 150 + 60 + 50 = 260

Required difference = 260 - 216 = 44

Common solution:

Let the total vehicles (Petrol, EV and Diesel) manufactured by D be 100a

Petrol vehicles manufactured = 100a × {25/100} = 25a

Diesel vehicles manufactured = 25a × {60/100} = 15a

Given,

100a – 25a – 15a = 240

60a = 240

so, a = 4

The total vehicles (Petrol, EV and Diesel) manufactured = 100a = 400

Petrol vehicles manufactured =100

Diesel vehicles manufactured = 60

Similarly,

 

Calculation:

From the calculated table:

Total vehicles manufactured by D = 400

Total vehicles manufactured by F =400 x {125}/100} = 500

Petrol vehicles manufactured by F = {300/2} = 150

Given,

Diesel vehicles manufactured by B: F = 10:19

Diesel vehicles manufactured by B = 50

Diesel vehicles manufactured by F = 50 x {19/10} = 95

Total EVs manufactured by F =500 – 150 – 95 = 255

Common solution:

Let the total vehicles (Petrol, EV and Diesel) manufactured by D be 100a

Petrol vehicles manufactured = 100a × {25/100} = 25a

Diesel vehicles manufactured = 25a × {60/100} = 15a

Given,

100a – 25a – 15a = 240

60a = 240

so, a = 4

The total vehicles (Petrol, EV and Diesel) manufactured = 100a = 400

Petrol vehicles manufactured =100

Diesel vehicles manufactured = 60

Similarly,

 

Calculation:

Total vehicles manufactured by C = 180 + 300 + 150 = 630

Total EVs manufactured by B = 120

Required ratio = 630:120 = 21:4

Common solution:

Let the total vehicles (Petrol, EV and Diesel) manufactured by D be 100a

Petrol vehicles manufactured = 100a × {25/100} = 25a

Diesel vehicles manufactured = 25a × {60/100} = 15a

Given,

100a – 25a – 15a = 240

60a = 240

so, a = 4

The total vehicles (Petrol, EV and Diesel) manufactured = 100a = 400

Petrol vehicles manufactured =100

Diesel vehicles manufactured = 60

Similarly,

 

Calculation:

Required percentage = (108 – 60)/60 x 100 = 80%

Common solution:

Let the total vehicles (Petrol, EV and Diesel) manufactured by D be 100a

Petrol vehicles manufactured = 100a × {25/100} = 25a

Diesel vehicles manufactured = 25a × {60/100} = 15a

Given,

100a – 25a – 15a = 240

60a = 240

so, a = 4

The total vehicles (Petrol, EV and Diesel) manufactured = 100a = 400

Petrol vehicles manufactured =100

Diesel vehicles manufactured = 60

Similarly,

 

Calculation:

Required difference = (120 + 200 + 50) – 60 = 370 – 60 = 310

Shortcut Trick

Let the Cost Price (CP) of both items be 100%.

Difference in Profit Percentage = 35% − 25% = 10%.

According to the question, 10% of CP = Rs 750.

Therefore, 100% of CP = 750 × (100 ÷ 10) = Rs 7500.

∴ The correct answer is Rs 7500.

Alternate Method

Given: CP_X = CP_Y, Profit_X = 25%, Profit_Y = 35%, Difference in Profit = Rs 750.

Formulas: Profit = CP × (Profit% ÷ 100)

⇒ Let the Cost Price of item X and item Y be 'C'.

⇒ Profit from item X = 0.25C and Profit from item Y = 0.35C.

⇒ Difference = 0.35C − 0.25C = 750.

⇒ 0.10C = 750.

⇒ C = 750 ÷ 0.10 = 7500.

∴ The correct answer is Rs 7500.

Additional Information

Common Cost Price Scenarios

When Cost Prices are equal, the ratio of profits is directly proportional to the ratio of profit percentages.

Profit Calculation

Profit is always calculated on the Cost Price unless specified otherwise in the question.

Shortcut Trick

Let the speed of boat in still water (u) = 4x and speed of current (v) = x.

Downstream speed (u + v) = 5x and Upstream speed (u − v) = 3x.

Equation: D/5x + (D − 10)/3x = 12.

Since we have one equation with two unknown variables (D and x), a unique value for D cannot be found.

∴ The correct answer is Can’t be determined.

Alternate Method

Given: Ratio of boat speed (u) to current speed (v) = 4 : 1.

Formula Used: Time = Distance ÷ Speed

⇒ Let u = 4x and v = x.

⇒ Downstream Speed = 4x + x = 5x.

⇒ Upstream Speed = 4x − x = 3x.

⇒ Total Time = [D / 5x] + [(D − 10) / 3x] = 12.

⇒ [3D + 5(D − 10)] / 15x = 12.

⇒ 3D + 5D − 50 = 180x.

⇒ 8D − 180x = 50.

⇒ As there are infinite pairs of (D, x) that satisfy this linear equation, D is not uniquely determined.

∴ The correct answer is Can’t be determined.

Additional Information

Downstream and Upstream Speed

Downstream speed is the sum of boat and stream speeds (u+v), while upstream speed is the difference (u−v).

Degrees of Freedom

To solve for 'n' variables, we strictly require 'n' independent equations. Here, D and x are two unknowns with only one relation.

Still Water Speed Formula

Still water speed (u) = 1/2 × (Downstream Speed + Upstream Speed).