SSC CHSL 2025 Tier-1 (Held On: 13 Nov, 2025 Shift 2) (Previous Year Paper)

The correct answer is '2' i.e. is responsible of .

Key Points

• The phrase "responsible of" is grammatically incorrect. The correct preposition to use with "responsible" is "for."
• The corrected phrase should be "is responsible for."
• It is important to use appropriate prepositions in formal writing to ensure clarity and accuracy.

Correct sentence: The new manager is responsible for the entire marketing campaign.

Additional Information

• Common Preposition Usage:
• Responsible for: Indicates accountability or duty. Example: She is responsible for managing the team.
• Responsible to: Indicates reporting to someone. Example: He is responsible to the CEO.
• Other Common Errors:
• Using "of" instead of "for" in phrases like "in charge of" or "responsible for."
• Mixing up prepositions, such as "interested in" being wrongly written as "interested of."

The correct answer is '3' i.e. against the clock .

Key Points

• The phrase "against the clock" is a commonly used idiom that means working under time pressure or with urgency to meet a deadline.
• In the given sentence, the phrase aligns perfectly with the context, as the team is described as working hard to finalize the report before the deadline.
• Let’s evaluate the other options:
• Option 1 - "under wraps": This phrase means keeping something secret or confidential, which doesn’t fit the context of the sentence.
• Option 2 - "around the corner": This phrase refers to something that is about to happen soon, but it doesn’t describe the urgency of the team’s work.
• Option 4 - "in high spirits": This phrase means being happy or cheerful, which doesn’t convey the sense of urgency described in the sentence.

Correct sentence: As the deadline approached, the team was working against the clock to finalize the report.

Additional Information

• Idiomatic Expressions:
• Against the clock: Working quickly to meet a deadline.
• Under wraps: Keeping something secret or confidential.
• Around the corner: Something that is about to happen soon.
• In high spirits: Being cheerful or happy.

The correct answer is '3' i.e. Unlucky .

Key Points

• The word "hapless" is used to describe someone or something that is unfortunate or unlucky.
• Among the given options:
• Fortunate means having good fortune or luck, which is the opposite of hapless.
• Lucky also means having good fortune, which is not a synonym of hapless.
• Unlucky directly matches the meaning of hapless, making it the correct synonym.
• Successful indicates achieving success, which again is not related to the meaning of hapless.
• Thus, the most appropriate synonym for "hapless" is Unlucky.

Correct Sentence: The synonym of "hapless" is unlucky.

Additional Information

• Synonyms are words that have similar meanings. They help in enhancing vocabulary and improving sentence construction.
• Antonyms are words that have opposite meanings. For example:
• The antonym of hapless is fortunate or lucky.

The correct answer is '3' i.e. in stride .

Key Points

• The phrase "in stride" is an idiom used to describe a calm and composed reaction to a challenging or difficult situation.
• In this context, the sentence mentions that the individual took the criticism positively and utilized it as a tool for self-improvement.
• Other options like "at face value," "with a grain of salt," or "out of context" do not convey the idea of responding constructively to criticism.

Correct sentence: She took the criticism in stride and used it to improve her performance.

Additional Information

• Idioms and their meanings:
• At face value: To accept something as it appears, without looking deeper.
• With a grain of salt: To view something skeptically or with caution.
• In stride: To handle something calmly and without being upset.
• Out of context: Misinterpreting something by removing it from its surrounding information.
• Using idioms appropriately enhances communication by adding depth and clarity to expressions.

The correct answer is '3' i.e. I saw a beautiful sunset last night .

Key Points

• The word "saw" in the sentence "He saw the car coming too late" is used as the past tense of the verb "see", which refers to the act of perceiving something with the eyes.
• Option 3, "I saw a beautiful sunset last night," uses "saw" with the same meaning as perceiving something visually.
• The other options (1, 2, and 4) use "saw" as a noun referring to a tool for cutting, which does not match the meaning of the word in the given sentence.

Correct sentence: "I saw a beautiful sunset last night".

Additional Information

• Homonyms: Words like "saw" can have different meanings depending on the context. In this case:
• As a verb: To perceive visually (e.g., "He saw the car").
• As a noun: A tool used for cutting (e.g., "She used a hand saw").
• Understanding context is essential to interpreting the correct meaning of a word in a sentence.

The correct answer is Option 2.

 

Key Points

• The passage explicitly identifies the primary benefit in the second sentence: "Accessibility is its main benefit; customers may explore and buy things from almost anywhere at any time, and there is frequently a greater selection than in physical stores."
• This captures the essence of convenience and variety that defines the modern e-commerce paradigm.
• Why other options are incorrect:
• Option 1: The text states the "inability to personally inspect things" is actually a drawback of the virtual nature of online shopping.
• Option 3: The passage mentions "competitive pricing" (often lower) due to reduced overhead, not higher prices.
• Option 4: The text notes that concerns over "shipping delays" are widespread, meaning shipping is very much a part of the process and not eliminated.

Therefore, the correct answer is 2.

 

Analytical Insight: For exams, watch out for "absolute" words like "eliminates" or "higher/lower." Authors usually provide a balanced view, and the correct answer will mirror the specific degree of benefit mentioned in the text.

 

Additional Information

• Unmatched ease: Level of convenience that cannot be equaled by other methods.
• Overhead: The regular and necessary costs of running a business, such as rent and utilities.
• Discontent: A lack of satisfaction or happiness.
• Virtual nature: Existing in a technological environment rather than a physical one.

The correct answer is Option 2.

 

Key Points

• The passage identifies competitive pricing as an important "lure" (attraction) for online shoppers.
• It explains the reason behind this: it is "made possible by internet retailers' reduced overhead." Since online stores don't have to pay for expensive physical storefronts or large in-person staff, they can pass those savings to the customer.
• Why other options are incorrect:
• Option 1: This is the opposite of what the text says. Physical stores have higher overhead, not online ones.
• Option 3: The passage highlights the "simplicity of comparing prices," which contradicts the idea of fixed prices with no comparison.
• Option 4: The text mentions the ability to compare prices from "several providers," implying that prices differ across platforms.

Therefore, the correct answer is 2.

 

Analytical Insight: In competitive exams, questions about "causality" (the reason something happens) are common. The text provides a clear cause (reduced overhead) for the effect (competitive pricing).

 

Additional Information

• Lures: Things that tempt or attract a person to do something.
• Overhead: General expenses of a business (rent, utilities, etc.) that are not directly tied to creating a product.
• Competitive Pricing: Setting the price of a product or service based on what the competition is charging.
• Virtual nature: Something that exists in code or online rather than in physical form.

The correct answer is Option 2.

 

Key Points

• The passage explicitly discusses the "drawbacks" resulting from the virtual nature of e-commerce.
• It states: "Delivery-related discontent may result from the inability to personally inspect things before purchase." This is a primary disadvantage because the consumer cannot verify the quality, size, or feel of a product until it arrives.
• Why other options are incorrect:
• Option 1: The text says there is frequently a "greater selection" online, not a lack of variety.
• Option 3: While the text mentions "unstated expenses" and environmental "effects of transportation," it does not explicitly state that shipping prices are higher than other costs; it emphasizes the uncertainty and delays.
• Option 4: "Faster delivery times" would be an advantage, not a drawback. Furthermore, the text mentions concerns over "shipping delays."

Therefore, the correct answer is 2.

 

Analytical Insight: In exams, questions about "drawbacks" often test your ability to distinguish between a factual disadvantage mentioned in the text and a general opinion. While shipping costs (Option 3) can be a drawback in real life, the text specifically emphasizes the inability to inspect items.

 

Additional Information

• Discontent: Dissatisfaction with one's circumstances.
• Virtual: Existing or occurring on computers or on the internet.
• Unstated expenses: Hidden costs that are not clearly mentioned upfront (e.g., hidden taxes or handling fees).
• Overhead: The regular costs of running a business, such as rent and insurance.

The correct answer is Option 2.

 

Key Points

• The passage groups environmental concerns together with other logistics-related issues. It states: "Concerns over shipping delays, unstated expenses, and the effects of packaging and transportation on the environment are becoming more widespread."
• While "shipping delays" are primarily a logistical frustration, the text places them in the same list of growing concerns that include the environmental effects of packaging and transportation.
• Why other options are incorrect:
• Option 1: Online shopping generally reduces store visits; it does not increase them.
• Option 3: The passage focuses on the environmental impact of packaging and transportation for online orders, not fuel consumption of physical stores.
• Option 4: The text mentions that online shopping offers a "greater selection," which is the opposite of limited availability.

Therefore, the correct answer is 2.

 

Analytical Insight: In competitive exams, questions often ask you to identify a group of items mentioned together in the text. Even if "shipping delays" doesn't sound like an "environmental" issue, it is part of the specific list provided by the author regarding modern widespread concerns.

 

Additional Information

• Unstated expenses: Hidden costs like taxes or convenience fees not shown in the initial price.
• Discontent: Dissatisfaction or lack of contentment.
• Overhead: The ongoing costs of operating a business (rent, utilities, etc.).
• Individualised: Tailored to the specific needs or preferences of a person.

The correct answer is Option 2.

 

Key Points

• The passage concludes by discussing the social/service aspect of e-commerce. It states: "Additionally, the individualised customer service experience may be weakened by a lack of human interaction."
• In physical stores, customers often benefit from immediate, face-to-face assistance. Online shopping, while efficient, often replaces this with automated systems or delayed digital communication, which can feel less personal.
• Why other options are incorrect:
• Option 1: The text describes the "simplicity of comparing prices" as an "important lure" (an advantage), not a weakness.
• Option 3: The passage notes there is "frequently a greater selection" online, meaning variety is a strength.
• Option 4: Accessibility and the ability to buy from anywhere are listed as the "main benefit" of online purchasing.

Therefore, the correct answer is 2.

 

Analytical Insight: In exams, questions about "weaknesses" or "negatives" are often placed at the end of the passage. Look for transition words like "However," "Additionally," or "Conversely" to find these shifts in focus.

 

Additional Information

• Individualised: Tailored to satisfy the specific requirements of an individual.
• Lures: Qualities that attract or tempt one to do something.
• Overhead: Business costs not directly related to the production of goods (e.g., rent, utilities).
• Unmatched ease: A level of convenience that is superior to all others.

The correct answer is '3' i.e. Bureaucrat .

Key Points

• The word "Bureaucrat" is derived from the French word "bureau" meaning desk or office, and the suffix "-crat" meaning ruler or member of a governing body.
• The correct spelling of the word is "Bureaucrat" (Option 3).
• Other options, such as "Beaurocrat", "Burocrat", and "Buroucrat", are misspelled versions of the word.

Correct sentence: Choose the correctly spelt word: Bureaucrat.

Additional Information

• Definition: A bureaucrat is an official in a government or administrative system, often associated with complex procedures and policies.
• Usage Example: The bureaucrat efficiently processed the paperwork for the new policy implementation.
• Tip for Correct Spelling: Remember the root word "bureau" and the suffix "-crat" to spell "Bureaucrat" correctly.

The correct answer is '3' i.e. Irresistible .

Key Points

• The word "Irresistible" is correctly spelt and means something that is too attractive or tempting to be resisted.
• Option 1 (Iresistible) is incorrect as it misses an 'r'.
• Option 2 (Irresistable) is incorrect as it uses 'able' instead of 'ible'.
• Option 4 (Irresistble) is incorrect as it omits an 'i' from the middle.

Correct spelling: Irresistible

Additional Information

• Words ending in "-ible" typically have Latin roots and are often used to describe qualities or conditions, e.g., possible, terrible, visible.
• Words ending in "-able" are often derived from verbs and indicate capability, e.g., adaptable, remarkable, achievable.

The correct answer is '1' i.e. Very close and loyal .

Key Points

• The idiom 'As thick as thieves' is used to describe a relationship where two or more people are extremely close and loyal to each other.
• This idiom originates from the idea of thieves working closely together, sharing secrets and trusting each other completely.
• Option 1, 'Very close and loyal,' is the correct meaning of the idiom.

Correct usage in a sentence: Ever since childhood, Jenny and Lisa have been as thick as thieves, sharing all their secrets.

Additional Information

• Incorrect options explained:
• Option 2: 'Very secretive' is incorrect because the idiom emphasizes closeness and loyalty, not secrecy.
• Option 3: 'Very sneaky' is incorrect as it misinterprets the context of the idiom.
• Option 4: 'Very quiet' is incorrect since the idiom does not imply silence.
• The idiom is often used to describe strong friendships or close relationships.

The correct answer is '2' i.e. Ornithologist .

Key Points

• An ornithologist is someone who studies birds, their behavior, and their habitats.
• The word is derived from the Greek words "ornis" (bird) and "logos" (study or discourse).
• Biologist is a broader term used for someone who studies living organisms, not specific to birds.
• Ecologist focuses on ecosystems and the interaction of living organisms with their environment.
• Zoologist is someone who studies animals in general.

Correct sentence: An ornithologist is a person who studies birds.

Additional Information

• The study of birds is called ornithology, and it is a branch of zoology.
• An ornithologist may study bird species, migration patterns, feeding habits, or even conservation efforts to protect endangered birds.
• Famous ornithologists include John James Audubon, known for his studies and illustrations of North American birds.

The correct answer is '1' i.e. Misery .

Key Points

• The word felicity means intense happiness or bliss.
• To find the antonym (opposite), we need to look for a word that represents the opposite of happiness or bliss.
• Let us evaluate the options:
• Option 1 - Misery: Misery means a state of great unhappiness or distress. This is the most appropriate antonym of felicity.
• Option 2 - Despair: Despair means a complete loss of hope, which is related to unhappiness but not the direct opposite of felicity.
• Option 3 - Sorrow: Sorrow refers to sadness, which is close but not as strong an antonym as misery.
• Option 4 - Anger: Anger refers to a strong feeling of annoyance or hostility, which is unrelated to the meaning of felicity.

Correct word: The most appropriate antonym of felicity is Misery.

Additional Information

• Synonyms of Felicity: Bliss, happiness, joy, delight.
• Antonyms of Felicity: Misery, unhappiness, anguish, distress.
• Always look for the closest match based on the intensity and meaning of the given word while solving antonym or synonym questions.

The correct answer is '4' i.e. Accept .

Key Points

• The word repudiate means to reject, disown, or deny something, particularly in a formal or strong manner.
• To find the antonym (opposite meaning), we need to select a word that conveys the opposite of rejecting or denying.
• The word accept means to agree to, take on, or acknowledge something, which is the opposite of rejecting or denying.
• The other options - reject, disown, and deny - are synonyms of repudiate, not antonyms.

Correct Sentence: The most appropriate antonym of the word repudiate is accept.

Additional Information

• Synonyms of Repudiate: Reject, disown, deny, renounce.
• Antonyms of Repudiate: Accept, approve, embrace, acknowledge.

The correct answer is '1' i.e. Archive .

Key Points

• An Archive refers to a place where records, historical documents, and other important information are stored and preserved for reference or research purposes.
• The other options are incorrect in this context:
• Library: A place where books and other materials are available for reading or borrowing, not specifically for storing records or documents.
• Storage: A general term for keeping items, but not specific to records or documents.
• Depository: A place where funds or valuables are stored, often in the context of banks or safes.

Correct sentence: A place where records and documents are stored is called an Archive.

Additional Information

• Archive: Used in contexts such as historical records, governmental documents, or institutional data preservation.
• Example: "The National Archives houses important historical documents of the country."

The correct answer is '1' i.e. Convene the emergency meeting at 10 AM without delay.

Key Points

• The given sentence is in the passive voice, where the subject is not performing the action but is instead receiving the action.
• The goal is to convert the sentence into the active voice, where the subject performs the action.
• The phrase "Let the emergency meeting be convened" in passive voice changes to "Convene the emergency meeting" in active voice.
• Option 1 accurately reflects the active voice construction.

Correct sentence: Convene the emergency meeting at 10 AM without delay.

Additional Information

• Passive voice structure: Object + be + past participle + (by subject).
• Active voice structure: Subject + verb + object.
• When converting from passive to active, identify the doer of the action (subject) and restructure the sentence accordingly.

The correct answer is '4' i.e. The company CEO announced that they would not be able to meet the deadline for that quarter, which was a great disappointment for all of them, but that they would have to work harder the next time.

Key Points

• The sentence is converted from direct to indirect speech, where the pronouns, tenses, and time references are adjusted accordingly.
• The direct speech "We will not be able" is changed to "they would not be able," as the reporting verb "announced" is in the past tense.
• "This quarter" is replaced with "that quarter" to reflect the shift in time reference.
• The indirect speech maintains the meaning of the original message while adhering to proper grammatical rules.

Correct sentence: The company CEO announced that they would not be able to meet the deadline for that quarter, which was a great disappointment for all of them, but that they would have to work harder the next time.

Additional Information

• Rules for changing direct speech to indirect speech:
• Change the pronouns according to the context.
• Adjust the tense of the verb if the reporting verb is in the past tense.
• Replace time and place references (e.g., "this" to "that," "here" to "there").
• Examples:
• Direct: She said, "I will go tomorrow."
• Indirect: She said that she would go the next day.
• Direct: He said, "We are working on the project."
• Indirect: He said that they were working on the project.

The correct answer is '2' i.e. believe .

Key Points

• The sentence states, "I am not one of these people who believes in rumours." The highlighted part is "believes," and the task is to replace it with the most suitable option.
• The subject of the relative clause ("who") is "people," which is plural. Therefore, the verb used in the clause should also agree with the plural subject.
• Out of the given options:
• Option 1: believer – This is a noun, and it does not fit grammatically in this context.
• Option 2: believe – This is a verb that agrees with the plural subject "people," making it the correct choice.
• Option 3: believing – This is the present participle form, which does not suit the sentence structure here.
• Option 4: to believe – This is the infinitive form, which is also incorrect in this context.
• Thus, the correct replacement is "believe."

Correct sentence: I am not one of these people who believe in rumours.

Additional Information

• In sentences with relative clauses, the verb in the clause should match the number (singular/plural) of the subject it refers to.
• For example:
• Singular subject: He is the kind of person who likes chocolate.
• Plural subject: They are the kind of people who like chocolate.

The correct answer is '1' i.e. should be able to maintain or improve profit margins .

Key Points

• The sentence is written in a formal and hypothetical context, describing a situation where organized sellers can manage their price-lines and pass on costs to customers.
• The highlighted part of the sentence needs to be grammatically correct, concise, and consistent with the tone of the sentence.
• Option 1 is correct because it uses proper subject-verb agreement and a plural form of "profit margins," which matches the plural subject "organized sellers."
• Other options fail due to grammatical errors or incorrect verb forms:
• Option 2: "maintains" is incorrect because it mismatches with the plural subject "sellers."
• Option 3: "improves" is incorrect for the same reason as Option 2.
• Option 4: "abled" is grammatically incorrect and not a valid word in this context.

Correct sentence: The organized sellers with the ability to control their price-lines, or pass on any increase in cost to customers, should be able to maintain or improve profit margins.

Additional Information

• Subject-Verb Agreement: Ensure that the verb matches the subject in number and tense.
• Clarity: Use concise and correct phrases to maintain the professional tone of the sentence.
• Common Errors:
• Using singular verbs for plural subjects or vice versa.
• Incorrect word forms, such as "abled" instead of "able."

The correct answer is '1' i.e. The assignments are being completed by the students.

Key Points

• The given sentence is in the present continuous tense (The students are completing their assignments).
• In passive voice transformation, the tense of the sentence must remain the same, and the object of the active sentence becomes the subject in the passive sentence.
• The passive voice structure for present continuous tense is: Object + is/are/am + being + past participle + by + subject.
• Here, the object is "the assignments", and the subject is "the students."

Correct sentence: The assignments are being completed by the students.

Additional Information

• Active Voice: The subject performs the action of the verb. (e.g., The students are completing their assignments.)
• Passive Voice: The object becomes the subject, and the action is performed on it. (e.g., The assignments are being completed by the students.)
• It is important to maintain the tense while transforming sentences between active and passive voice.

The correct answer is '3' i.e. The captain explained, "The ship has been sailing for three weeks, and we faced a severe storm last night.".

Key Points

• The given sentence is in indirect speech, where the speaker reports what someone else said without quoting their exact words.
• To convert it into direct speech, the exact words of the speaker must be quoted, with proper tense and context preservation.
• In the indirect sentence: - "The ship had been sailing for three weeks" refers to a past perfect continuous action. - "They had faced a severe storm the previous night" also uses past perfect tense for a completed action.
• In direct speech, the tenses will remain the same to maintain the original meaning: - "The ship has been sailing for three weeks." - "We faced a severe storm last night." (Changing "they" to "we" and "the previous night" to "last night" for direct speech).

Correct sentence: The captain explained, "The ship has been sailing for three weeks, and we faced a severe storm last night.".

Additional Information

• Indirect Speech to Direct Speech Conversion Rules:
• Change pronouns appropriately (e.g., "they" → "we").
• Adjust time expressions (e.g., "the previous night" → "last night").
• Maintain the original tense of the sentence to preserve meaning.
• Tense Overview in Reported Speech:
• Past Perfect Continuous changed to Present Perfect Continuous in direct speech.
• Past Perfect is simplified to Past Simple for clarity in some contexts.

The correct answer is '3' i.e. Q, S, P, R.

Key Points

• The paragraph starts with sentence Q, which sets the context of the admiral giving orders and describing the strategy of blockading the enemy port.
• Next is sentence S, which elaborates on the details of the strategy (cutting off supplies and forcing a surrender).
• Sentence P follows, describing the unexpected storm that caught the fleet off guard.
• Finally, sentence R concludes, emphasizing the desperate struggle for survival caused by the storm.

Correct paragraph: Confident in their strategy to blockade the enemy port, the admiral gave the order for the ships to proceed. Without firing a shot, they were to cut off supplies and compel a surrender. But the fleet was caught off guard as a sudden, strong storm blew in from the sea. The conflict became a desperate struggle for survival due to the unanticipated weather.

Additional Information

• Logical flow: The sentences are arranged to maintain coherence and to narrate the events chronologically while ensuring grammatical correctness.
• Tip: Look for connecting ideas and cause-effect relationships between sentences when rearranging them.

The correct answer is '4' i.e. Q, S, P, R .

Key Points

• The sequence of the sentence parts should logically and sequentially describe the Roman Empire, its achievements, challenges, and eventual decline.
• Q: "The Roman Empire was the most powerful civilisation in history at its height" introduces the topic of the Roman Empire and its prominence.
• S: "Its vast network of roads, laws, and military outposts brought a period of peace and prosperity" explains the achievements and contributions of the Empire.
• P: "However, as the Empire grew, a series of internal and external pressures began to mount" transitions to the challenges faced by the Empire.
• R: "Its gradual decline was caused by a confluence of political corruption, military overstretch, and economic instability" concludes the paragraph by describing the reasons for its decline.

Correct sequence: Q, S, P, R.

Additional Information

• Logical Flow: When rearranging sentences, always ensure the introduction comes first, followed by supporting details, transitions, and conclusions.
• Transition Words: Words like "however" (in P) signal a shift in tone or topic and help in identifying proper placement.
• Chronology: Historical paragraphs often follow a timeline, moving from the Empire's peak (Q, S) to its challenges (P) and decline (R).

Here, each letter of the word is shifted 3 positions forward in the English alphabet.

H → K

A → D

R → U

M → P

O → R

N → Q

Y → B

Hence, the logic followed is: Each letter is replaced by the letter that is 3 positions ahead in the alphabet.

Now apply the same logic to BALANCE:

B → E

A → D

L → O

A → D

N → Q

C → F

E → H

Thus, BALANCE → EDODQFH

Hence, the correct answer is EDODQFH.

Observe the pattern:

Each letter of the given word is replaced by the next letter in the English alphabet (+1 shift).

Example from the first word:

A → B

R → S

C → D

H → I

A → B

E → F

O → P

L → M

O → P

G → H

I → J

C → D

A → B

L → M

Hence, the logic followed is: Each letter is replaced by the next letter in the English alphabet.

Now apply the same logic to PSYCHOLOGICAL:

P → Q

S → T

Y → Z

C → D

H → I

O → P

L → M

O → P

G → H

I → J

C → D

A → B

L → M

Thus, PSYCHOLOGICAL → QTZDIPMPHJDBM

Hence, the correct answer is QTZDIPMPHJDBM.

Observe the pattern:

M → N

A → B

T → U

H → I

E → F

M → N

A → B

T → U

I → J

C → D

S → T

Similarly,

G → H

E → F

O → P

G → H

R → S

A → B

P → Q

H → I

Y → Z

Hence, the logic followed is: Each letter is replaced by the next letter in the English alphabet (+1 shift).

Now apply the same logic to CHEMISTRY:

C → D

H → I

E → F

M → N

I → J

S → T

T → U

R → S

Y → Z

Thus, CHEMISTRY → DIFNJTUSZ

Hence, the correct answer is DIFNJTUSZ.

Analysis of Conclusions:

Conclusion I: Surveillance technology has both benefits and risks.

The statement mentions improvement in security (benefit) and privacy concerns (risk). Therefore, this conclusion follows.

Conclusion II: Public oversight and clear policies are needed to balance privacy and security.

The statement clearly says critics demand transparent policies and public oversight. Hence, this conclusion follows.

Conclusion III: Surveillance should be completely banned to protect individual freedom.

The statement only mentions concerns and demand for oversight, not a complete ban. Hence, this conclusion does not follow.

Hence, the correct answer is: Only Conclusions I and II follow.

Situation:

A student has only 3 days left before an exam and half the syllabus is still incomplete.

Analysis of Options:

Watch motivational videos to calm nerves

This may reduce stress, but it does not directly help in completing the syllabus. Hence, it is not the most practical strategy.

Sleep less and cover all topics

Reducing sleep can harm concentration and efficiency, which may negatively affect exam performance.

Focus on high-weightage and familiar topics

This is a practical and effective strategy when time is limited. Prioritizing important and known topics can maximize marks within the available time.

Give up and skip the exam

This is not a reasonable response because the student still has time to prepare.

Hence, the correct answer is Focus on high-weightage and familiar topics.

Expression:

13 % 9 * 12 % 14

Replace the symbols:

13 − 9 + 12 − 14

Now solve according to BODMAS:

13 − 9 = 4

4 + 12 = 16

16 − 14 = 2

Hence, the correct answer is 2.

Expression:

4 % 13 ? 9 $ 14

Replace the symbols:

4 − 13 + 9 × 14

Now apply BODMAS rule:

9 × 14 = 126

9 × 14 = 126 Substitute:

4 − 13 + 126

⇒ −9 + 126 = 117

Hence, the correct answer is 117.$

Evaluation of Options:

1. Spread their issues as office gossip to get sympathy

This breaks trust and is unprofessional. Hence, it is not appropriate.

2. Offer to help them prioritize tasks and suggest they talk to HR or supervisor

This response shows empathy, support, and professionalism while guiding them toward the proper authority who can help.

3. Tell them to leave work at home

This response is insensitive and does not provide any support.

4. Ignore since it's not your concern

Ignoring the situation shows a lack of teamwork and empathy.

Hence, the correct answer is 2) Offer to help them prioritize tasks and suggest they talk to HR or supervisor.

Given:

Total number of children = 40

Position of Sita from the beginning = 15

Position of Rita from the end = 18

Formula Used:

Position from beginning = Total number − Position from end + 1

Children between two persons = Difference of positions − 1

Calculation:

Position of Rita from the beginning = 40 − 18 + 1 = 23

Position of Sita from the beginning = 15

Children between them = 23 − 15 − 1

= 8 − 1

= 7

Hence, the correct answer is 7.

Given:

Total number of lamps = 25

Position of the lamp from the left = 9

Formula Used:

Position from right = Total number − Position from left + 1

Calculation:

Position from right = 25 − 9 + 1

= 16 + 1

= 17

Hence, the correct answer is 17^th.

Analysis of Courses of Action:

Course of Action I: Install automated signaling systems at the crossing immediately.

This directly addresses the problem mentioned in the statement (lack of proper signaling). Hence, this course of action logically follows.

Course of Action II: Ban train services on that route.

This is an extreme step and does not logically solve the core problem. The issue can be resolved by improving the signaling system.

Hence, the correct answer is: Only Course of Action I follows.

Analysis of Arguments:

Argument I: Yes, it ensures better representation.

If voting is compulsory, more citizens will participate in elections, which can lead to broader and more representative results. Hence, this is a strong argument.

Argument II: No, people should have freedom of choice.

In a democratic system, individuals should have the freedom to decide whether to vote or not. Hence, this is also a strong argument.

Hence, the correct answer is: Both Argument I and Argument II are strong.

Here, the alphabetical positions are:

C = 3, G = 7, L = 12, R = 18

The pattern is +4, +5, +6.

So the next increase will be +7.

18 + 7 = 25, and the 25^th letter is Y.

Hence, the correct answer is Y.

Logic Followed:

Each letter moves 4 positions backward in the English alphabet.

U → Q (−4)

Q → M (−4)

M → I (−4)

Continuing the same pattern:

I → E (−4)

Hence, the correct answer is E.

Situation:

A municipal council has a limited budget and must choose between repairing a bridge, building a park, improving water supply, or enhancing transportation. The town has recently faced water shortages.

Analysis:

Since the town is experiencing water shortages, the most logical and urgent action is to address the water supply problem, as it directly affects the daily needs and well-being of the people.

Hence, the correct answer is 3) Improve the water supply.

Checking Options:

AGENT → A, G, E, N, T (all letters available) ✔

MEANT → M, E, A, N, T (all letters available) ✔

MANGE → M, A, N, G, E (all letters available) ✔

MANTLE → M, A, N, T, L, E (letter L is not present in MANAGEMENT) ✘

Hence, the correct answer is MANTLE.

Analysis of Options:

Investigate by collecting evidence from both sides

This is a fair and logical approach because HR should first understand the facts before taking any action.

Ignore to avoid conflict

Ignoring the issue may worsen workplace trust and morale.

Promote the claimant to appease

Promotion without proper investigation is not a justified solution.

Fire the colleague immediately

Taking such a drastic action without investigation is unfair.

Hence, the correct answer is 1) Investigate by collecting evidence from both sides.

Logic Followed:

Each letter moves 3 positions backward in the English alphabet.

U → S (−2)

V → T (−2)

Applying the same pattern:

Q → O (−2)

R → P (−2)

Hence, the correct answer is OP.

Logic Followed:

The second letter of the first pair becomes the first letter of the next pair, and the next vowel in sequence is added.

AE → EI

(E becomes the first letter, and the next vowel after E is I)

Applying the same logic:

IO → OU

(O becomes the first letter, and the next vowel after O is U)

Hence, the correct answer is OU.

Logic Followed:

The differences between consecutive numbers increase by 2 each time.

71 − 56 = 15

88 − 71 = 17

107 − 88 = 19

Next difference = 21

So,

107 + 21 = 128

Hence, the correct answer is 128.

Logic Followed:

The pattern follows n³ − 1.

1³ − 1 = 0

2³ − 1 = 7

3³ − 1 = 26

4³ − 1 = 63

Next term:

5³ − 1 = 125 − 1 = 124

Hence, the correct answer is 124.

Find differences:

14 − 2 = 12

38 − 14 = 24

86 − 38 = 48

The differences are doubling each time:

12 × 2 = 24

24 × 2 = 48

48 × 2 = 96

Next difference = 96

Now add to the last term:

86 + 96 = 182

Hence, the correct answer is 182.

Logic Followed:

In most pairs, the second number is 9 more than the first number.

18 + 9 = 27 ✔

36 + 9 = 45 ✔

54 + 9 = 63 ✔

72 + 9 = 81 ✘ (but given 80)

So, the fourth pair does not follow the pattern.

Hence, the correct answer is 72 : 80.

Logic Followed:

In dictionary order, words are arranged alphabetically by comparing letters one by one.

Circulation comes first because l comes before u in the fourth position.

Among the remaining words starting with Circum, compare the next letters:

Circumference (f)

Circumscribed (s + c)

Circumstance (s + t)

Circumstantial (s + t + i)

So the correct order is:

Circulation → Circumference → Circumscribed → Circumstance → Circumstantial

Hence, the correct order is:

Circulation, Circumference, Circumscribed, Circumstance, Circumstantial.

Logic Followed:

All words start with M, so compare the next letters.

Memory (Me) comes before Method (Me but t after m).

Then Method.

Middle (Mi) comes after Me words.

Among Mo words: compare next letters

Modern (Mod)

Moment (Mom)

Monday (Mon)

Alphabetically: Modern < Moment < Monday.

So the correct dictionary order is:

Memory → Method → Middle → Modern → Moment → Monday

Hence, the correct order is 1, 2, 3, 4, 5, 6.

Given:

A capital = 80000

B capital = 60000

C capital = 40000

B increases capital by 25% after 6 months

C decreases capital by 10% after 6 months

Total profit = 120000

Formula Used:

Profit share ∝ Capital × Time

Calculation:

⇒ A investment for 12 months = 80000 × 12

⇒ A = 960000

⇒ B investment for first 6 months = 60000 × 6

⇒ B investment for next 6 months = (60000 × 125 ÷ 100) × 6

⇒ B = 360000 + 450000

⇒ B = 810000

⇒ C investment for first 6 months = 40000 × 6

⇒ C investment for next 6 months = (40000 × 90 ÷ 100) × 6

⇒ C = 240000 + 216000

⇒ C = 456000

⇒ Ratio A : B : C = 960000 : 810000 : 456000

⇒ Ratio = 320 : 270 : 152

⇒ Total ratio = 320 + 270 + 152

⇒ Total ratio = 742

⇒ C share = 120000 × 152 ÷ 742

⇒ C share = 18240000 ÷ 742

⇒ C share ≈ 24582.21

∴ The correct answer is ₹24582.

Given:

sin A = 7 ÷ 25

cos B = 24 ÷ 25

Formula Used:

sin²θ + cos²θ = 1

sin A cos B + cos A sin B = sin(A + B)

Calculation:

⇒ cos A = √(1 − (7 ÷ 25)²)

⇒ cos A = √(1 − 49 ÷ 625)

⇒ cos A = √(576 ÷ 625)

⇒ cos A = 24 ÷ 25

⇒ sin B = √(1 − (24 ÷ 25)²)

⇒ sin B = √(1 − 576 ÷ 625)

⇒ sin B = √(49 ÷ 625)

⇒ sin B = 7 ÷ 25

⇒ sin A cos B + cos A sin B

⇒ (7 ÷ 25 × 24 ÷ 25) + (24 ÷ 25 × 7 ÷ 25)

⇒ 168 ÷ 625 + 168 ÷ 625

⇒ 336 ÷ 625

∴ The correct answer is 336 ÷ 625.

Given:

First quantity = 50 kg

Cost price of first variety = 50 per kg

Second quantity = 30 kg

Cost price of second variety = 60 per kg

Selling price = 55 per kg

Formula Used:

Total cost price = Sum of (Quantity × Cost price)

Total selling price = Total quantity × Selling price per kg

Profit or Loss = Total selling price − Total cost price

Calculation:

⇒ Cost of first variety = 50 × 50

⇒ Cost = 2500

⇒ Cost of second variety = 30 × 60

⇒ Cost = 1800

⇒ Total cost price = 2500 + 1800

⇒ Total cost price = 4300

⇒ Total quantity = 50 + 30

⇒ Total quantity = 80 kg

⇒ Total selling price = 80 × 55

⇒ Total selling price = 4400

⇒ Profit = 4400 − 4300

⇒ Profit = 100

∴ The correct answer is Profit of ₹100.

Shortcut Trick

Assume the third number is 100.

The first number (20% less than 100) = 80.

The second number (30% more than 100) = 130.

The required ratio = 80 : 130 = 8 : 13.

∴ The correct answer is 8:13.

Alternate Method

Given:

Let the third number be x.

First number = x − (20/100) × x

Second number = x + (30/100) × x

Calculations:

⇒ First number = 0.8x

⇒ Second number = 1.3x

⇒ Ratio = First number : Second number

⇒ Ratio = 0.8x : 1.3x

⇒ Ratio = 8 : 13

∴ The correct answer is 8:13.

Additional Information

Percentage to Fraction Conversion

To simplify calculations, convert percentages to fractions: 20% = 1/5 and 30% = 3/10. If the third number is 1, the first is 1 − 1/5 = 4/5 and the second is 1 + 3/10 = 13/10.

Base Value Selection

In problems where two values are compared to a common third value, always assume the third value to be 100 or a multiple of the denominators to avoid decimal calculations.

Ratio Properties

The ratio a : b is the same as ka : kb for any non-zero constant k. Multiplying 0.8 : 1.3 by 10 removes the decimal to give 8 : 13.

Shortcut Trick

Net change in total sum = (4 × 5) + (4 × (−3)) = 20 − 12 = +8

Net change in average = Total change ÷ Total numbers = 8 ÷ 8 = +1

New Average = Old Average + Change = 45 + 1 = 46

∴ The correct answer is 46.

Alternate Method

Given:

Total numbers = 8

Original Average = 45

Formula Used:

Total Sum = Average × Total Numbers

New Average = New Total Sum ÷ Total Numbers

Calculations:

⇒ Original Sum of 8 numbers = 8 × 45 = 360

⇒ Increase in first 4 numbers = 4 × 5 = 20

⇒ Decrease in last 4 numbers = 4 × 3 = 12

⇒ New Total Sum = 360 + 20 − 12 = 368

⇒ New Average = 368 ÷ 8 = 46

∴ The correct answer is 46.

Additional Information

Basic Average Property

If a constant 'k' is added to or subtracted from every number in a set, the new average increases or decreases by 'k'.

Weighted Average

When two or more groups are combined, the new average is calculated as A_avg = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Sum Property

The total sum of observations is always the product of the average and the total number of observations (Sum = Avg × n).

Given:

First number = 2⁴ × 3² × 5³ × 7

Second number = 23 × 5 × 7 × 11

Formula used:

HCF = Product of common prime factors with the smallest powers

Calculation:

Prime factors of first number

⇒ 2⁴, 3², 5³, 7

Prime factors of second number

⇒ 23, 5, 7, 11

Common prime factors = 5 and 7

Smallest powers

⇒ 5¹, 7¹

⇒ HCF = 5 × 7

⇒ 35

∴ HCF = 35.

Given:

Initial population = 40000

First year increase = 20%

Second year decrease = 10%

Third year increase = 25%

Formula Used:

New value after increase = Original value × (1 + Percentage ÷ 100)

New value after decrease = Original value × (1 − Percentage ÷ 100)

Calculation:

⇒ Population after first year = 40000 × (1 + 20 ÷ 100)

⇒ Population = 40000 × 1.20

⇒ Population = 48000

⇒ Population after second year = 48000 × (1 − 10 ÷ 100)

⇒ Population = 48000 × 0.90

⇒ Population = 43200

⇒ Population after third year = 43200 × (1 + 25 ÷ 100)

⇒ Population = 43200 × 1.25

⇒ Population = 54000

∴ The correct answer is 54000.

Given:

Thief's speed = 20 km/h

Police car's speed = 30 km/h

Thief starts at 10:00 AM

Police car starts at 10:30 AM

Formula Used:

Distance = Speed × Time

Relative speed = Speed of police car - Speed of thief

Time = Distance ÷ Relative speed

Calculation:

⇒ Thief's head start time = 10:30 AM - 10:00 AM = 0.5 hours

⇒ Distance covered by thief in 0.5 hours = 20 × 0.5 = 10 km

⇒ Relative speed = 30 - 20 = 10 km/h

⇒ Time taken by police car to catch thief = 10 ÷ 10 = 1 hour

⇒ Police car catches thief at 10:30 AM + 1 hour = 11:30 AM

∴ The correct answer is 11:30 AM.

Shortcut Trick

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

Efficiency of A = 2 and B = 1 (Combined = 3 units/day).

Work done by (A+B) in 5 days = 3 × 5 = 15 units.

Remaining work = 30 − 15 = 15 units.

Time for B to finish remaining work = 15 ÷ 1 = 15 days.

∴ The correct answer is 15 days.

Alternate Method

Given: Time taken by A = 15 days and B = 30 days. They work together for 5 days.

Formula: Total Work = LCM of individual time; Efficiency = Total Work ÷ Time taken.

⇒ Combined efficiency of A + B = 2 + 1 = 3 units/day.

⇒ Work done by A and B together in 5 days = 5 × 3 = 15 units.

⇒ Remaining work = Total Work − Completed Work = 30 − 15 = 15 units.

⇒ Time taken by B to complete the remaining work = 15 ÷ 1 = 15 days.

∴ The correct answer is 15 days.

Additional Information

Relation between Time and Efficiency

Time and efficiency are inversely proportional to each other. If the ratio of time taken is x:y, then the ratio of efficiency is y:x.

Pipes and Cisterns

The same LCM method applies to pipes, where filling pipes have positive efficiency and outlet/leakage pipes have negative efficiency.

Work and Wages

Wages are distributed among workers based on the ratio of the actual work done by each person.

Given:

Selling price = 1800

Profit = 20%

Formula Used:

Selling price = Cost price × (1 + Profit ÷ 100)

Calculation:

⇒ 1800 = Cost price × (1 + 20 ÷ 100)

⇒ 1800 = Cost price × 1.20

⇒ Cost price = 1800 ÷ 1.20

⇒ Cost price = 1500

∴ The correct answer is 1500.

Shortcut Trick

For Simple Interest, use the ratio: (n₁ − 1) / T₁ = (n₂ − 1) / T₂

Here, n₁ = 2 (doubles), T₁ = 8 years, and n₂ = 5 (five times).

(2 − 1) / 8 = (5 − 1) / T₂

1 / 8 = 4 / T₂ ⇒ T₂ = 4 × 8 = 32 years.

∴ The correct answer is 32 years.

Alternate Method

Given: Sum doubles (A = 2P) in 8 years.

Formula: Simple Interest (SI) = (P × R × T) / 100

⇒ Case 1: SI₁ = Amount − Principal = 2P − P = P

⇒ P = (P × R × 8) / 100 ⇒ R = 100 / 8 = 12.5%

⇒ Case 2: New Amount = 5P, so SI₂ = 5P − P = 4P

⇒ 4P = (P × 12.5 × T₂) / 100

⇒ 4 = (12.5 × T₂) / 100

⇒ T₂ = (4 × 100) / 12.5 = 400 / 12.5 = 32 years

∴ The correct answer is 32 years.

Additional Information

Simple Interest Multiplier Rule

If a sum becomes n times in T years, the rate R is given by R = [(n − 1) × 100] / T.

Constant Interest Property

In Simple Interest, the interest earned for every equal interval of time remains the same.

Compound Interest Comparison

In Compound Interest, if a sum doubles in T years, it becomes n^k times in k × T years.

Shortcut Trick

Investment Scheme A : Scheme B = 150 : 100 = 3 : 2

Given Scheme A = ₹2,400 ⇒ 3 units = ₹2,400, so 2 units (Scheme B) = ₹1,600

Total SI = (2,400 × 4 × r/100) + (1,600 × 5 × (r+2)/100) = 1,920

96r + 80r + 160 = 1,920 ⇒ 176r = 1,760 ⇒ r = 10%

∴ The correct answer is 10%.

Alternate Method

Given:

Investment in Scheme A (P_A) = ₹2,400

Time for Scheme A (T_A) = 4 years, Rate (R_A) = r%

Investment in Scheme B (P_B): P_A is 50% more than P_B ⇒ 2,400 = 1.5 × P_B

Time for Scheme B (T_B) = 5 years, Rate (R_B) = (r + 2)%

Total Simple Interest = ₹1,920

Formula Used: Simple Interest (SI) = (P × R × T) / 100

⇒ P_B = 2,400 / 1.5 = ₹1,600

⇒ SI_A = (2,400 × r × 4) / 100 = 96r

⇒ SI_B = (1,600 × (r + 2) × 5) / 100 = 80(r + 2) = 80r + 160

⇒ Total SI = SI_A + SI_B = 1,920

⇒ 96r + 80r + 160 = 1,920

⇒ 176r = 1,920 − 160

⇒ 176r = 1,760

⇒ r = 1,760 / 176 = 10

∴ The correct answer is 10%.

Additional Information

Simple Interest (SI)

The interest is calculated only on the initial Principal amount for the entire duration. Formula: SI = (P × R × T) / 100.

Amount in SI

The total money accumulated after the time period. Amount = Principal + Simple Interest.

Effective Interest Rate

For Simple Interest, the total effective rate over T years is simply (R × T)% of the principal.

Given:

a + b + c = 12

ab + bc + ca = 40

Formula Used:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Calculation:

⇒ (12)² = a² + b² + c² + 2 × 40

⇒ 144 = a² + b² + c² + 80

⇒ a² + b² + c² = 144 − 80

⇒ a² + b² + c² = 64

∴ The correct answer is 64.

Shortcut Trick

A perfect square never ends with the unit digits 2, 3, 7, or 8.

Checking the given options by their unit digits:

(1) 245982 ends in 2 (Eliminated) | (2) 496838 ends in 8 (Eliminated)

(3) 178343 ends in 3 (Eliminated) | (4) 571536 ends in 6 (Possible)

∴ The correct answer is 571536.

Alternate Method

Given numbers: 245982, 496838, 178343, 571536.

Method Used: Unit digit verification and Digital Sum analysis (The sum of digits of a perfect square must be 1, 4, 7, or 9).

Analyze 571536:

⇒ Unit digit = 6. Property: If a square ends in 6, its tens digit must be odd.

⇒ Tens digit of 571536 is 3 (Odd), which satisfies the condition.

⇒ Digital sum of 571536 = 5 + 7 + 1 + 5 + 3 + 6 = 27.

⇒ Reduced digital sum = 2 + 7 = 9.

⇒ Since 9 is a valid digital sum for squares, 571536 is a potential perfect square (756² = 571536).

∴ The correct answer is 571536.

Additional Information

Unit Digit Rule

A perfect square always ends in 0, 1, 4, 5, 6, or 9. It never ends in 2, 3, 7, or 8.

Digital Sum Rule

The sum of the digits of a perfect square (root digit) is always 1, 4, 7, or 9. For example, 12² = 144 (1+4+4=9).

Last Two Digits Rule

The last two digits of any perfect square must be among the last two digits of the squares of numbers from 1 to 24.

Ending in 6 Rule

If a perfect square ends in 6, the digit in the tens place is always an odd number (e.g., 16, 36, 196, 256).

Shortcut Trick

Ratio of the milk solutions = 4 : 6 = 2 : 3.

Net fat percentage = [(Ratio₁ × Fat₁) + (Ratio₂ × Fat₂)] ÷ Total Ratio parts.

Net fat percentage = [(2 × 25) + (3 × 40)] ÷ (2 + 3) = (50 + 120) ÷ 5 = 170 ÷ 5 = 34%.

∴ The correct answer is 34%.

Alternate Method

Given:

Quantity of first solution = 4 liters with 25% fat.

Quantity of second solution = 6 liters with 40% fat.

Formula Used:

Total Fat Content = (Quantity₁ × Fat %₁) + (Quantity₂ × Fat %₂)

Final Fat Percentage = (Total Fat Content ÷ Total Quantity) × 100

⇒ Fat in 4 liters of solution = 4 × (25 ÷ 100) = 1.0 liter

⇒ Fat in 6 liters of solution = 6 × (40 ÷ 100) = 2.4 liters

⇒ Total quantity of final mixture = 4 + 6 = 10 liters

⇒ Total fat in final mixture = 1.0 + 2.4 = 3.4 liters

⇒ Final fat percentage = (3.4 ÷ 10) × 100 = 34%

∴ The correct answer is 34%.

Additional Information

Rule of Alligation

It states that the ratio of the quantities is the inverse ratio of the differences from the mean: (Quantity₁ ÷ Quantity₂) = (C₂ − M) ÷ (M − C₁), where M is the mean value.

Weighted Average

The combined average of two or more groups can be calculated using A_avg = (n₁a₁ + n₂a₂ + ...) ÷ (n₁ + n₂ + ...).

Percentage Concentration

In mixture problems, concentration refers to the amount of solute (like fat or salt) present in the total volume of the solution.

Given:

Increase in radius = 20%

Formula Used:

Volume of sphere = 4πr³ ÷ 3

Volume ∝ r³

Calculation:

⇒ New radius = r × (1 + 20 ÷ 100)

⇒ New radius = 1.2r

⇒ New volume ∝ (1.2r)³

⇒ New volume ∝ 1.2³ × r³

⇒ New volume ∝ 1.728r³

⇒ Increase factor = 1.728 − 1

⇒ Increase factor = 0.728

⇒ Percentage increase = 0.728 × 100

⇒ Percentage increase = 72.8%

∴ The correct answer is 72.8%.

Given:

Total surface area of hemisphere = 300π

Formula Used:

Total surface area of hemisphere = 3πr²

Volume of hemisphere = 2πr³ ÷ 3

Calculation:

⇒ 3πr² = 300π

⇒ r² = 300π ÷ 3π

⇒ r² = 100

⇒ r = 10

⇒ Volume = 2π × 10³ ÷ 3

⇒ Volume = 2π × 1000 ÷ 3

⇒ Volume = 2000π ÷ 3

∴ The correct answer is 2000π ÷ 3.

Given:

1 ÷ 2

0.55

3 ÷ 5

0.625

Formula Used:

Fraction to decimal = Numerator ÷ Denominator

Calculation:

⇒ 1 ÷ 2 = 0.5

⇒ 3 ÷ 5 = 0.6

⇒ 0.5 < 0.55 < 0.6 < 0.625

⇒ 1 ÷ 2 < 0.55 < 3 ÷ 5 < 0.625

∴ The correct answer is 1 ÷ 2, 0.55, 3 ÷ 5, 0.625.

Given:

Area of the circle = 144π cm²

Formula Used:

Area of a circle = πr²

Circumference of a circle = 2πr

Calculation:

⇒ πr² = 144π

⇒ r² = 144

⇒ r = √144

⇒ r = 12 cm

⇒ Circumference = 2πr

⇒ Circumference = 2π × 12

⇒ Circumference = 24π cm

⇒ Circumference ≈ 75.4 cm

∴ The correct answer is 75.4 cm.

Given:

27³ ÷ 3⁵ = 3ⁿ

Formula Used:

a^m ÷ aⁿ = a^{(m − n)}

27 = 3³

Calculation:

⇒ 27³ = (3³)³

⇒ 27³ = 3⁹

⇒ 3⁹ ÷ 3⁵

⇒ 3^{(9 − 5)}

⇒ 3⁴

⇒ n = 4

∴ The correct answer is 4.

Given:

x − y = 8

xy = 5

Formula Used:

x³ − y³ = (x − y)(x² + xy + y²)

(x − y)² = x² − 2xy + y²

Calculation:

⇒ x² − 2xy + y² = 8²

⇒ x² + y² = 64 + 2 × 5 = 74

⇒ x² + xy + y² = 74 + 5 = 79

⇒ x³ − y³ = 8 × 79 = 632

⇒ (x + y)² = x² + 2xy + y²

⇒ (x + y)² = 74 + 10 = 84

⇒ 8(x + y)² = 8 × 84 = 672

⇒ x³ − y³ + 8(x + y)² = 632 + 672 = 1304

∴ The correct answer is 1304.

Given:

$\frac{(\sin(x) + \cos(x))^2}{1 + \sin(x)\cos(x)}$

Formula Used:

$(a + b)^2 = a^2 + b^2 + 2ab$

$\sin^2(x) + \cos^2(x) = 1$

Calculation:

⇒ $(\sin x + \cos x)^2 = \sin^2 x + \cos^2 x + 2\sin x \cos x = 1 + 2\sin x \cos x$

⇒ $\frac{1 + 2\sin x \cos x}{1 + \sin x \cos x}$

∴ The simplified form is $\frac{1 + 2\sin(x)\cos(x)}{1 + \sin(x)\cos(x)}$.

Given:

sin A = 5/13

Formula Used:

sin²A + cos²A = 1

tan A = sin A / cos A

Calculation:

⇒ sin²A = (5/13)² = 25/169

⇒ cos²A = 1 - sin²A = 1 - 25/169 = 144/169

⇒ cos A = √(144/169) = 12/13

⇒ tan A = sin A / cos A = (5/13) ÷ (12/13)

⇒ tan A = 5/12

∴ The correct answer is 5/12.

Given:

$\tan A = \frac{1}{\sqrt{3}}$

Formula Used:

$2 \sin A \cos A = \sin 2A$

$\tan 30^\circ = \frac{1}{\sqrt{3}}$

Calculation:

⇒ $\tan A = \frac{1}{\sqrt{3}} \Rightarrow A = 30^\circ$

⇒ $2 \sin A \cos A = \sin 2A$

⇒ $\sin(2 \times 30^\circ) = \sin 60^\circ$

⇒ $\sin 60^\circ = \frac{\sqrt{3}}{2}$

∴ The correct answer is $\frac{\sqrt{3}}{2}$.

Given:

5x − 2y = 10

Formula Used:

Equation of line: y = mx + c

Slope of perpendicular line = −1 ÷ m

Calculation:

⇒ 5x − 2y = 10

⇒ −2y = −5x + 10

⇒ y = (5/2)x − 5

⇒ Slope of given line m = 5/2

⇒ Slope of perpendicular line = −1 ÷ (5/2)

⇒ Slope = −2/5

∴ The correct answer is −2/5.

The correct answer is Debala Mitra.

Key Points

• Debala Mitra was the first woman Director-General of the Archaeological Survey of India (ASI), serving from 1981 to 1983.
• She was a renowned archaeologist and a distinguished scholar in Buddhist studies.
• During her tenure as Director-General, Mitra conducted significant archaeological excavations and conservation projects, including the protection of Buddhist monuments and sites such as Sanchi, Ajanta, and Ellora.
• Her work emphasized the preservation of India’s cultural heritage and contributed to the global recognition of Indian archaeological sites.
• Mitra was widely respected for her scholarly contributions, including her academic publications on Buddhist art and architecture.

Additional Information

• Archaeological Survey of India (ASI):
• The Archaeological Survey of India was established in 1861 by Alexander Cunningham, who is regarded as the "Father of Indian Archaeology."
• It functions under the Ministry of Culture, Government of India, and is responsible for the archaeological research, conservation, and protection of cultural monuments in India.
• ASI oversees the maintenance of more than 3,600 protected monuments, including sites of historical importance like the Taj Mahal, Qutub Minar, and Khajuraho temples.
• The organization plays a significant role in UNESCO World Heritage Site conservation projects in India.
• Buddhist Art and Architecture:
• Buddhist architecture in India includes stupas, rock-cut caves, and monasteries, with prominent examples being Sanchi Stupa, Ajanta, and Ellora caves.
• The Sanchi Stupa, a UNESCO World Heritage Site, is one of the oldest stone structures in India and a significant monument of Buddhism.
• Rock-cut caves such as Ajanta and Ellora are famous for their intricate paintings, sculptures, and carvings.
• These sites reflect the evolution of Buddhist art from the Mauryan period to the Gupta era.
• Other Prominent Archaeologists in India:
• Alexander Cunningham: Founder of ASI and notable for his surveys of Buddhist sites.
• R.E.M. Wheeler: Known for introducing scientific excavation techniques in Indian archaeology.
• John Marshall: Played a crucial role in the discovery of the Indus Valley Civilization.
• Amalananda Ghosh: Worked extensively on the Harappan Civilization.
• Women in Indian Archaeology:
• Debala Mitra was a trailblazer and served as an inspiration for women in archaeology.
• Her contributions paved the way for greater representation of women in archaeological research and cultural heritage conservation.
• She demonstrated that women could lead significant institutions like ASI and contribute to the preservation of India’s rich history.

Important Points

• Director-General of ASI: The position of Director-General is the highest-ranking official in the ASI, responsible for shaping policies and overseeing archaeological projects across India.
• UNESCO World Heritage Sites: India is home to 40 UNESCO World Heritage Sites, many of which are managed and conserved by ASI.
• Conservation Techniques: ASI employs advanced techniques for monument preservation, including chemical treatment and structural restoration.
• Legislation: The Ancient Monuments and Archaeological Sites and Remains Act, 1958 governs the conservation of monuments in India.
• Historical Importance: ASI’s efforts ensure that India’s rich cultural heritage is preserved for future generations while promoting tourism and education.

The correct answer is N. Chandrababu Naidu.

Key Points

• N. Chandrababu Naidu is a prominent Indian politician and the President of the Telugu Desam Party (TDP), which was founded by his father-in-law Nandamuri Taraka Rama Rao (NTR).
• He has served as the Chief Minister of Andhra Pradesh multiple times, first assuming office in 1995 and leading the state through various terms with a focus on economic growth and technological development.
• Under his leadership, Andhra Pradesh saw significant growth in the IT sector, earning him the title of the "IT Visionary of India." His efforts transformed Hyderabad into a global IT hub, with the establishment of major tech parks like Cyberabad and HITEC City.
• In the 2024 Andhra Pradesh Legislative Assembly elections, his party, the TDP, secured a majority, leading to his swearing-in as the Chief Minister of the state in June 2024.
• Naidu is known for his administrative expertise and focus on development projects, including improving infrastructure, agriculture, and governance systems in Andhra Pradesh.

Additional Information

• N. Chandrababu Naidu's Political Career:
• He became the youngest assembly member and a minister at the age of 28 in the Congress government of Andhra Pradesh in 1978.
• In 1983, he joined the Telugu Desam Party (TDP) and became a key player in its organizational structure.
• He served as the Leader of the Opposition in the Andhra Pradesh Assembly during multiple terms when TDP lost power.
• Achievements as Chief Minister:
• Naidu's tenure is noted for his focus on economic reforms, making Andhra Pradesh a business-friendly state.
• He introduced various welfare schemes, including programs aimed at improving agriculture and irrigation, such as the Pattiseema Lift Irrigation Project.
• He played a pivotal role in the division of Andhra Pradesh and oversaw the development of the new state capital, Amaravati.
• Telugu Desam Party (TDP):
• The TDP was established in 1982 by NTR to represent the interests of the Telugu-speaking people.
• It has been a major political party in Andhra Pradesh, with its ideology based on regionalism, development, and welfare.
• Other Candidates in the Question:
• Revanth Reddy: A prominent Congress leader from Telangana, not Andhra Pradesh, making this option incorrect.
• Mohan Yadav: A BJP leader from Madhya Pradesh, unrelated to Andhra Pradesh politics.
• Vishnu Deo Sai: A BJP leader from Chhattisgarh, also unrelated to Andhra Pradesh politics.

Important Points

• Economic Vision: Naidu's policies focused on digital governance, e-governance initiatives like e-Seva, and promoting IT and software exports.
• Challenges Faced: His tenure saw challenges, including public dissatisfaction with agricultural reforms and the bifurcation of Andhra Pradesh.
• Recognition: He has received several awards, including the IT Indian of the Millennium by India Today and recognition as South Asian of the Year by the Time Asia Magazine in 1999.

The correct answer is NITI Aayog.

Key Points

• NITI Aayog is a premier policy think tank of the Government of India, established in 2015 to replace the Planning Commission.
• On February 2025, NITI Aayog launched a policy report titled 'Expanding Quality Higher Education through States and State Public Universities'. This report aimed to improve the quality and accessibility of higher education in India.
• The report emphasized the role of state governments and state public universities in transforming the higher education landscape by addressing challenges such as funding, governance, and infrastructure.
• NITI Aayog’s initiative aligns with its mandate to foster cooperative federalism and provide strategic policy guidance to states for sustainable development.
• The report highlights the importance of empowering state universities to cater to the needs of diverse populations and enhance their contribution to India’s economic and social progress.

Additional Information

• NITI Aayog:
• Established on January 1, 2015, it replaced the Planning Commission to better align with contemporary economic realities.
• Its primary objectives include fostering cooperative federalism, formulating long-term policies, and promoting sustainable development.
• NITI Aayog plays a pivotal role in strategizing and implementing initiatives such as Digital India, Atal Innovation Mission, and Sustainable Development Goals (SDGs).
• Higher Education in India:
• India has one of the largest higher education systems globally, with over 1,000 universities and 40,000 colleges.
• State universities and colleges cater to a significant portion of students, especially from rural and economically disadvantaged backgrounds.
• Challenges include insufficient funding, lack of infrastructure, and governance issues.
• Policy interventions like the above-mentioned report aim to address these gaps and improve the overall quality of education.
• Relevant Government Policies:
• National Education Policy (NEP) 2020: Focuses on universalizing education, improving governance, and promoting multidisciplinary learning.
• Rashtriya Uchchatar Shiksha Abhiyan (RUSA): Aims to provide strategic funding to state higher education institutions for infrastructure development and quality enhancement.
• Study in India Initiative: Promotes India as a global education hub and aims to attract international students.
• Importance of State Public Universities:
• State universities account for a large proportion of higher education enrollments, providing education at affordable costs.
• They play a critical role in regional development and cater to diverse linguistic and cultural groups.
• Strengthening state universities is vital for achieving equitable access to quality education across India.

Important Points

• NITI Aayog’s Role in Education:
• Acts as a think tank for the central and state governments, providing evidence-based recommendations.
• Focuses on innovation, technology integration, and partnerships to strengthen India’s education system.
• Collaborates with international organizations and experts to bring global best practices to India.
• Emphasizes data-driven policy formulation to address challenges such as access, equity, and quality.
• Significance of Reports like 'Expanding Quality Higher Education':
• Provides actionable insights for policymakers to address systemic issues in higher education.
• Serves as a roadmap for improving governance, infrastructure, and funding mechanisms in state universities.
• Encourages public-private partnerships and innovative solutions to enhance educational outcomes.