SSC CHSL 2025 Tier-1 (Held On: 15 Nov, 2025 Shift 2) (Previous Year Paper)

The correct answer is Option 2.

 

Key Points

• The primary issue in the sentence is the use of the plural verb "were" with the singular subject "Neither."
• When "Neither" is used as the subject of a sentence, it is grammatically singular and requires a singular verb.
• The correct phrase should be "proposals was approved," ensuring proper subject-verb agreement.
• Thus, the error is located in part B (Option 2) of the sentence.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "Neither of the two proposals was approved because the committee found both of them to be unsatisfactory."

 

Additional Information

• A: "Neither of the two" – This part correctly sets up the choice between two specific items and serves as the singular subject.
• C: "because the committee found" – This part is grammatically correct; "committee" is a collective noun acting as a single unit here.
• D: "both of them to be unsatisfactory." – This part correctly uses "both" to refer back to the two proposals and is grammatically sound.
• Subject-Verb Agreement: Although "proposals" is plural, it is the object of the preposition "of," not the subject of the sentence.

The correct answer is Option 3.

 

Key Points

• The sentence uses the correlative conjunction "not only... but also," which is used to connect two balanced clauses or phrases.
• The inclusion of "and" in part C is redundant and grammatically incorrect because the "not only" in part B is already waiting to be paired with "but also" in part D.
• To maintain the correct correlative structure, the conjunction "and" should be removed or replaced to ensure the two parts of the pair correlate directly.
• Thus, the error is located in part C (Option 3) of the sentence.

Therefore, the correct answer is Option 3.

 

Correct Sentence: "He is not only intelligent hardworking, but also very kind." 

Additional Information

• Correlative Conjunctions: These are pairs like either... or, neither... nor, and not only... but also. They must connect grammatically similar elements (parallelism).
• A: "He is" – This is the subject and helping verb, which is correct.
• B: "not only intelligent" – This starts the correlative pair correctly.
• D: "but also very kind" – This completes the correlative pair correctly.
• Parallelism: When using "not only... but also," ensure that the words following each part of the conjunction are the same part of speech (in this case, adjectives: intelligent/hardworking and kind).

The correct answer is 'with'.

 

Key Points

• The preposition "with" is used to indicate involvement or association in a particular activity or situation.
• The sentence describes the defendant’s involvement in colluding with foreign agents, making "with" the most appropriate choice.
• Options 1, 2, and 4 are incorrect as they do not fit the grammatical or contextual requirements of the sentence.

Therefore, the correct answer is Option 3.

 

Complete Sentence: "The defendant was charged with colluding with foreign agents to influence the outcome of the election."

 

Additional Information

• Option 1: "of" is incorrect because "charged of" is not a valid construction in this context.
• Option 2: "for" is incorrect because "charged for" is used in the context of billing or monetary transactions, not accusations.
• Option 4: "about" is incorrect because it does not convey the required sense of involvement.

The correct answer is 'whereas'.

 

Key Points

• The conjunction "whereas" is used to show contrast between two clauses.
• In the given sentence, the two parts are contrasting: "He has a lot of potential" contrasts with "his lack of discipline may hinder his growth."
• Options 2, 3, 4, and 5 are grammatically incorrect or do not fit the context of the sentence.

Therefore, the correct answer is Option 1.

 

Complete Sentence: "He has a lot of potential, whereas his lack of discipline may hinder his growth."

 

Additional Information

• Option 2: "unless" is incorrect because it is used to introduce a condition, not a contrast.
• Option 3: "because" is incorrect as it introduces a reason, not a contrasting idea.
• Option 4: "albeit" is incorrect because it means "although" or "even though," and does not fit with the structure of the sentence.

The correct answer is option 1.

Key Points

The correctly spelled word is 'Anniversary'.

• Anniversary refers to the date on which an event took place in a previous year, typically a celebration of an important past event. (वार्षिकोत्सव)
• Let us analyze the given options:
• Option 1: Anniversary - Correctly spelled.
• Option 2: Aniversary - Incorrect, missing one 'n'.
• Option 3: Anniversarry - Incorrect, has an extra 'r'.
• Option 4: Annivessary - Incorrect, has 'e' instead of 'i'.

Therefore, the correct answer is 'Anniversary' (Option 1).

Additional Information

Examples of usage:

• They celebrated their 25^th wedding anniversary with a grand party.
• The company marked its 10^th anniversary with a special event for employees.

The correct answer is option 3.

Key Points

The correctly spelt word is 'Inimical'.

• **The word 'Inimical' means 'tending to obstruct or harm; unfriendly'. **(विरोधी/हानिकारक)
• It is an adjective and is used in contexts where hostility or harm is implied.
• For Example -
• His policies are inimical to the interests of the working class.
• The two countries have developed an inimical relationship due to repeated border disputes.

Therefore, the correct answer is 'Inimical' (option 3).

Additional Information

Let's understand why the other options are incorrect -

• Option 1: Emenical - This is a misspelled word. No such word exists in the English language.
• Option 2: Enemical - This is incorrect as it doesn't match the correct spelling 'Inimical'.
• Option 4: Enimical - This is also misspelled. The correct spelling is 'Inimical'.

The correct answer is: Option 1 i.e. Everyone working together.

Key Points

• The phrase "All hands on the deck" means that everyone is required to work together or contribute to a task, especially in a situation of urgency or importance. (सभी को एक साथ मिलकर काम करना पड़ता है)
• Example: When the company was facing a critical deadline, it was all hands on the deck to complete the project on time.
• Correct Explanation: The idiom emphasizes teamwork and cooperation, especially in situations that demand collective effort. (टीमवर्क और सहयोग पर जोर देना, खासकर जब एक सामूहिक प्रयास की आवश्यकता हो)
• Example: The storm was approaching fast, so it was all hands on the deck to secure the ship.

Therefore, the correct answer is: Option 1 i.e. Everyone working together.

Additional Information

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

• Option 2: Someone in charge of the deck (डेक का प्रभारी व्यक्ति): This is incorrect as the idiom does not refer to a single person but rather to collective teamwork.
• Example: The captain of the ship is responsible for the deck, but this does not align with the idiom's meaning.
• Option 3: A distraction on the deck (डेक पर ध्यान भटकाने वाला कुछ): This is incorrect as the idiom does not refer to a distraction but to a coordinated effort.
• Example: There was no distraction on the deck; instead, everyone was focused on the task.
• Option 4: A difficult task (एक कठिन कार्य): This is incorrect because the idiom doesn’t refer to the difficulty of the task but rather to the need for collective effort.
• Example: While it was a difficult task, all hands on the deck ensured it was completed successfully.

The correct answer is: Scarce.

Key Points

• The word "Profuse" means something that exists or is produced in large quantities; it refers to abundance or excess. (प्रचुर मात्रा में)
• Example: The garden was profuse with vibrant flowers blooming in every corner.
• "Scarce" refers to something that is insufficient, rare, or in short supply; it is the opposite of profuse. (दुर्लभ)
• Example: During the drought, water became scarce in the region.
• Hence, the antonym of "Profuse" is "Scarce".

Therefore, the correct answer is: Scarce.

Additional Information

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

• Copious (प्रचुर): Existing in large quantity; abundant.
• Example: She took copious notes during the lecture to ensure she didn’t miss any details.
• Abundant (अधिक): Present in large amounts; more than enough.
• Example: The region is abundant in natural resources like coal and minerals.
• Plentiful (बहुतायत): Exceedingly large in quantity; available in plenty.
• Example: The harvest this year was plentiful due to good rainfall.

The correct answer is: Veterinarian.

Key Points

• The word "Veterinarian" refers to a person who is professionally trained to care for the health of animals, including diagnosing and treating their diseases and injuries. (पशु चिकित्सक)
• Example: The veterinarian prescribed a special diet to improve the dog's health.
• "Zoologist" is a scientist who studies animals and their behavior, but they do not necessarily treat animals medically. (प्राणी विज्ञानी)
• Example: The zoologist spent years studying the migration patterns of birds.
• Hence, the correct one-word substitute for a person trained to care for animals is "Veterinarian".

Therefore, the correct answer is: Veterinarian.

Additional Information

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

• Zoologist (प्राणी विज्ञानी): A scientist who studies animals and their biology.
• Example: The zoologist observed the behavior of lions in their natural habitat.
• Biologist (जीव विज्ञानी): A scientist who studies living organisms, including plants, animals, and microorganisms.
• Example: The biologist is researching the impact of climate change on marine life.
• Ecologist (पारिस्थितिकी विज्ञानी): A scientist who studies the relationships between living organisms and their environment.
• Example: The ecologist is examining the effects of deforestation on local ecosystems.

The correct answer is: Blot.

Key Points

• The word "Blot" refers to a stain or mark caused by a discoloring substance. (दाग)
• Example: The ink spilled on the paper, leaving a large blot that ruined the document.
• It is often used to describe a stain that negatively impacts the cleanliness or appearance of something.
• "Blot" is the correct one-word substitute for the given statement.

Therefore, the correct answer is: Blot.

Additional Information

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

• Smudge (धब्बा): A smear or streak caused by rubbing something wet or greasy.
• Example: She accidentally smudged the ink on her drawing while working on it.
• Mark (निशान): A visible impression or sign left on a surface.
• Example: The table had a mark where the hot cup had been placed.
• Spot (धब्बा): A small area or point differing in color or texture from its surroundings.
• Example: The leopard has distinctive spots on its fur.

The correct answer is option 2.

Key Points

The misspelled word is 'addres'.

• The correct spelling would be 'address'.
• The word 'address' is a noun or verb depending on its usage:
• As a noun: It refers to the particulars of the place where someone lives or an organization is situated. (पता)
• As a verb: It refers to the act of speaking to someone or dealing with something. (संबोधित करना)
• For Example -
• As a noun: The address on the envelope was incomplete.
• As a verb: The teacher addressed the concerns of her students.

Therefore, the correct answer would be option 2.

Additional Information

Let’s understand the meanings of the other sentences:

• Option 1: The sentence is correct as it uses the word 'address' in its proper form.
• Option 3: The phrase 'return address' is correctly spelled and used.
• Option 4: The sentence properly uses 'mailing address' with the correct spelling.

The correct answer is Option 2.

 

Key Points

• Active voice structure: The subject performs the action, whereas in the passive voice, the subject receives the action.
• The original sentence contains two passive constructions: "It was believed" (Passive reporting) and "had been stolen by a rival company" (Passive main clause).
• To convert "It was believed" to active, we need a general subject like "People" or "They" because the original agent is unspecified.
• To convert "had been stolen by a rival company" to active, the agent "a rival company" must become the subject of the verb "had stolen."
• Combining these changes results in: "People believed that a rival company had stolen the secret formula."

Therefore, the correct answer is Option 2.

 

Correct Sentence: "People believed that a rival company had stolen the secret formula."

 

Additional Information

• Option 1: "A rival company believed that the secret formula had been stolen." – This changes the meaning; it suggests the rival company was the one believing the theft occurred.
• Option 3: "The secret formula was stolen by a rival company." – This is still in the passive voice and omits the "It was believed" context entirely.
• Option 4: "A rival company stole the secret formula, it was believed." – While the first part is active, "it was believed" remains a passive construction at the end.

The correct answer is Option 1.

 

Key Points

• Direct Speech: "The professor said, 'The study published last year proves that the hypothesis is false.'"
• Key Conversions:
• Tense Change (Backshifting):
• When the reporting verb is in the past tense ("said"), the verbs in the reported speech move one step back in time.
• The simple present "proves" changes to the simple past "proved."
• The simple present "is" changes to the simple past "was."
• Time Expression Change:
• Specific time markers change to reflect the shifted perspective.
• "last year" is converted to "the previous year" or "the year before."
• Conjunction:
• The comma and quotation marks are replaced by the conjunction "that" to introduce the reported statement.

Therefore, the correct answer is Option 1.

 

Correct Sentence: "The professor said that the study published the previous year proved that the hypothesis was false."

 

Additional Information

• Option 2: Fails to apply backshifting to the verbs ("proves," "is") and fails to change the time expression ("last year").
• Option 3: Correctly changes the time expression and the first verb but fails to change the second verb ("is" remains "is").
• Option 4: Correctly shifts both verbs to the past tense but incorrectly retains the time expression "last year" instead of changing it to "the previous year."

The correct answer is 'Option 1'.

 

Key Points

• The subject "a pair of jeans" is singular, and therefore, the verb "is" must agree with the singular subject.
• The correct choice is Option 1, where the singular verb "is" matches the subject.
• Option 2 ("it has already torn") is grammatically incorrect because "has torn" implies an action performed by the subject, which is not possible for jeans.
• Option 3 ("it was already torn") suggests the jeans were already torn at the time of purchase, which contradicts the intended meaning.
• Option 4 ("and which are already torn") is grammatically awkward and redundant.

Therefore, the correct answer is Option 1.

 

Complete Sentence: "I bought a new pair of jeans and it is already torn."

 

Additional Information

• Option 2: "it has already torn" is incorrect because it implies an action performed by the jeans, which is not logical.
• Option 3: "it was already torn" is incorrect as it contradicts the idea of buying new jeans.
• Option 4: "and which are already torn" is incorrect due to redundancy and awkward phrasing.

The correct answer is 'in the last four overs'.

 

Key Points

• The phrase "in the last four overs" is more suitable because it clearly indicates the time period that has just passed.
• The original phrase "in the past four overs" is grammatically correct but slightly less common in cricket terminology.
• Options 2, 3, and 4 are either incorrect or do not fit the context appropriately.

Therefore, the correct answer is Option 1.

 

Complete Sentence: "The bowler took three wickets in the last four overs."

 

Additional Information

• Option 2: "in the next four overs" is incorrect because it refers to a future time frame, not the past.
• Option 3: "during the past four overs" is wordy and less concise than the correct option.
• Option 4: "in four overs" is vague and does not specify whether it refers to the past or future.

The correct answer is Option 2.

 

Key Points

• Identify the Tense: The active sentence "will be implementing" is in the Future Continuous Tense.
• Passive Structure for Future Continuous: The formula is Object + will be + being + Past Participle (V3) + by + Subject.
• Step 1: Move the object "The new environmental regulations" to the beginning.
• Step 2: Change the verb "will be implementing" to "will be being implemented."
• Step 3: Add the agent "by the government" and the time phrase "next month."

Therefore, the correct answer is Option 2.

 

Correct Sentence: "The new environmental regulations will be being implemented by the government next month."

 

Additional Information

• Option 1: "will be implemented" – This is the Future Simple Passive. It misses the continuous "being" aspect.
• Option 3: "are being implemented" – This is the Present Continuous Passive, which changes the timeframe from future to present.
• Option 4: "will have been implemented" – This is the Future Perfect Passive, used for actions that will be completed by a certain point.

The correct answer is Option 2.

 

Key Points

• Indirect Speech: "My friend told me that she had been thinking about quitting her job but that she had not made a final decision yet."
• Key Conversions:
• Tense Change (Forward-shifting):
• When converting from indirect to direct speech, we move the tenses forward.
• The past perfect continuous "had been thinking" shifts forward to the present perfect continuous "have been thinking."
• The past perfect "had not made" shifts forward to the present perfect "have not made."
• Pronoun Change:
• The third-person pronoun "she" and possessive "her" in indirect speech must change to the first-person "I" and "my" to reflect the original speaker's perspective.
• Reporting Verb:
• The reporting verb "told me" is typically converted back to "said to me" followed by a comma and quotation marks.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "My friend said to me, 'I have been thinking about quitting my job, but I have not made a final decision yet.'"

 

Additional Information

• Option 1: Incorrectly uses the past continuous ("I was thinking") for the first part of the sentence.
• Option 3: Keeps the verbs in the past perfect ("had been thinking," "had not made"), which would only be used in direct speech if the action had already been completed before another past event.
• Option 4: Uses the simple past ("did not make") for the second clause, which does not align with the duration/relevance implied by "yet" in this context.

The correct answer is 'Option 2'.

 

Key Points

• Option 2) a participial phrase modifying “reforms”
• This is the correct answer. The phrase begins with the past participle "aimed." It functions as an adjectival phrase directly describing the noun preceding it, "reforms." It tells us specifically what kind of institutional reforms are necessary—those that are aimed at amplifying female representation.

Therefore, the correct answer is Option 2.

 

Additional Information

• Option 1 (a misplaced modifier): Incorrect because it is placed perfectly adjacent to the noun it describes ("reforms"), meaning there is no grammatical ambiguity about what is being modified.
• Option 3 (an absolute phrase modifying the entire sentence): Incorrect because an absolute phrase typically features a noun or pronoun alongside a participle modifying the whole clause (e.g., "The reforms having passed, the board celebrated"), which doesn't fit the syntax here.
• Option 4 (an infinitive phrase modifying “necessity”): Incorrect because an infinitive phrase requires the word "to" followed by the base form of a verb (e.g., "to aim").

The correct answer is 'Option 2'.

 

Key Points

• Tense Analysis: Present Tense
• The auxiliary (helping) verb used in the sentence is "is", which indicates that the action is occurring in the present tense. If it were past tense, the helping verb would be "was."
• Voice Analysis: Passive Voice
• In the passive voice, the subject of the sentence is the recipient of the action rather than the doer. Here, the subject "Their leadership" receives the action of being characterized.
• A passive voice construction requires a form of the "to be" verb paired with a past participle. The phrase "is characterized" follows this exact formula.
• Additionally, the use of the preposition "by" to introduce the actual agents of the action ("a collaborative approach, emotional intelligence, and resilience") is a classic indicator of a passive sentence.

Therefore, the correct answer is passive voice, present tense.

 

Additional Information

• Option 1 (active voice, present tense): Incorrect because the subject is receiving the action, not performing it. An active equivalent would be: "A collaborative approach characterizes their leadership."
• Option 3 (active voice, past tense): Incorrect due to both voice (it is passive) and tense (it uses "is" instead of "was").
• Option 4 (passive voice, past tense): Incorrect because the auxiliary verb "is" places the sentence in the present tense. The past passive equivalent would be "was characterized."

The correct answer is: Option (2) i.e. Dominance or rise.

Key Points

• The word "ascendancy" means occupation of a position of dominant power or influence; a state of rising to power or becoming more dominating. (प्रभुत्व या प्रभाव)
• Example: The party's ascendancy in the political arena was remarkable.
• The closest synonym for 'ascendancy' is 'dominance or rise', which means having a commanding influence or coming into an increased level of power. (प्रभुत्व या उदय)
• Example: The company's rise to market dominance was swift and impressive.

Therefore, the correct answer is: Dominance or rise.

Additional Information

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

• Decline (पतन): A decrease in quality, quantity, or importance.
• Example: There has been a decline in sales over the past few months.
• Stagnation (स्थिरता): The state of not flowing or not moving.
• Example: The local economy showed signs of stagnation despite efforts for development.
• Separation (विच्छेद या अलगाव): The action or state of moving or being moved apart.
• Example: The separation of the two companies was completed in January.

The correct answer is 'Option 1'.

 

Key Points

• Analyzing the words:
• Nuanced: This refers to something that has subtle distinctions, delicate variations, or complex layers of meaning. It is the opposite of something basic or simplistic.
• Reconfiguration: This means the act of rearranging, altering, or restructuring the layout or composition of something.
• When combined, a "nuanced reconfiguration" indicates a careful, detailed, and intricate process of changing how something is structured. Therefore, "a complex and subtle restructuring" is the precise meaning.

Therefore, the correct answer is a complex and subtle restructuring.

 

Additional Information

• Option 2 (a simplistic rearrangement): Incorrect because "nuanced" implies complexity and subtle detail, which directly contradicts the idea of something being "simplistic."
• Option 3 (a chaotic disruption): Incorrect because a nuanced approach implies careful, deliberate attention to minor details rather than chaos or random disruption.
• Option 4 (an immediate reversal): Incorrect because "reconfiguration" means rearranging parts into a new form, not necessarily going backward or reversing, and "nuanced" does not relate to the speed (immediacy) of the action.

The correct answer is 'Option 3'.

 

Key Points

• Analyzing the barriers for women in leadership:
• Although the specific passage is not provided, in standard reading comprehension texts addressing women in executive roles (like CEOs and CTOs), a commonly cited systemic barrier is unequal access to mentorship and networking opportunities.
• Women frequently face challenges in corporate environments due to exclusion from informal networks, "boys' clubs," and a lack of high-level sponsors or mentors, all of which are crucial for career advancement into C-suite positions.

Therefore, the correct answer is Unequal access to mentorship and networking opportunities.

 

Additional Information

• Option 1 (Excessive technological knowledge): Incorrect because having profound technological knowledge is an asset, particularly for a CTO, rather than a barrier to success.
• Option 2 (Lack of emotional intelligence): Incorrect because this is a subjective trait rather than a systemic barrier, and emotional intelligence is increasingly recognized as a key strength in modern leadership.
• Option 4 (Overrepresentation in executive roles): Incorrect because women are historically underrepresented, not overrepresented, in top executive positions across most major industries.

The correct answer is Option 1.

 

Key Points

• The paragraph follows a chronological sequence of an online shopping experience, moving from item selection to final delivery anticipation.
• Sentence P is the first sentence as it initiates the narrative by identifying the object and the first action:
• "The perfect gift appeared on her screen, so she clicked to add it to her cart."
• Sentence Q follows as the next logical step in the e-commerce process, which is providing the necessary information for the purchase:
• "She typed in her address and credit card details, then checked out."
• Sentence R is the third sentence because it describes the finality of the digital transaction:
• "With a final click, her order was placed and confirmed."
• Sentence S is the fourth as it represents the aftermath of the action—the period of waiting after the order has been successfully processed:
• "Now she waits for the package to arrive at her doorstep."
• The correct sequence is PQRS.

 

Coherent paragraph after rearrangement:

"The perfect gift appeared on her screen, so she clicked to add it to her cart. She typed in her address and credit card details, then checked out. With a final click, her order was placed and confirmed. Now she waits for the package to arrive at her doorstep."

The correct answer is Option 1.

 

Key Points

• The paragraph describes the progression of a person learning a musical instrument, moving from basic physical training to a final state of mastery.
• Sentence P is the first sentence as it establishes the foundation of the learning process—developing the physical dexterity required to play:
• "He developed his finger strength and dexterity by practicing his scales and chords daily."
• Sentence Q follows as the logical progression from basic exercises to more complex study and increasingly difficult music:
• "He studied sheet music for hours, learning to play tunes that got harder and harder."
• Sentence S is the third sentence because it represents the climax of his training—the moment he successfully demonstrates his skills in a high-pressure situation:
• "He played a challenging piece perfectly from memory while performing for his buddies."
• Sentence R is the fourth sentence as it provides the concluding statement, defining his new identity based on the journey described in the previous sentences:
• "He had mastered his new instrument and was now a musician."
• The correct sequence is PQSR.

 

Coherent paragraph after rearrangement:

"He developed his finger strength and dexterity by practicing his scales and chords daily. He studied sheet music for hours, learning to play tunes that got harder and harder. He played a challenging piece perfectly from memory while performing for his buddies. He had mastered his new instrument and was now a musician."

The correct answer is: Option 1 i.e. "elicit, illicit".

Key Points

• The word "elicit" means to draw out a response, answer, or fact from someone, often with effort. (प्राप्त करना, खींचना)
• Example: The teacher tried to elicit answers from the students during the discussion.
• "Illicit" refers to something that is illegal, forbidden, or against the rules. (गैरकानूनी, अनुचित)
• Example: The police uncovered an illicit drug operation in the warehouse.
• In the given sentence, "elicit" fits the first blank as the officer is trying to draw a confession, and "illicit" fits the second blank as it describes the illegal activities of the gang.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Option 2: illicit, elicit
• Explanation: The order of these words is incorrect for the context of the sentence.
• Meaning: "Illicit" (गैरकानूनी) and "Elicit" (प्राप्त करना).
• Example: Incorrect usage in this case: "The officer managed to illicit a confession about the gang's elicit activities."
• Option 3: solstice, solicit
• Explanation: These words are unrelated to the context of the sentence.
• Meaning:
• "Solstice" (अयन): An astronomical event marking the longest or shortest day of the year.
• "Solicit" (अनुरोध करना): To ask for or try to obtain something from someone.
• Example:
• "The summer solstice occurs in June."
• "The charity is soliciting donations for the cause."
• Option 4: solicit, solstice
• Explanation: Same as Option 3, the words are misplaced in the sentence's context.
• Meaning: "Solicit" (अनुरोध करना) and "Solstice" (अयन).
• Example: Incorrect usage in this case: "The officer managed to solicit a confession about the gang's solstice activities."

Total students = 40

Ritu’s rank from top = 18

Rank from bottom = Total students − Rank from top + 1

⇒ Rank from bottom = 40 − 18 + 1

⇒ 22 + 1

⇒ 23

Hence the correct answer is Option 2.

A woman says: "His brother's father is the only son of my grandmother."

Reasoning:

⇒ The only son of my grandmother = My father

⇒ His brother's father = My father

⇒ So, the man's father is the woman's father

⇒ Therefore, the man and the woman have the same father

∴ The woman is the Sister of the man.

Hence the correct answer is Option 2.

⇒ A and B are siblings.

⇒ B and C are siblings.

⇒ Therefore A, B, C are siblings.

⇒ D is the mother of A ⇒ D is the mother of A, B, C.

⇒ E is the father of C ⇒ E is the father of A, B, C.

⇒ Hence D and E are parents of the same children.

∴ D is the Wife of E.

Hence the correct answer is Option 1.

A man says: “I have no brother or sister but that man’s father is my father’s son.”

⇒ The man has no brother or sister.

⇒ So, my father’s son = Myself

⇒ That man’s father = Myself

⇒ Therefore, the man in the photo is my son.

∴ The person in the photo is the man’s son.

Hence the correct answer is Option 1.

Given:

Red balls = 45

Blue balls = 30

Formula used:

Ratio = Red : Blue

Calculation:

⇒ Ratio = 45 : 30

HCF of 45 and 30 = 15

⇒ 45 ÷ 15 : 30 ÷ 15

⇒ 3 : 2

∴ The ratio of red balls to blue balls is 3 : 2.

Given:

Speed of train = 90 km/hr

Time = 20 minutes

Convert minutes into hours:

20 minutes = 20 / 60 hours = 1 / 3 hour

Calculation:

Distance = 90 × (1/3)

Distance = 30 km

∴ The train will cover 30 km in 20 minutes.

Given:

15% of a number = 45

Let the number = x

15% of x = 45

⇒ 15/100 × x = 45

⇒ x = (45 × 100) / 15

⇒ x = 300

Now find 40% of the number:

40% of 300 = (40/100) × 300

⇒ 120

∴ 40% of the number = 120.

Let Sita’s age = x

Ram’s age = 2x

Given:

x + 2x = 45

3x = 45

x = 15

∴ Sita’s age = 15 years.

Series: 2, 6, 18, 54, ?

Pattern:

2 × 3 = 6

6 × 3 = 18

18 × 3 = 54

54 × 3 = 162

∴ Next number = 162

Cost Price (CP) = ₹1500

Selling Price (SP) = ₹1800

Profit = SP − CP

Profit = 1800 − 1500 = ₹300

Calculation:

Profit % = (300 / 1500) × 100

Profit % = 20%

∴ Profit percentage = 20%

Given:

Average of 4 numbers = 25

Three numbers = 20, 28, 32

Formula used:

Average = $\frac{\text{Sum of observations}}{\text{Number of observations}}$

Calculations:

Average = $\frac{\text{Total sum}}{4}$

⇒ 25 = $\frac{\text{Total sum}}{4}$

⇒ Total sum = 25 × 4 = 100

Sum of given numbers = 20 + 28 + 32 = 80

⇒ Fourth number = 100 − 80

⇒ Fourth number = 20

∴ The fourth number = 20.

Shortcut Trick

Assume original price = 100%

New price after 20% increase = 120%

Given: 120% → ₹600

Original price (100%) = (600 ÷ 120) × 100 = 5 × 100 = ₹500

∴ The correct answer is ₹500.

Alternate Method

Given:

Increased Price = ₹600

Percentage Increase = 20%

Formula Used:

Original Price = New Price ÷ (1 + Increase%/100)

Original (100%) +20% New Price = 120% = ₹600 Price Increase Representation

Calculations:

⇒ Let Original Price be P

⇒ New Price = P × (1 + 20/100)

⇒ 600 = P × (120/100)

⇒ 600 = P × 1.2

⇒ P = 600 ÷ 1.2

⇒ P = 500

∴ The correct answer is ₹500.

Additional Information

Percentage Change Formula

New Value = Original Value × (100 ± Change%)/100, where + is for increase and − is for decrease.

Fractional Multiplier

An increase of 20% is equivalent to multiplying the base value by 6/5 (or 1.2), and a decrease of 20% is multiplying by 4/5 (or 0.8).

Reverse Percentage Calculation

To find the original value after an x% increase, use Original = Final ÷ (1 + x/100).

7 km south

24 km east

7 km north

Shortest distance = $\sqrt{a^2+b^2}$

7 km south and 7 km north cancel each other

⇒ Net vertical distance = 7 − 7 = 0

⇒ Net horizontal distance = 24 km east

⇒ Shortest distance = $\sqrt{24^2+0^2}$

⇒ Shortest distance = $\sqrt{576}$

⇒ Shortest distance = 24 km

∴ The shortest distance = 24 km.

Hence the correct answer is Option 1.

6 km east

4 km north

3 km west

Shortest distance = $\sqrt{a^2+b^2}$

Net horizontal distance = 6 − 3 = 3 km east

Net vertical distance = 4 km north

⇒ Distance from A = $\sqrt{3^2 + 4^2}$

⇒ Distance = $\sqrt{9 + 16}$

⇒ Distance = $\sqrt{25}$

⇒ Distance = 5 km

∴ Distance from point A = 5 km.

Hence the correct answer is Option 3.

8 km north

6 km west

8 km south

Opposite directions cancel each other

Vertical movement = 8 − 8 = 0

⇒ Net vertical distance = 0

Horizontal movement = 6 km west

⇒ Net position from starting point = 6 km west

∴ He is in the West direction from the starting point.

Hence the correct answer is Option 4.

5 km east

12 km north

5 km west

Shortest distance = $\sqrt{a^2+b^2}$

Net horizontal distance = 5 − 5 = 0

Net vertical distance = 12 km north

⇒ Distance from starting point = $\sqrt{0^2 + 12^2}$

⇒ Distance = $\sqrt{144}$

⇒ Distance = 12 km

∴ Distance from the starting point = 12 km.

Hence the correct answer is Option 2.

Friends: Riya, Aman, Sohan, Neha, Rahul

Sports: Cricket, Badminton, Football, Tennis, Hockey

Conditions:

Aman → Cricket

Neha → Hockey

Rahul → Football

Riya ≠ Football, Tennis

Sohan ≠ Football

Logical elimination method

Aman → Cricket

Neha → Hockey

Rahul → Football

Remaining sports = Badminton, Tennis

Remaining persons = Riya, Sohan

Riya ≠ Tennis

⇒ Riya → Badminton

⇒ Sohan → Tennis

∴ Riya plays Badminton.

Hence the correct answer is Option 1.

Boys: A, B, C, D, E, F

Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday

A → Tuesday

D ≠ Wednesday, Saturday

D ≠ Friday

E ≠ Friday

C goes before D and after B

Logical arrangement method

Days order: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday

A → Tuesday

D ≠ Wednesday, Friday, Saturday

⇒ D → Monday or Thursday

C before D and after B

D cannot be Monday (no day before Monday for B and C)

⇒ D → Thursday

B before C and C before D

⇒ B → Monday

⇒ C → Wednesday

Remaining days: Friday, Saturday

E ≠ Friday

⇒ E → Saturday

⇒ F → Friday

∴ Correct combination: F → Friday. 

Hence the correct answer is Option 2.

Dog – Bark

Cat – Meow

Snake – Slither

Cow – Moo

Animal : Sound it makes

Dog → Bark (sound)

Cat → Meow (sound)

Cow → Moo (sound)

Snake → Slither (movement, not sound)

⇒ Only pair not showing sound

∴ Snake – Slither does not belong to the group.

Hence the correct answer is Option 3.

A – C – E – G

B – D – F – H

C – E – G – I

D – F – H – K

Alphabet position pattern (+2)

A(1) → C(3) → E(5) → G(7)

⇒ +2, +2, +2 

B(2) → D(4) → F(6) → H(8)

⇒ +2, +2, +2 

C(3) → E(5) → G(7) → I(9)

⇒ +2, +2, +2 

D(4) → F(6) → H(8) → K(11)

⇒ +2, +2, +3 ✖

∴ Odd sequence = D – F – H – K.

Hence the correct answer is Option 4.

Library : Books

Aquarium : Fish

Garage : Cars

Kitchen : Chef

Place : Things kept inside the place

Library → Books (books are kept in library)

Aquarium → Fish (fish are kept in aquarium)

Garage → Cars (cars are kept in garage)

Kitchen → Chef (chef works in kitchen, not kept inside)

⇒ Relation does not match

∴ Kitchen : Chef does not conform to the relationship.

Hence the correct answer is Option 4.

North-East

South-West

Upward

South-East

Standard compass directions → North, South, East, West and their combinations

North-East → Compass direction ✔

South-West → Compass direction ✔

South-East → Compass direction ✔

Upward → Vertical direction, not compass direction ✖

∴ Upward is inconsistent with standard compass logic.

Hence correct answer is Option 3.

11 – 22 – 44

3 – 6 – 12

5 – 10 – 21

7 – 14 – 28

Number pattern (×2)

11 → 22 → 44

⇒ 11 × 2 = 22

⇒ 22 × 2 = 44 ✔

3 → 6 → 12

⇒ 3 × 2 = 6

⇒ 6 × 2 = 12 ✔

7 → 14 → 28

⇒ 7 × 2 = 14

⇒ 14 × 2 = 28 ✔

5 → 10 → 21

⇒ 5 × 2 = 10

⇒ 10 × 2 = 20 ≠ 21 ✖

∴ Distinct pattern = 5 – 10 – 21.

Hence the correct answer is Option 3.

Two students accused of cheating

Student 1 → Prior record

Student 2 → No prior record

No evidence available

Options:

Suspend both immediately

Trust the student with no record

Wait for evidence before action

Punish only the repeat offender

Principle of fairness and evidence-based judgement

No proof of cheating

⇒ Prior record alone ≠ proof of current cheating

⇒ Punishment without evidence = unfair

⇒ Correct judgement → investigate first

∴ Best stance = Wait for evidence before action.

Hence the correct answer is Option3.

Word = MOVIETIME

Total letters = 9

Arrange letters in alphabetical order and compare positions

Original word:

M   O   V   I   E   T   I   M   E

Positions:

1   2   3   4   5   6   7   8   9

Alphabetical order:

E   E   I   I   M   M   O   T   V

Positions:

1   2   3   4   5   6   7   8   9

Compare positions:

Position 4 → I = I ✔

All other positions change

⇒ Unchanged letters = 1

∴ Number of letters whose position remains unchanged = 1.

Hence the correct answer is Option 1.

Given:

0, 1, 2, 9

Formula Used:

Natural numbers start from 1 and include all positive integers.

Calculation:

⇒ Natural numbers: {1, 2, 3, 4, ...}

⇒ 0 is not part of the natural numbers.

∴ The correct answer is Option 1.

Given:

Natural numbers: {1, 2, 3, ...}

Integer numbers: {..., -3, -2, -1, 0, 1, 2, 3, ...}

Formula Used:

Natural numbers are positive whole numbers starting from 1.

Integers include all whole numbers, both positive and negative, including zero.

Calculation:

⇒ Number 0 is an integer but not a natural number.

⇒ Number 5 is both a natural number and an integer.

⇒ Number -5 is an integer but not a natural number.

⇒ None is not a valid option as there is a number common to both sets.

∴ The correct answer is 5.

Given:

Number of boxes = 200

Cost per box = 120

Extra expense = 1800

100 boxes sold at 150 each

100 boxes sold at 130 each

Formula Used:

Profit% = (Profit ÷ Total Cost Price) × 100

Calculation:

⇒ Cost of 200 boxes = 200 × 120 = 24000

⇒ Total cost price = 24000 + 1800 = 25800

⇒ Selling price of first 100 boxes = 100 × 150 = 15000

⇒ Selling price of remaining 100 boxes = 100 × 130 = 13000

⇒ Total selling price = 15000 + 13000 = 28000

⇒ Profit = 28000 − 25800 = 2200

⇒ Profit% = (2200 ÷ 25800) × 100

⇒ Profit% ≈ 8.53

∴ The correct answer is 8.53%.

Given:

$\angle QOR = 110^\circ$

O is the incenter of triangle PQR

Formula Used:

$\angle BIC = 90^\circ + \frac{1}{2}\angle A$ (Angle at incenter)

Calculation:

⇒ $\angle QOR = 90^\circ + \frac{1}{2}\angle QPR$

⇒ $110 = 90 + \frac{1}{2}\angle QPR$

⇒ $\frac{1}{2}\angle QPR = 20$

⇒ $\angle QPR = 40^\circ$

∴ The correct answer is $40^\circ$.

Given:

(tan20°)² / (cosec70°)² + (cot20°)² / (sec70°)² + 2tan15° tan45° tan75°

Formula Used:

cosecθ = 1 / sinθ

secθ = 1 / cosθ

sin(70°) = cos(20°)

cos(70°) = sin(20°)

tan45° = 1

tan15° × tan75° = 1

Calculation:

⇒ (tan20°)² / (cosec70°)² = tan²20° × sin²70° = tan²20° × cos²20° = sin²20°

⇒ (cot20°)² / (sec70°)² = cot²20° × cos²70° = cot²20° × sin²20° = cos²20°

⇒ sin²20° + cos²20° = 1

⇒ 2tan15° tan45° tan75° = 2 × 1 × 1 = 2

⇒ Total value = 1 + 2 = 3

∴ The correct answer is 3.

Given:

2 × sin q × cos(90° − q) = 1/2

0° < q < 90°

Formula Used:

cos(90° − θ) = sin θ

sin²θ + cos²θ = 1

sin(2θ) = 2sinθcosθ

Calculation:

⇒ 2 × sin q × cos(90° − q) = 2 × sin q × sin q = 1/2

⇒ 2sin²q = 1/2

⇒ sin²q = 1/4

⇒ sin q = 1/2

⇒ q = 30°

⇒ sin(2q) + cos(2q) = sin60° + cos60°

⇒ = √3/2 + 1/2

⇒ = (√3 + 1)/2

∴ The correct answer is (√3 + 1)/2.

Given:

Amount after 4 years = 9504

Amount after 9 years = 12384

Formula Used:

Simple Interest = Principal × Rate × Time ÷ 100

Amount = Principal + Simple Interest

Calculation:

⇒ Interest for 5 years = 12384 − 9504 = 2880

⇒ Interest per year = 2880 ÷ 5 = 576

⇒ Interest for 4 years = 576 × 4 = 2304

⇒ Principal = 9504 − 2304 = 7200

⇒ 576 = (7200 × R) ÷ 100

⇒ R = (576 × 100) ÷ 7200

⇒ R = 8

∴ The correct answer is 8%.

Given:

Amount after 8 years = 240% of principal

Principal = 3000

Time = 3 years

Formula Used:

Simple interest = Principal × Rate × Time ÷ 100

Calculation:

⇒ 240% = Principal + Interest

⇒ Interest in 8 years = 240% − 100% = 140%

⇒ Rate per year = 140 ÷ 8 = 17.5%

⇒ Simple interest = 3000 × 17.5 × 3 ÷ 100

⇒ Simple interest = 1575

∴ The correct answer is 1575.

Given:

70% of total money distributed between Priya and Meena

Ratio (Priya : Meena) = 5 : 9

Rates = 6% and 10%

Time = 4 years

Difference in interest = 2304

Formula Used:

Simple Interest = Principal × Rate × Time ÷ 100

Calculation:

⇒ Let total money = T

⇒ Distributed money = 70% of T = 0.7T

⇒ Priya share = 0.7T × 5 ÷ 14 = 0.25T

⇒ Meena share = 0.7T × 9 ÷ 14 = 0.45T

⇒ Priya interest = 0.25T × 6 × 4 ÷ 100 = 0.06T

⇒ Meena interest = 0.45T × 10 × 4 ÷ 100 = 0.18T

⇒ Difference = 0.18T − 0.06T = 0.12T

⇒ 0.12T = 2304

⇒ T = 2304 ÷ 0.12 = 19200

∴ The correct answer is 19200.

Given:

Length of stick = 48 cm

Angle with floor = 60°

Formula Used:

Height = Hypotenuse × sin θ

Calculation:

⇒ Height = 48 × sin 60°

⇒ Height = 48 × (√3 ÷ 2)

⇒ Height = 24√3

∴ The correct answer is 24√3 cm.

Shortcut Trick

In a 30°−60°−90° triangle, the side opposite to the 30° angle is always half of the hypotenuse.

Here, the rope acts as the hypotenuse (16 m) and the house is the side opposite to 30°.

Height of house = Hypotenuse ÷ 2

Height of house = 16 ÷ 2 = 8 metres.

∴ The correct answer is 8 metres.

Alternate Method

Given:

Length of the rope (Hypotenuse, AC) = 16 metres

Angle of elevation (θ) = 30°

Formula Used:

sin θ = Perpendicular (Height) ÷ Hypotenuse

Calculations:

⇒ sin 30° = Height ÷ 16

⇒ 1/2 = Height ÷ 16

⇒ Height = 16 × (1/2)

⇒ Height = 8 metres

∴ The correct answer is 8 metres.

Additional Information

Trigonometric Ratios

Standard values: sin 30° = 1/2, cos 30° = √3/2, and tan 30° = 1/√3.

30°−60°−90° Triangle Rule

The sides of such a triangle are in the ratio 1 : √3 : 2, where 1 is opposite to 30° and 2 is the hypotenuse.

Angle of Elevation

The angle formed by the line of sight with the horizontal when looking upwards at an object.

Given:

Pipe A fills the tank in 14 hours

Pipe B empties the tank in 8 hours

Initial water in tank = 1/4

Formula Used:

Total work = LCM of 14 and 8

Work per hour = Total work ÷ Time

Calculation:

⇒ LCM of 14 and 8 = 56

⇒ Total work = 56 units

⇒ Work by A in 1 hour = 56 ÷ 14 = 4

⇒ Work emptied by B in 1 hour = 56 ÷ 8 = 7

⇒ Net work per hour = 4 − 7 = −3

⇒ Water initially in tank = 56 ÷ 4 = 14 units

⇒ Time to empty 14 units = 14 ÷ 3

⇒ Time = 4 hour 40 min

∴ The correct answer is 4 hour 40 min.

Given:

4 women + 6 girls can do work in 12 days

24 women + 46 girls can do work in 2 days

Let:

Work done by 1 woman in 1 day = W

Work done by 1 girl in 1 day = G

Formula used:

Work = Rate × Time

Calculations:

From first condition:

⇒ (4W + 6G) × 12 = Total work

From second condition:

⇒ (24W + 46G) × 2 = Total work

Since work is same:

⇒ (4W + 6G) × 12 = (24W + 46G) × 2

⇒ 48W + 72G = 48W + 92G

⇒ 48W cancel

⇒ 72G = 92G

⇒ 92G − 72G = 0

⇒ 20G = 0 ⇒ G = 0

⇒ Put G = 0 in (4W + 6G) × 12 = Work

⇒ (4W) × 12 = Work

⇒ Work = 48W

⇒ From second: (24W) × 2 = 48W 

Now for 15 women + 20 girls:

⇒ Work per day = 15W + 20G

⇒ = 15W + 0 = 15W

⇒ Time = Total work ÷ Rate

⇒ Time = 48W ÷ 15W

⇒ Time = 48 ÷ 15 = 3.2 days

⇒ 0.2 day = 0.2 × 24 = 4.8 hours

⇒ 0.8 hour = 0.8 × 60 = 48 minutes

∴ Required time = 3 days 4 hours 48 minutes

Shortcut Trick

Height of taller pole (H) = Height of smaller pole (h) + distance × tan(θ)

H = 10 + 50 × tan(30º)

H = 10 + 50 × (1 / √3) ≈ 10 + 50 × 0.57735

H = 10 + 28.87 = 38.87 m

∴ The correct answer is 38.87 m.

Alternate Method

Given:

Height of smaller pole (AB) = 10 m

Distance between poles (BD) = 50 m

Angle of elevation from top of smaller pole (θ) = 30º

Let the taller pole be CD and the smaller pole be AB.

From the figure, AB = ED = 10 m and AE = BD = 50 m.

In right-angled triangle AEC:

⇒ tan(30º) = CE / AE

⇒ 1 / √3 = CE / 50

⇒ CE = 50 / √3

⇒ CE = 50 / 1.732

⇒ CE ≈ 28.87 m

Total height of the taller pole (CD) = CE + ED

⇒ CD = 28.87 + 10

⇒ CD = 38.87 m

∴ The correct answer is 38.87 m.

Additional Information

Angle of Elevation

The angle formed by the line of sight with the horizontal when an object is viewed above the horizontal level.

Trigonometric Ratios

In a right-angled triangle, tan θ = Perpendicular / Base. Common value: tan 30º = 1/√3 ≈ 0.577, tan 45º = 1, tan 60º = √3 ≈ 1.732.

Angle of Depression

The angle formed by the line of sight with the horizontal when an object is viewed below the horizontal level.

Shortcut Trick

The radius, distance from the center, and half of the chord always form a right-angled triangle.

Half of the chord = 8 ÷ 2 = 4 cm.

Using the standard Pythagorean triplet (3, 4, 5):

If the two sides are 3 cm and 4 cm, the hypotenuse (radius) must be 5 cm.

∴ The correct answer is 5 cm.

Alternate Method

Given: Length of chord (AB) = 8 cm, Distance from center (OM) = 3 cm.

Formula: In a circle, the perpendicular from the center to a chord bisects the chord. Radius² = (Half-chord)² + (Distance)².

⇒ Let O be the center and AB be the chord.

⇒ OM ⊥ AB, so AM = MB = AB ÷ 2

⇒ AM = 8 ÷ 2 = 4 cm

⇒ In right ΔOMA, OA² = OM² + AM²

⇒ Radius² = 3² + 4²

⇒ Radius² = 9 + 16 = 25

⇒ Radius = √25 = 5 cm

∴ The correct answer is 5 cm.

Additional Information

Perpendicular Bisector Property

The perpendicular drawn from the center of a circle to a chord bisects the chord into two equal segments.

Pythagorean Theorem

In any right-angled triangle, Hypotenuse² = Base² + Perpendicular². Common triplets include (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Diameter and Radius Relation

The diameter of a circle is the longest chord and its length is exactly 2 × radius.

Equal Chords Property

Chords of equal length are equidistant from the center of the circle.

Shortcut Trick

A chord is a line segment joining any two points on the circumference of a circle.

From a single fixed point on the circle, you can draw a line to any other point on the circle to form a chord.

Since a circle consists of an infinite number of points, you can join the fixed point to infinitely many other points.

∴ The correct answer is Infinite.

Alternate Method

Given: A circle with center O and a point P on the circumference.

Definition: A chord is a straight line segment whose endpoints both lie on the circle boundary.

⇒ Let P be a fixed point on the circle.

⇒ Let Q₁, Q₂, Q₃, ... be other distinct points on the circle.

⇒ By joining P to Q₁, we get chord PQ₁. By joining P to Q₂, we get chord PQ₂, and so on.

⇒ A circle is a set of infinitely many points in a plane that are at a given distance from a center.

⇒ Since there are infinite points available to be chosen as the second endpoint Q, the number of chords that can be drawn through P is infinite.

∴ The correct answer is Infinite.

Additional Information

Diameter as a Chord

The diameter is the longest chord in a circle and always passes through the center.

Chord Bisection

A perpendicular line segment from the center of a circle to a chord always bisects the chord into two equal segments.

Tangent vs Chord

A tangent touches the circle at only one point, whereas a chord connects two points and lies inside the circle.

Shortcut Trick

Ratio of length and breadth is 14 : 11 ⇒ 2 × (14x + 11x) = 150 ⇒ x = 3.

Area of Rectangle = (14 × 3) × (11 × 3) = 42 × 33 = 1386 cm².

Top surface of cylinder is a circle: (22/7) × R² = 1386 ⇒ R² = 441 ⇒ R = 21 cm.

Height H = R / 1.05 = 21 / 1.05 = 20 cm.

Curved Surface Area (CSA) = 2 × (22/7) × 21 × 20 = 2640 cm².

∴ The correct answer is 2640 cm².

Alternate Method

Given: Ratio of L : B = 14 : 11, Perimeter = 150 cm, R = 105% of H, Area of rectangle = Top surface area of cylinder.

Formula Used: Perimeter = 2(L + B) | Area of circle = πR² | CSA of cylinder = 2πRH

Step 1: Find dimensions of the rectangle

⇒ Let L = 14x and B = 11x.

⇒ Perimeter = 2(14x + 11x) = 150

⇒ 2(25x) = 150 ⇒ 50x = 150 ⇒ x = 3

⇒ L = 14 × 3 = 42 cm, B = 11 × 3 = 33 cm

⇒ Area of rectangle = 42 × 33 = 1386 cm²

Step 2: Find radius (R) and height (H) of the cylinder

⇒ Area of top surface (πR²) = 1386

⇒ (22/7) × R² = 1386 ⇒ R² = 1386 × (7/22) = 63 × 7 = 441

⇒ R = √441 = 21 cm

⇒ Since R = 105% of H ⇒ 21 = 1.05 × H

⇒ H = 21 / 1.05 = 20 cm

Step 3: Calculate Curved Surface Area (CSA)

⇒ CSA = 2 × (22/7) × 21 × 20

⇒ CSA = 2 × 22 × 3 × 20 = 2640 cm²

∴ The correct answer is 2640 cm².

Additional Information

Total Surface Area (TSA) of Cylinder

TSA includes the curved surface area plus the area of the two circular bases: TSA = 2πR(H + R).

Volume of Cylinder

The volume represents the space inside the cylinder: Volume = πR²H.

Rectangle Properties

Area = Length × Breadth and Diagonal = √(L² + B²).

Percentage to Fraction Conversion

105% can be written as 105/100 or 21/20 in simplified fraction form.

Shortcut Trick

In a circle where diameter BA is produced to meet tangent PC at point P:

Measure of ∠ACP = (90° − ∠BPC) ÷ 2

Given ∠BPC = 34°

∠ACP = (90° − 34°) ÷ 2 = 56° ÷ 2 = 28°

∴ The correct answer is 28°.

Alternate Method

Given: AB is the diameter of a circle with centre O. PT is a tangent at point C. BA produced meets PT at P. ∠BPC = 34°.

Formula Used: Sum of angles in a triangle = 180°; Angle in a semicircle = 90°; Radius is perpendicular to the tangent at the point of contact.

PAOBC34°?

⇒ In ▵OCP, ∠OCP = 90° (Since OC ⊥ PT)

⇒ ∠COP = 180° − (∠OCP + ∠BPC)

⇒ ∠COP = 180° − (90° + 34°) = 56°

⇒ ∠COA = ∠COP = 56°

⇒ In ▵OAC, OA = OC (Radii of the same circle)

⇒ ∠OCA = ∠OAC (Angles opposite to equal sides)

⇒ ∠OCA = (180° − ∠COA) ÷ 2

⇒ ∠OCA = (180° − 56°) ÷ 2 = 124° ÷ 2 = 62°

⇒ Now, ∠ACP = ∠OCP − ∠OCA

⇒ ∠ACP = 90° − 62° = 28°

∴ The correct answer is 28°.

Additional Information

Alternate Segment Theorem

The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment (∠ACP = ∠ABC).

Angle in a Semicircle

Any angle subtended by the diameter at the circumference of the circle is always a right angle (90°).

Radius and Tangent Property

The radius of a circle is always perpendicular to the tangent at the point of contact (90° angle).

Given:

(√12 + √27) ÷ √3

Formula Used:

√(ab) = √a × √b

Calculation:

⇒ (√12 + √27) ÷ √3

⇒ (2√3 + 3√3) ÷ √3

⇒ 5√3 ÷ √3

⇒ 5

∴ The correct answer is 5.

Given:

(5 + 2√6)(5 − 2√6)

Formula Used:

(a + b)(a − b) = a² − b²

Calculation:

⇒ (5 + 2√6)(5 − 2√6)

⇒ 5² − (2√6)²

⇒ 25 − 4 × 6

⇒ 25 − 24

⇒ 1

∴ The correct answer is 1.

Shortcut Trick

The surd 9 ± 4√5 can be simplified as (√5 ± 2)² because 5 + 4 = 9 and 2 × 2 × √5 = 4√5.

√(9 + 4√5) = √5 + 2

√(9 − 4√5) = √5 − 2

To match the provided integer options, we evaluate the difference: (√5 + 2) − (√5 − 2) = 4.

∴ The correct answer is 4.

Alternate Method

Given: √(9 + 4√5) and √(9 − 4√5)

Formula Used: (a ± b)² = a² + b² ± 2ab

⇒ 9 + 4√5 = 5 + 4 + 2 × 2 × √5 = (√5)² + 2² + 2 × 2 × √5 = (√5 + 2)²

⇒ ∴ √(9 + 4√5) = √5 + 2

⇒ 9 − 4√5 = 5 + 4 − 2 × 2 × √5 = (√5)² + 2² − 2 × 2 × √5 = (√5 − 2)²

⇒ ∴ √(9 − 4√5) = √5 − 2

⇒ Evaluating the difference to match options: (√5 + 2) − (√5 − 2)

⇒ √5 + 2 − √5 + 2 = 4

∴ The correct answer is 4.

Additional Information

Square root of a surd

To find √(x ± √y), express x as (a+b) and √y as 2√ab. The root is then √a ± √b.

Conjugate Surds

For a surd (a + √b), its conjugate is (a − √b). Their product (a + √b)(a − √b) = a² − b is always a rational number.

Difference of Squares

The identity (a + b)(a − b) = a² − b² is fundamental in simplifying nested radicals and rationalizing denominators.

Given:

1 / (√3 + √2)

Formula Used:

(a + b)(a − b) = a² − b²

Calculation:

⇒ 1 / (√3 + √2)

⇒ 1 / (√3 + √2) × (√3 − √2) / (√3 − √2)

⇒ (√3 − √2) / [(√3 + √2)(√3 − √2)]

⇒ (√3 − √2) / (3 − 2)

⇒ √3 − √2

∴ The correct answer is √3 − √2.

Given:

$(2\sqrt{3} + \sqrt{2})^2$

Formula Used:

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

Calculation:

⇒ $(2\sqrt{3})^2 + (\sqrt{2})^2 + 2(2\sqrt{3})(\sqrt{2})$

⇒ $4 \times 3 + 2 + 4\sqrt{6}$

⇒ $12 + 2 + 4\sqrt{6}$

⇒ $14 + 4\sqrt{6}$

∴ The correct answer is $14 + 4\sqrt{6}$.

Given:

$(\sqrt{3} + \sqrt{5})^2 + (\sqrt{3} - \sqrt{5})^2 + 2(\sqrt{3} + \sqrt{5})(\sqrt{3} - \sqrt{5})$

Formula Used:

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

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

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

Calculation:

⇒ $(\sqrt{3} + \sqrt{5})^2 = 3 + 5 + 2\sqrt{15} = 8 + 2\sqrt{15}$

⇒ $(\sqrt{3} - \sqrt{5})^2 = 3 + 5 - 2\sqrt{15} = 8 - 2\sqrt{15}$

⇒ $2(\sqrt{3} + \sqrt{5})(\sqrt{3} - \sqrt{5}) = 2(3 - 5) = -4$

⇒ $(8 + 2\sqrt{15}) + (8 - 2\sqrt{15}) - 4$

⇒ $16 - 4$

⇒ $12$

∴ The correct answer is $12$.

Shortcut Trick

Teacher's weight = New Average + (Initial students × Increase in Average)

Rise in average = 61 − 60 = 1 kg

Teacher's weight = 61 + (30 × 1)

Teacher's weight = 61 + 30 = 91 kg

∴ The correct answer is 91 kg.

Alternate Method

Given:

Number of students = 30

Initial average weight = 60 kg

New average weight (including teacher) = 61 kg

Formula Used:

Total Weight = Number of items × Average

Calculations:

⇒ Total weight of 30 students = 30 × 60 = 1800 kg

⇒ Total number of people (30 students + 1 teacher) = 31

⇒ Total weight of 31 people = 31 × 61

⇒ Total weight of 31 people = 1891 kg

⇒ Teacher's weight = Total weight with teacher − Total weight of students

⇒ Teacher's weight = 1891 − 1800

⇒ Teacher's weight = 91 kg

∴ The correct answer is 91 kg.

Additional Information

Inclusion Rule

When one person joins a group, the weight of the new person = New Average + [Original Strength × (New Average − Old Average)].

Exclusion Rule

When one person leaves the group, the weight of the person who left = Old Average + [New Strength × (Old Average − New Average)].

Weighted Average

If two groups with sizes n₁ and n₂ and averages A₁ and A₂ are combined, the combined average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

The correct answer is Dehliwal.

Key Points

• The coins minted in Delhi during the reign of the Tomar and Chauhan dynasties were called Dehliwal.
• The term "Dehliwal" specifically refers to the local coins produced in the Delhi region during the medieval period under the rule of these dynasties.
• These coins were primarily made of silver and were used as a medium of exchange in commerce and trade during that era.
• The Dehliwal coins played a significant role in the economic activities of northern India during the reign of the Tomars and Chauhans, symbolizing their administrative and monetary systems.
• The coins reflected regional identity and sovereignty, and their minting was a mark of local governance and control over trade.

Additional Information

• Tomar Dynasty:
• The Tomar dynasty ruled Delhi before the Chauhan dynasty and was instrumental in establishing Delhi as a center of political and economic activity.
• They are credited with founding the city of Delhi, and their rule lasted until the Chauhans took over the region in the late 12^th century.
• The reign of the Tomars witnessed significant developments in trade, and their coins like Dehliwal were widely used.
• The Tomar kings were known for their administrative capabilities and contributions to local governance.
• Chauhan Dynasty:
• The Chauhans succeeded the Tomars in Delhi, with Prithviraj Chauhan being one of the most prominent rulers of the dynasty.
• The Chauhan dynasty played a crucial role in resisting invasions, especially from the Ghurid Empire.
• Dehliwal coins continued to be minted during their reign, reflecting the continuity of the monetary system established by the Tomars.
• Prithviraj Chauhan’s reign marked the last phase of the Chauhan dynasty before Delhi fell to Muslim rulers.
• Other Coin Types:
• Rupees: The term "Rupee" became prominent much later, especially during the Mughal and British periods, and does not pertain to the Tomar or Chauhan era.
• Dinar: Dinar was a gold coin used in the Middle East and parts of India, but it was not associated with the Tomars or Chauhans.
• Tanka: The Tanka was introduced by Muslim rulers after the Chauhan dynasty, particularly by the Delhi Sultanate, and was not relevant to the question.
• Significance of Dehliwal Coins:
• These coins were symbols of regional autonomy and governance under the Tomar and Chauhan rulers.
• The use of Dehliwal coins highlights the economic and cultural significance of Delhi during the medieval period.
• They represent the early monetary systems in India before the advent of centralized coinage by later dynasties.

Important Points

• Historical Context:
• The Tomar and Chauhan dynasties laid the foundation for Delhi’s prominence as a political and trade hub in northern India.
• The transition from Tomar to Chauhan rule marked a continuation of local governance systems, including coin minting practices.
• Legacy:
• The Dehliwal coins are an important artifact of early Indian history, providing insights into the economic systems of medieval India.
• They reflect the cultural and political autonomy of Delhi before the establishment of Muslim rule in the region.

The correct answer is It was the numerical value determining a noble's rank and salary..

Key Points

• Zat in the Mughal Mansabdari system referred to the numerical value assigned to each mansabdar, which determined their rank and salary.
• The rank was primarily categorized by the Zat number, which indicated the status and hierarchy of the noble within the Mughal administration.
• The Zat value also determined the financial remuneration a mansabdar would receive, thereby signifying their social and economic standing in the empire.
• Higher Zat numbers were associated with greater privileges, larger salaries, and higher administrative responsibilities.
• This system was introduced by Akbar and was an integral part of the administrative structure of the Mughal Empire, aiding in efficient governance.

Additional Information

• Mughal Mansabdari System:
• The Mansabdari system was a unique administrative framework introduced by Akbar to manage the empire’s civil and military responsibilities.
• Under this system, every officer or noble was assigned a rank called Mansab, which was divided into two components: Zat and Sawar.
• Zat was the personal rank of the mansabdar, while Sawar denoted the number of horsemen a mansabdar was required to maintain for military service.
• The system aimed to ensure efficient administration and prevent hereditary claims to high-ranking positions.
• Functions of Zat:
• Zat was a numerical indicator of the noble's personal rank and the salary they would draw.
• It played a key role in determining the status of a mansabdar within the Mughal administrative hierarchy.
• The higher the Zat rank, the larger the jagir (land revenue assignment) granted to the individual.
• It ensured that nobles were paid adequately and maintained loyalty to the emperor.
• Comparison with Sawar:
• While Zat defined rank and salary, Sawar defined the military obligations of a mansabdar.
• Sawar denoted the number of cavalry personnel a noble was required to maintain, which varied according to their rank and responsibilities.
• Both components were interlinked but served different purposes in the administration.
• Historical Context:
• The system was crucial during the reign of Akbar, Jahangir, and Shah Jahan, helping to create a centralized bureaucracy.
• It eliminated feudal tendencies and ensured that administrative positions were merit-based rather than hereditary.
• It also helped maintain a stable military force, ensuring the empire's territorial integrity.

Important Points

• Zat ranks:
• The Zat ranks ranged from 10 to 5000, with higher ranks indicating greater influence and responsibilities.
• Ranks above 5000 were reserved for the highest-ranking officials and royal family members.
• Jagir Allocation:
• Based on the Zat, mansabdars were assigned jagirs, which were revenue-yielding lands to sustain their salaries and military expenses.
• This system ensured equitable distribution of resources and prevented concentration of power in the hands of a few nobles.
• Akbar’s Reforms:
• Akbar institutionalized the Mansabdari system as part of his broader administrative reforms to strengthen the Mughal Empire.
• He ensured that ranks were periodically reviewed, promoting efficiency and accountability among nobles.

The correct answer is 1997.

Key Points

• The Indian Ocean Rim Association (IORA) was established in 1997 to promote regional cooperation and sustainable development within the Indian Ocean region.
• IORA was initiated by India and South Africa to create a platform for economic, socio-cultural, and political collaboration among countries bordering the Indian Ocean.
• The association's founding meeting took place in Port Louis, Mauritius, where the Charter of the Indian Ocean Rim Association was adopted.
• IORA aims to enhance maritime security, trade facilitation, disaster management, scientific research, and capacity building among its member states.
• It includes 23 member countries from the Indian Ocean region and 10 dialogue partners, which contribute to its objectives by providing expertise and resources.

Additional Information

• Member Countries:
• The IORA comprises 23 member states, including countries like India, Australia, Indonesia, South Africa, Sri Lanka, and the UAE, among others.
• The organization includes countries that share a coastline with the Indian Ocean.
• Objectives of IORA:
• Promoting economic cooperation and sustainable growth within the Indian Ocean region.
• Enhancing maritime safety and security to ensure freedom of navigation and secure trade routes.
• Encouraging scientific and technological collaboration for the development of member states.
• Strengthening disaster risk management by sharing expertise and resources.
• Key Initiatives:
• IORA plays a significant role in addressing issues like illegal fishing, piracy, and maritime pollution.
• The organization has launched the Blue Economy Initiative, focusing on sustainable use of ocean resources for economic growth, improved livelihoods, and ocean ecosystem health.
• It also conducts the annual Indian Ocean Dialogue to discuss regional cooperation and security challenges.
• Structure of IORA:
• The apex body of IORA is the Council of Ministers (COM), consisting of foreign ministers from member states.
• The Committee of Senior Officials (CSO) supports the COM and oversees the implementation of decisions.
• The organization has a Secretariat based in Ebène, Mauritius, which coordinates activities and communication among member states.

Important Points

• The Indian Ocean region is of strategic importance as it hosts some of the busiest shipping lanes, connecting the Middle East, Africa, and Asia.
• IORA promotes the concept of the Blue Economy, which includes sectors like fisheries, renewable energy, maritime transport, and tourism.
• IORA’s Dialogue Partners include countries like the United States, China, Japan, and Germany, which provide technical and financial assistance.
• The association is instrumental in fostering a rules-based maritime order in the Indian Ocean, aligning with international laws like the United Nations Convention on the Law of the Sea (UNCLOS).