SSC CHSL 2025 Tier-1 (Held On: 29 Nov, 2025 Shift 2) (Previous Year Paper)

The correct answer is: Unimaginable.

Key Points

• The word "incredible" means something that is extraordinary, amazing, or difficult to believe. (अविश्वसनीय)
• Example: The view from the mountaintop was incredible—it felt like a dream.
• "Unimaginable" refers to something that cannot be comprehended or envisioned due to its extraordinary nature. (अकल्पनीय)
• Example: The destruction caused by the earthquake was unimaginable.
• Hence, the word "unimaginable" is similar in meaning to "incredible."

Therefore, the correct answer is: Unimaginable.

Additional Information

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

• Unremarkable (असाधारण नहीं): Refers to something that is ordinary or not worth noticing.
• Example: The movie was unremarkable and failed to leave an impression.
• Apparent (स्पष्ट): Refers to something that is clearly visible or understood.
• Example: It became apparent that he was not interested in the conversation.
• Unacceptable (अस्वीकार्य): Refers to something that cannot be tolerated or approved.
• Example: The rude behavior of the customer was completely unacceptable.

The correct answer is: Option 1 i.e. Teetotaler.

Key Points

• The word "Teetotaler" refers to a person who abstains completely from alcohol consumption. (शराब से पूर्ण रूप से परहेज करने वाला व्यक्ति)
• Example: John is a teetotaler and prefers drinking juice at parties.
• "Non-drinker" is also used for someone who does not drink alcohol but may not carry the strong implication of total abstinence like "Teetotaler." (शराब न पीने वाला व्यक्ति)
• Example: Sarah is a non-drinker and avoids alcohol at social events.
• Hence, the correct answer is "Teetotaler."

Therefore, the correct answer is: Option 1 i.e. Teetotaler.

Additional Information

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

• Non-drinker (शराब न पीने वाला): A person who does not consume alcohol but may not abstain totally in all situations.
• Example: He is a non-drinker but occasionally enjoys a glass of wine for celebrations.
• Beverages man (पेय पदार्थों का व्यक्ति): This is not a correct term in the context of alcohol abstinence. It refers to someone involved in the beverage industry or someone who enjoys beverages in general.
• Example: The beverages man delivered a variety of drinks for the party.
• Tougher (कठोर): Refers to someone who is strong or resilient but is unrelated to the context of alcohol consumption.
• Example: He became tougher after facing difficult challenges in life.

The correct answer is: Option 2 i.e. Aquatic.

Key Points

• The word "Aquatic" refers to something that is related to water or lives in or near water. (जल संबंधी)
• Example: Fishes, turtles, and dolphins are examples of aquatic animals.
• In the given sentence, aquatic habitats are mentioned, which include diverse forms of life thriving in water, such as animals and plants.
• Example: Ravi marvelled at the diverse forms of life, including animals and plants, thriving in aquatic habitats.

Therefore, the correct answer is: Option 2 i.e. Aquatic.

Additional Information

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

• Terrestrial (स्थलीय): Refers to life forms that live on land.
• Example: Lions and elephants are terrestrial animals that inhabit forests and grasslands.
• Arboreal (वृक्षवासी): Refers to creatures that live in trees.
• Example: Monkeys and squirrels are arboreal animals that spend most of their time in trees.
• Polar (ध्रुवीय): Refers to life forms or habitats found in the polar regions of the Earth.
• Example: Polar bears and seals are examples of polar animals adapted to cold climates.

The correct answer is Option 1.

Key Points

• The error in the sentence is the incorrect use of the phrasal verb "kick up."
• The intended meaning in this context is to start or commence the holiday season. The appropriate phrasal verb for this is "kick off."
• "Kick off" means to begin or start an event or a period of time (e.g., The festival kicks off this Friday).
• "Kick up" typically means to create something unpleasant, such as a fuss, trouble, or to stir up dust (e.g., The wind kicked up a lot of dust).

Therefore, the correct answer is 1.

Correct Sentence: "Amazon Prime Day is going to kick off the holiday season and holiday shopping for many consumers."

Additional Information

• Option 2: "for many consumers" – This prepositional phrase is used correctly to indicate the people affected by the shopping season.
• Option 3: "up the holiday season" – While this contains the incorrect particle "up," the primary grammatical error is rooted in the phrasal verb structure found in Option 1.
• Option 4: "holiday season and holiday shopping" – This compound direct object is grammatically correct and logically connected by the conjunction "and."
• Usage Note: Phrasal verbs are highly context-dependent. Always verify if the particle (up, off, on, out) aligns with the intended action of the base verb.

The correct answer is option 1.

Key Points

• The correctly spelt word is 'Accelerate'.
• The word 'Accelerate' is a verb which means 'to begin to move more quickly or to increase the rate of something'. (तेज़ी लाना)

Correct Usage: The car can accelerate from 0 to 100 km/h in just 10 seconds.

Additional Information

• Common Misspellings:
• Accellerate: Incorrect spelling due to the addition of an extra 'l'.
• Accelarate: Incorrect spelling due to the replacement of 'e' with 'a'.
• Accellrate: Incorrect spelling due to the addition of 'll' and omission of 'e'.
• Tips to Remember: The correct spelling is 'Accelerate', with a single 'l' and 'e' in the middle.

The correct answer is 'suffering from'.

Key Points

• The correct preposition to use with the verb "suffering" is "from."
• "Suffering from" is used to describe the cause of pain, distress, or difficulty, typically due to illness or a problem.
• Options 1 ("suffering by"), 2 ("suffering in"), and 4 ("No substitution") are grammatically incorrect or do not fit the context.

Therefore, the correct answer is Option 3.

Complete Sentence: "The villagers are suffering from a shortage of clean water."

Additional Information

• Option 1: "suffering by" is incorrect because "by" does not convey the correct relationship between the verb "suffering" and the cause.
• Option 2: "suffering in" is incorrect because "in" does not fit the grammatical context of the sentence.
• Option 4: "No substitution" is incorrect because the original sentence needs improvement for grammatical accuracy.

The correct answer is 'focus on'.

Key Points

• The correct preposition to use with the verb "focus" is "on."
• The phrase "focus on" is used to refer to concentrating or giving attention to a particular subject or task.
• Options 1, 2, and 4 are grammatically incorrect in this context.

Therefore, the correct answer is Option 3.

Complete Sentence: "We need to focus on finding a sustainable solution."

Additional Information

• Option 1: "focus to" is incorrect because "to" is not the appropriate preposition to use with "focus."
• Option 2: "focus at" is incorrect because "at" does not convey the meaning of concentration or attention.
• Option 4: "No substitution" is incorrect because the given sentence requires substitution to make it grammatically correct.

The correct answer is Option 2.

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the active voice, the sentence is: "The shopkeeper must have misguided the customers to purchase the faulty watches."
• To convert to passive voice: Place the object "the customers" at the beginning.
• Change the active verb form "must have misguided" to "must have been misguided" (modal perfect passive).
• Ensure the rest of the sentence retains its original meaning, including "to purchase the faulty watches."

Therefore, the correct answer is Option 2.

Correct Sentence: "The customers must have been misguided by the shopkeeper to purchase the faulty watches."

Additional Information

• Option 1: "The customers must be misguided by the shopkeeper to purchase the faulty watches." – Incorrect tense (present modal passive).
• Option 3: "The customers must have been misguided by the shopkeeper to have purchased the faulty watches." – Incorrect meaning and usage of "to have purchased."
• Option 4: "The customers must have been misguided by the shopkeeper to be purchasing the faulty watches." – Incorrect use of "to be purchasing."

The correct answer is Option 2.

Key Points

• Indirect Speech: The farmers said that it was time to plough their fields as the soil had become damp.
• Key Conversions:
• "It is time" becomes "it was time":
• In indirect speech, present tense ("is") changes to past tense ("was").
• "The soil has become damp" becomes "the soil had become damp":
• Present perfect tense ("has become") changes to past perfect tense ("had become") in indirect narration.
• Pronouns:
• The possessive pronoun "our" changes to "their" to match the context of the farmers talking about their own fields.
• Reporting Verb:
• The reporting verb "said" remains unchanged as it fits the context of simple narration.
• Punctuation and Format:
• Quotation marks are removed in indirect speech.
• The sentence structure is simplified to align with indirect narration rules.

Therefore, the correct answer is Option 2.

Correct Sentence: The farmers said that it was time to plough their fields as the soil had become damp.

Additional Information

• Option 1: "The farmers said that it has been time to plough their fields as the soil had become damp."
• Incorrect: "has been" does not match the tense shift required in indirect speech.
• Option 3: "The farmers said that it had been time to plough their fields as the soil had become damp."
• Incorrect: "had been" suggests a completed action in the past, which distorts the original meaning.
• Option 4: "The farmers said that it was time to plough their fields as the soil has been damp."
• Incorrect: "has been" is inconsistent with the tense shift required in indirect speech.

The correct answer is 'of'.

Key Points

• The preposition "of" is used to indicate a connection or association, which fits the context of the sentence.
• In the sentence, "She is fond __________ classical music," the word "fond" is typically followed by the preposition "of."
• Options 2, 3, and 4 are not suitable because "fond" does not pair with "in," "with," or "for" in standard usage.

Therefore, the correct answer is Option 1.

Complete Sentence: "She is fond of classical music."

Additional Information

• Option 2: "in" is incorrect because "fond" is not followed by "in" in standard English.
• Option 3: "with" is incorrect because "fond" is not followed by "with" in standard English.
• Option 4: "for" is incorrect because "fond" is not followed by "for" in standard English.

The correct answer is: Reserved.

Key Points

• The word "Garrulous" means excessively talkative, especially on trivial matters. (बातूनी)
• Example: The garrulous neighbor constantly chatted about her garden and pets.
• The word "Reserved" refers to someone who is quiet, restrained, or not given to excessive talking. (संकोची)
• Example: Despite being part of the group, she remained reserved and preferred listening to others.
• Since "Reserved" is the opposite of "Garrulous," it is the most appropriate antonym.

Therefore, the correct answer is: Reserved.

Additional Information

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

• Quit (छोड़ना): To stop or leave something.
• Example: He decided to quit his job to pursue his passion for painting.
• Shy (शर्मीला): Being nervous or timid in social situations.
• Example: The shy boy hesitated to answer the teacher's question.
• Silent (चुप): Completely quiet or without sound.
• Example: The room was silent after the announcement of the results.

The correct answer is Option 2.

Key Points

• The given sentence is in the passive voice, and the active voice form must be derived.
• Passive voice structure: Object + auxiliary verb + past participle.
• Active voice structure: Subject + verb + object.
• In the sentence "The school building was constructed in 1980," the subject performing the action is omitted.
• To convert this to active voice, add a generic subject like "someone" to indicate the doer of the action.

Therefore, the correct answer is Option 2.

Correct Sentence: "Someone constructed the school building in 1980."

Additional Information

• Option 1: "The school building had been constructed in 1980." – Incorrect because it is in the passive voice and uses the past perfect tense unnecessarily.
• Option 3: "The school building constructs in 1980." – Incorrect verb form; "constructs" is present tense, which does not match the timeline of 1980.
• Option 4: "Someone is constructing the school building in 1980." – Incorrect tense usage; "is constructing" implies present continuous and does not align with 1980.

The correct answer is Option 2.

Key Points

• Reported Speech: She told me that she had been learning French for three months.
• Key Conversions:
• "She had been learning" becomes "I have been learning"
• Indirect speech tense (past perfect continuous) is converted to direct speech tense (present perfect continuous).
• Pronoun "she" is changed to "I" for direct speech.
• "French for three months" remains unchanged
• The time duration does not change in conversion.
• Reporting verb:
• Indirect: "She told me"
• Converted to: "She said to me," which is appropriate for direct speech.
• Punctuation and Format:
• Direct speech is enclosed in quotation marks.
• Starts with a capital letter "I" and ends with a period ".".
• Reporting clause follows the quoted speech, separated by a comma.

Therefore, the correct answer is Option 2.

Correct Sentence: "She said to me, "I have been learning French for three months.""

Additional Information

• Option 1: "She said to me, "I am learning French for three months.""
• Incorrect tense: "am learning" does not match the original past perfect continuous tense.
• Option 3: "She said to me, "I had learnt French for three months.""
• Incorrect tense: "had learnt" changes the meaning to past perfect, indicating a completed action, which is inconsistent with the original continuous action.
• Option 4: "She said to me, "I learnt French for three months.""
• Incorrect tense: "learnt" changes the meaning to simple past, losing the continuous aspect of the action.

The correct answer is 'on, with'.

Key Points

• The preposition "on" is used to indicate insistence or focus in the context of a subject or action (e.g., "insisted on a thorough investigation").
• The preposition "with" is appropriate when referring to proceeding or continuing in relation to something (e.g., "proceeding with any decision").
• Other options (e.g., "in, by," "of, to," and "to, under") do not fit logically or grammatically in the context of the sentence.

Therefore, the correct answer is Option 2.

Complete Sentence: "The committee insisted on a thorough investigation before proceeding with any decision."

Additional Information

• Option 1: "in, by" is incorrect because "insisted in" and "proceeding by" are not suitable phrases for this context.
• Option 3: "of, to" is incorrect because "insisted of" and "proceeding to" are not grammatically correct in this sentence.
• Option 4: "to, under" is incorrect because "insisted to" and "proceeding under" do not fit the context of the sentence.

The correct answer is option 3 i.e. Seperately.

Key Points

The misspelled word is 'Seperately'.

• The correct spelling is 'Separately'.
• The word 'separately' is an adverb that means 'apart from others or individually' (अलग-अलग).
• For Example -
• The twins were asked to sit separately during the exam.

Therefore, the correct answer is option 3 i.e. Seperately.

Additional Information

Let's understand the meanings of the other marked words:

• Bureaucracy - a system of government in which most of the important decisions are made by state officials rather than by elected representatives (नौकरशाही).
• Millennium - a period of a thousand years, especially when calculated from the traditional date of the birth of Christ (सहस्राब्दी).
• Consensus - general agreement (सामान्य सहमति).

The correct answer is Option 3.

Key Points

• Indirect Speech: In indirect speech, the tense of the verb changes according to the reporting verb's tense. Here, "spoke" in direct speech changes to "had spoken" in indirect speech as the reporting verb "said" is in the past tense.
• Key Conversions:
• "yesterday" becomes "the previous day"
• In indirect speech, time expressions are adjusted according to the context.
• "I spoke" becomes "he had spoken"
• The pronoun "I" is changed to "he" to match the subject of the reporting clause.
• The verb "spoke" is changed to "had spoken" to reflect the past perfect tense.
• Punctuation:
• Direct speech quotation marks are removed in indirect speech.
• The sentence follows proper grammatical structure without punctuation marks used in direct speech.

Therefore, the correct answer is Option 3.

Correct Sentence: He said that he had spoken with his parents the previous day.

Additional Information

• Option 1: "He said that he spoke with his parents the previous day."
• Incorrect tense: "spoke" should be changed to "had spoken" in indirect speech.
• Option 2: "He said that he should have speak with his parents the previous day."
• Incorrect modal verb and grammar: "should have speak" is ungrammatical.
• Option 4: "He said that he would speak with his parents the day before."
• Incorrect tense and time expression: "would speak" is future tense and "the day before" does not match the context.

The correct answer is option 4.

Key Points

The misspelled word is 'Conviviel'.

• The correct spelling would be 'Convivial'.
• The word 'convivial' is an adjective which means 'friendly, lively, and enjoyable'. (मिलनसार)
• For Example -
• The party was a convivial gathering filled with laughter and joy.

Therefore, the correct answer would be 'Conviviel'.

Additional Information

Let's understand the meanings of the other marked words - 

• Ambiguous - open to more than one interpretation; not having one obvious meaning (अस्पष्ट)
• Conscientious - wishing to do one's work or duty well and thoroughly (सजग)
• Irrepressible - not able to be controlled or restrained (अदम्य)

The correct answer is 'Option 3 (Present perfect)'.

Key Points

• Option 1: Past simple
• This is incorrect. Past simple would be “There was a noticeable surge,” but the sentence uses “has been,” which indicates continuity into the present.
• Option 2: Future perfect
• This is incorrect. Future perfect would be “There will have been,” which refers to a completed action in the future, not the present.
• Option 3: Present perfect
• This is correct. “Has been” is the present perfect tense, used to describe an action that began in the past and continues to have relevance or effect in the present.
• Option 4: Past continuous
• This is incorrect. Past continuous would be “There was being a surge,” which is ungrammatical and does not match the sentence structure.

Therefore, the correct answer is Option 3 (Present perfect).

Additional Information

• Present perfect tense is formed with has/have + past participle.
• It is used to describe actions that started in the past but are still relevant or continuing in the present.
• Example: “She has lived here for five years.” → She started living in the past and continues to live here now.
• In the passage: “There has been a noticeable surge in gold prices” → The surge began earlier and is still relevant now.

The correct answer is 'Option 4'.

Key Points

• Option 1: The perception of scarcity fuels investments
• This is active voice. The subject “perception of scarcity” performs the action “fuels.”
• Option 2: Gold holds cultural value
• This is active voice. The subject “Gold” performs the action “holds.”
• Option 3: Several factors contribute to the rise
• This is active voice. The subject “Several factors” performs the action “contribute.”
• Option 4: The current hype surrounding gold rates is not entirely based on practical factors
• This is passive voice. The subject “hype” is described as being “based on” something, showing the action is received rather than performed.

Therefore, the correct passive voice sentence is Option 4: “The current hype surrounding gold rates is not entirely based on practical factors.”

Additional Information

• In active voice, the subject performs the action (e.g., “Gold holds cultural value”).
• In passive voice, the subject receives the action (e.g., “is based on practical factors”).
• Passive voice often uses forms of “be + past participle.”

The correct answer is: Option 2 i.e. Sudden and emotional.

Key Points

• The word "impulsive" means:
• Acting or done without forethought, typically as a result of a sudden strong and unreflective urge or desire. (बिना विचार के किया हुआ कार्य, अक्सर एक अचानक और अनियंत्रित प्रेरणा या इच्छा के परिणामस्वरूप)
• Example: She made an impulsive decision to buy the dress without considering the price.
• "Correct answer" means:
• Referring to the specific answer that properly defines or fits the context of the question. (सही उत्तर)
• Example: The correct answer to the quiz question assured him a perfect score.

Therefore, the word “impulsive” in the given context means: Sudden and emotional.

Additional Information

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

• Well-planned (अच्छी तरह योजनाबद्ध): Thought out carefully in advance.
• Example: The event was well-planned and executed flawlessly.
• Economical (किफायती): Using no more of something than is necessary.
• Example: Buying in bulk is often more economical than purchasing items individually.
• Delayed and thoughtful (विलंबित और विचारशील): Done after careful consideration, taking time to think.
• Example: His response to the offer was delayed and thoughtful as he wanted to weigh all options.

The correct answer is: Option 3 i.e. A secure place to park money during uncertainty.

Key Points

• The phrase "safe haven" refers to:
• A secure place or investment where money can be parked or stored during times of economic or financial uncertainty. (आर्थिक या वित्तीय अनिश्चितता के दौरान जहाँ पैसे को सुरक्षित स्थान या निवेश में रखा जा सकता है)
• Example: During market volatility, investors often seek safe havens like bonds and stable currencies.
• "Correct answer" means:
• Referring to the specific answer that properly defines or fits the context of the question. (सही उत्तर)
• Example: The correct answer to the quiz question assured him a perfect score.

Therefore, the term "safe haven" in the given context means: A secure place to park money during uncertainty.

Additional Information

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

• A dangerous investment (एक खतरनाक निवेश): An investment that carries a high level of risk.
• Example: Investing in highly volatile stocks can be a dangerous investment.
• A long-term liability (दीर्घकालीन दायित्व): A financial obligation or debt that is payable over a long period.
• Example: The company's mortgage is considered a long-term liability.
• A place to store gold (सोना रखने का स्थान): A location designated for keeping gold secure.
• Example: The bank's vault is a secure place to store gold.

The correct answer is 'Option 3 (Emotional buying influenced by cultural traditions)'.

Key Points

• Option 1: Strict government policies on gold trade
• This is incorrect. The passage does not mention government restrictions as a cause of rising prices.
• Option 2: Increased mining of gold
• This is incorrect. Mining is not discussed in the passage; the focus is on demand and emotional factors.
• Option 3: Emotional buying influenced by cultural traditions
• This is correct. The passage highlights India’s cultural and emotional attachment to gold, especially during weddings and festivals. This leads to panic buying and impulsive investments, which further push prices upward.
• Option 4: Lack of interest in other investment options
• This is incorrect. The passage does not claim that gold prices rise because people avoid other investments; instead, it stresses emotional and media-driven buying.

Therefore, the correct answer is Option 3: Emotional buying influenced by cultural traditions.

Additional Information

• Gold in India is not just an asset but a symbol of tradition and security.
• Festivals and weddings often trigger panic buying, amplifying price surges.
• Social media updates on price movements create a sense of urgency, fueling impulsive investments.
• Thus, besides economic factors, plays a crucial role in driving demand and prices upward.

The correct answer is Option 2.

Key Points

• The paragraph follows a chronological and logical progression of setting up a technical system, starting with physical installation and ending with performance verification.
• Sentence P is the first sentence as it establishes the physical foundation required for the process:
• "He connected the modem to the wall and the wireless router to the modem."
• Sentence Q follows because once the hardware is physically linked, the next logical step is to configure the software settings:
• "He followed the setup wizard on his computer, configuring the network's name and password."
• Sentence R is the third sentence as it describes the action taken once the network is live and secured:
• "He connected all his devices to the new network, from his phone to his smart TV."
• Sentence S is the fourth because it represents the final step of the process—verifying that the setup was successful and functional:
• "He performed a speed test, confirming his home now had a strong and reliable connection."
• The correct sequence is PQRS.

Coherent paragraph after rearrangement:

"He connected the modem to the wall and the wireless router to the modem. He followed the setup wizard on his computer, configuring the network's name and password. He connected all his devices to the new network, from his phone to his smart TV. He performed a speed test, confirming his home now had a strong and reliable connection."

The correct answer is Option 2.

Key Points

• The paragraph follows a logical narrative arc: establishing a historical catalyst, explaining the motivation for human movement, describing the resulting societal growth, and concluding with the reality of the outcome.
• Sentence P is the first sentence as it introduces the specific event and time period that serves as the foundation for the entire paragraph:
• "A large-scale migration was triggered in 1848 by the discovery of gold in California."
• Sentence Q follows by identifying the people involved and their motivation for participating in this migration:
• "Prospectors from all over the world were drawn to the promise of immediate fortune."
• Sentence S is the third sentence as it describes the broader geographical and structural impact that this massive influx of people had on the region:
• "Towns and communities in the American West proliferated as a result of this migration."
• Sentence R is the fourth sentence because it provides a concluding observation or "reality check" regarding the individuals mentioned earlier in the text:
• "Few of the 'Forty-Niners' did become wealthy."
• The correct sequence is PQSR.

Coherent paragraph after rearrangement:

"A large-scale migration was triggered in 1848 by the discovery of gold in California. Prospectors from all over the world were drawn to the promise of immediate fortune. Towns and communities in the American West proliferated as a result of this migration. Few of the 'Forty-Niners' did become wealthy."

The correct answer is: Option 2 i.e. Preventable.

Key Points

• The word "Ineluctable" refers to something that is inevitable or unavoidable, meaning that it cannot be escaped or prevented. (अपरिहार्य)
• Example: The ineluctable passage of time impacts everyone eventually.
• "Preventable" refers to something that can be stopped or avoided, indicating the opposite meaning of "Ineluctable." (रोकने योग्य)
• Example: Many diseases are preventable through vaccination and proper hygiene.
• Hence, the antonym of "Ineluctable" is "Preventable".

Therefore, the correct answer is: Option 2 i.e. Preventable.

Additional Information

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

• Unavoidable (अपरिहार्य): Something that cannot be avoided or escaped, similar to "Ineluctable."
• Example: Traffic congestion is often an unavoidable part of urban life.
• Inevitable (अनिवार्य): Something that is certain to happen and cannot be avoided, synonymous with "Ineluctable."
• Example: Change is inevitable as society progresses.
• Inescapable (अपरिहार्य): Something that cannot be escaped or avoided, also synonymous with "Ineluctable."
• Example: The consequences of his actions were inescapable.

Given: 14, 41, 121, 360, 1076, ?, 9663

The logic followed here is:

14

14 × 3 − 1 = 42 - 1 = 41

41 × 3 − 2 = 123 - 2 = 121

121 × 3 − 3 = 363 - 3 = 360

360 × 3 − 4 = 1080 - 4 = 1076

1076 × 3 − 5 = 3228 - 5 = 3223

3223 × 3 − 6 = 9669 - 6 = 9663

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: A ! B = (A − B) × 5

34 ! 68 = -170 → (34 − 68) × 5 = (−34) × 5 = −170 

9 ! 62 = -265 → (9 − 62) × 5 = (−53) × 5 = −265

Similarly,

3 ! 42? → (3 − 42) × 5 = (−39) × 5 = −195

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: A $ B = A × B × 4

16 $ 8 = 512 → (16 × 8 × 4) = 512

45 $ 28 = 5040 → (45 × 28 × 4) = 5040

Similarly,

51 $ 27? → 51 × 27 × 4 = 1377 × 4 = 5508

Hence, the correct answer is "Option 4".

Logic: 6, 15, 33, 69, ?

Logic: Previous term × 2 + 3 = Next term

The logic followed here is:

6 × 2 + 3 = 12 + 3 = 15

15 × 2 + 3 = 30 + 3 = 33

33 × 2 + 3 = 66 + 3 = 69

69 × 2 + 3 = 138 + 3 = 141

Hence, the correct answer is "Option 4".

Given: 10, 44, 180, 724, ?

Logic: Next term = Previous term × 4 + 4

The logic followed here is:

10

10 × 4 + 4 = 40 + 4 = 44

44 × 4 + 4 = 176 + 4 = 180

180 × 4 + 4 = 720 + 4 = 724

724 × 4 + 4 = 2896 + 4 = 2900

Hence, the correct answer is "Option 3".

The position and positional values or English Alphabets are:

Given: C, F, L, X, ?

The logic followed here is:

Thus, V will come next to the series.

Hence, the correct answer is "Option 2".

Given: Length of 5 rectangles J, K, L, M and N is compared. Length of no two rectangles is same.

1. Length of K is less than only three rectangles. 2. Length of no rectangle is less than M. 3. Length of L is not more than N but more than J. 

M < K < J < L < N

Thus, length of 2 rectangles is more than K but less than N.

Hence, the correct answer is "Option 2".

Given: 5 persons A, B, C, D and E are sitting around a circular table facing towards the centre (not necessarily in the same order).

1. C is not an immediate neighbour of D or A. 2. A is sitting second to the left of C.

Thus, D can be only be placed to second tot he right of C.

3. B is sitting second to the left of E.

Thus, C is sitting fourth to the left of B.

Hence, the correct answer is "Option 1".

Given: There are 6 flats on a floor in two rows (three in each row opposite to each other). Flats of one row are facing north. Flats of other row are facing south. These flats are alloted to A, B, C, D, E and F.

1. C gets a South facing flat.  2. The direction in which the flats of B and E are facing is same. 3.  B 's flat is not next to D. 

It implies D's having North facing flat.

4. F's flat is next to C's flat. 5. D and F get diagonally opposite flats.

A, the only person left will occupy the vacant position.

Thus, pair FA represents people having south facing flat.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: a : b = a + 950 = b

1622 : 2572 → 1622 + 950 = 2572

8785 : 9735 → 8785 + 950 = 9735

Similarly,

? : 5985 → 5985 – 950 = 5035

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: a : b = (a ÷ 6) − 3 = b

2976 : 493 → (2976 ÷ 6) - 3 = 496 - 3 = 493 

4902 : 814 → (4902 ÷ 6) - 3 = 817 - 3 = 814 

Similarly,

2466 : ? → (2466 ÷ 6) - 3 = 411 − 3 = 408

Hence, the correct answer is "Option 4".

BODMAS Rule:

Given equation: 

l. 60 + 20 - 5 ÷ 18 × 3 = 10

After interchanging '- and ÷' the given two signs, we get:

​⇒ 60 + 20 ÷ 5 − 18 × 3 = 10

​⇒ 60 + 4 − 18 × 3 = 10

​⇒ 60 + 4 − 54 = 10

​⇒ 64 − 54 = 10

​⇒ 10 = 10

⇒ L.H.S = R.H.S

II. 40 + 80 ÷ 16 - 9 × 2 = 30

After interchanging '- and ÷' the given two signs, we get:

⇒ 40 + 80 − 16 ÷ 9 × 2 = 30

⇒ 40 + 80 − 1.77 × 2 = 30

⇒ 40 + 80 − 3.5 = 30

⇒ 120 − 3.5 = ?

⇒ 116.5 ≠ 30

⇒ LHS ≠ RHS

Thus, 'Only II' equation will NOT be correct.

Hence, the correct answer is "Option 2".

BODMAS Rule:

Given equation: 210 * 7 * 2 * 60 * 30 = 90

Let's check each option:

1. ×, ÷, −, +

Given equation: 210 * 7 * 2 * 60 * 30 = 90

After replacing the '*' from left to right in the equation, we get:

⇒ 210 × 7 ÷ 2 − 60 + 30 = 90

⇒ 210 × 3.5 − 60 + 30 = 90

⇒ 735 − 60 + 30 = 90

⇒ 676 - 60 = 90

⇒ 616 ≠ 90

⇒ L.H.S ≠ R.H.S

2: +, ÷, ×, −

Given equation: 210 * 7 * 2 * 60 * 30 = 90

After replacing the '*' from left to right in the equation, we get:

⇒ 210 + 7 ÷ 2 × 60 − 30 = 90

⇒ 210 + 3.5 × 60 − 30 = 90

⇒ 210 + 210 − 30 = 90

⇒ 420 − 30 = 90

⇒ 390 ≠ 90

⇒ L.H.S ≠ R.H.S

 3: ÷, ×, +, −

Given equation: 210 * 7 * 2 * 60 * 30 = 90

After replacing the '*' from left to right in the equation, we get:

⇒ 210 ÷ 7 × 2 + 60 − 30 = 90

⇒ 30 × 2 + 60 − 30 = 90

⇒ 60 + 60 − 30 = 90

⇒ 120 − 30 = 90

⇒ 90 = 90

⇒ L.H.S = R.H.S

4: −, ×, ÷, +

Given equation: 210 * 7 * 2 * 60 * 30 = 90

After replacing the '*' from left to right in the equation, we get:

⇒ 210 − 7 × 2 ÷ 60 + 30 = 90

⇒ 210 − 7 × 0.03 + 30 = 90

⇒ 210 − 0.233 + 30 = 90

⇒ 240 - 0.233 = 90

⇒ 239.766 ≠ 90

⇒ L.H.S ≠ R.H.S

Hence, the correct answer is "Option 3".

The position and positional values or English Alphabets are:

The logic followed here is:

Logic: Number = sum of positions of letters

1. GIKM40

2. PRTV76

3. TVXZ92

4. OQSU82

Thus, 'OQSU82' is the odd one out.

Hence, the correct answer is "Option 4".

The position and positional values or English Alphabets are:

The logic followed here is:

Logic: 

1. VD240 - AJ610

2. LP310 - QV680

3. SK420 - XQ770

4. BH370 - GN740

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: a - b → a = b³

1. 1728-12 → 1728 = 123 2. 1331-11 → 1331 = 113 3. 2197-13 → 2197 = 133 4. 2764-14 → 2764 ≠ 143 [14³ = 2744]

Thus, '2764-14' is the odd one out.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: a - b → (a + 2)² = b

1. 13-225 → (13 + 2)2 = 15² = 225
2. 11-169 → (11 + 2)2 = 132 = 225
3. 15-289 → (15 + 2)2 = 172 = 225
4. 17-381  → (17 + 2)2 = 192 = 361 ≠ 381

Thus, '17-381' is the odd one out.

Hence, the correct answer is "Option 4".

The position and positional values or English Alphabets are:

The logic followed here is:

'FEAR' is coded as '31'

'CHAIR' is coded as '40'

Similarly,

Thus, 'MATE' is coded as 40 in that code language.

Hence, the correct answer is "Option 1".

Let's check each option:

1. NEST → MOUNTAINS → Cannot be formed as 'E' is missing.
2. MOUND → MOUNTAINS → Cannot be formed as 'D' is missing.
3. AMOUNT → MOUNTAINS → Can be formed.
4. STRAIN → MOUNTAINS → Cannot be formed as 'R' is missing.

Thus, 'AMOUNT' can be formed.

Hence, the correct answer is "Option 3".

Let's check each option:

1. INVERT → TWINE → Cannot be formed as 'W' is missing. 2. NITEWR → TWINE → Can be formed. 3. ENTIL → TWINE → Cannot be formed as 'W' is missing. 4. THINER → TWINE → Cannot be formed as 'W' is missing.

Thus, TWINE can be formed by using the letters of the word NITEWR.

Hence, the correct answer is "Option 2".

The position and positional values or English Alphabets are:

Given: ? : MX760 : : KD1130 : LF1320 : : AG340 : BI530

The logic followed here is:

Similarly,

Thus, LV570 is related to MX760.

Hence, the correct answer is "Option 4".

The position and positional values or English Alphabets are:

Given: GW100 : JR150 : : FB160 : ? : : PS200 : SN300

The logic followed here is:

100 + (100 ÷ 2) = 100 + 50 = 150

200 + (200 ÷ 2) = 200 + 100 = 300

Similarly,

160 + (160 ÷ 2) = 160 + 80 = 240

Thus, IW240 is related to FB160.

Hence, the correct answer is "Option 1".

The logic followed here is:

1. (SL23 : RY11)

2. (MB39 : HS27)

3. (EW26 : ?)

Thus, EW26 is coded as CK14.

Hence, the correct answer is Option 3;

The position and positional values or English Alphabets are:

Given: HF40, BZ81, VT163, PN327, ?

The logic followed here is:

Thus, JH655 is the correct alternative from the given ones that will complete the series.

Hence, the correct answer is "Option 3".

The position and positional values or English Alphabets are:

Given: AC21, IL68, QU209, YD632, HM1901

The logic followed here is:

Thus, HM1901 is the wrong term from the given alternatives.

Hence, the correct answer is "Option 2".

Shortcut Trick

The area of a square plot is always a perfect square if the side is a whole number.

Area = (Side)²

Check the options for a perfect square: 29 × 29 = 841.

Since 841 is the only perfect square among the options, it must be the area.

∴ The correct answer is 841 square yards.

Alternate Method

Given: Each dimension (side) of the square plot is a whole number.

Formula Used: Area of a square = (Side)²

⇒ Let the side of the square plot be s yards.

⇒ Area = s² square yards.

⇒ Since s is a whole number, the area must be a perfect square.

⇒ √861 ≈ 29.34 (Not a whole number)

⇒ √841 = 29 (A whole number)

⇒ √881 ≈ 29.68 (Not a whole number)

⇒ √891 ≈ 29.84 (Not a whole number)

⇒ Since 841 is the square of 29, it is the only possible area.

∴ The correct answer is 841 square yards.

Additional Information

Properties of Perfect Squares

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

Area and Perimeter of Square

The area is given by s² and the perimeter is 4 × s, where s is the side length.

Diagonal of a Square

The diagonal of a square with side s is s√2. Also, Area = (Diagonal²) ÷ 2.

Given:

Selling Price (SP) = Rs. 135

Loss = Rs. 15

Formula Used:

Cost Price (CP) = SP + Loss

Calculation:

⇒ CP = 135 + 15

⇒ CP = 150

∴ The correct answer is Rs. 150.

Given:

Principal (P) = ₹5000

Rate of Interest (R) = 8% p.a.

Time (T) = 1 year

Formula Used:

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

Calculation:

⇒ SI = (5000 × 8 × 1) ÷ 100

⇒ SI = 40000 ÷ 100

⇒ SI = ₹400

∴ The correct answer is ₹400.

Shortcut Trick

For any regular polygon with n sides, the exterior angle is calculated as 360° ÷ n.

For a regular decagon, n = 10.

Exterior Angle = 360° ÷ 10 = 36°.

Internal Angle = 180° − Exterior Angle = 180° − 36° = 144°.

∴ The correct answer is 144°.

Alternate Method

Given:

The window is in the shape of a regular decagon.

Number of sides (n) = 10.

Formula Used:

The sum of internal angles of a polygon with n sides = (n − 2) × 180°.

Each internal angle of a regular polygon = [(n − 2) × 180°] ÷ n.

Calculations:

⇒ Number of sides (n) = 10

⇒ Sum of all internal angles = (10 − 2) × 180°

⇒ Sum = 8 × 180° = 1440°

⇒ Value of each internal angle = 1440° ÷ 10

⇒ Internal angle = 144°

∴ The correct answer is 144°.

Additional Information

Sum of Exterior Angles

For any convex polygon, the sum of all exterior angles is always 360°, regardless of the number of sides.

Interior and Exterior Angle Relation

At any vertex of a polygon, the sum of the interior angle and the exterior angle is exactly 180° (Linear Pair).

Common Polygon Angles

Regular Pentagon (n=5): 108° | Regular Hexagon (n=6): 120° | Regular Octagon (n=8): 135°.

Given:

r = 0.4 cm

h = 1.5 cm

Formula Used:

Total Surface Area of cylinder = 2 × π × r × (r + h)

Calculation:

⇒ Total Surface Area = 2 × 3.14 × 0.4 × (0.4 + 1.5)

⇒ = 2 × 3.14 × 0.4 × 1.9

⇒ = 2 × 3.14 × 0.76

⇒ = 2 × 2.3864

⇒ = 4.77 cm²

∴ The correct answer is 4.77 cm².

Given:

Sides of triangle = 9, 10, 17

Height of prism = 25

Number of prisms = 20

Formula Used:

Area of triangle (Heron) = √[s × (s − a) × (s − b) × (s − c)]

Volume = Base area × height

Calculation:

⇒ s = (9 + 10 + 17) ÷ 2 = 18

⇒ Area = √[18 × 9 × 8 × 1]

⇒ Area = √1296 = 36

⇒ Volume of one prism = 36 × 25 = 900

⇒ Total volume = 900 × 20 = 18000

∴ The correct answer is 18000 cm³.

Given:

[(sinx − 2sin³x) ÷ (2cos³x − cosx)]² + 1

Formula used:

1 − 2sin²x = cos2x

2cos²x − 1 = cos2x

1 + tan²x = sec²x

Calculations:

⇒ sinx − 2sin³x = sinx(1 − 2sin²x) = sinx cos2x

⇒ 2cos³x − cosx = cosx(2cos²x − 1) = cosx cos2x

⇒ Fraction = (sinx cos2x) ÷ (cosx cos2x) = tanx

⇒ Final Expression = tan²x + 1 = sec²x

∴ The correct answer is sec²x.

Given:

x = 6cosA + 8sinA

y = 6sinA − 8cosA

Formula Used:

(a + b)² = a² + b² + 2ab

(a − b)² = a² + b² − 2ab

sin²A + cos²A = 1

Calculation:

⇒ x² = (6cosA + 8sinA)² = 36cos²A + 64sin²A + 96sinAcosA

⇒ y² = (6sinA − 8cosA)² = 36sin²A + 64cos²A − 96sinAcosA

⇒ x² + y² = 36(cos²A + sin²A) + 64(sin²A + cos²A)

⇒ x² + y² = 36 × 1 + 64 × 1

⇒ x² + y² = 100

∴ The correct answer is 100.

Given:

Radius of sphere = 6

Height of cylinder = 8

Formula Used:

Volume of sphere = (4 ÷ 3) × π × r³

Volume of cylinder = π × r² × h

Calculation:

⇒ (4 ÷ 3) × π × 6³ = π × R² × 8

⇒ (4 ÷ 3) × π × 216 = π × R² × 8

⇒ 288π = 8π × R²

⇒ 288 = 8 × R²

⇒ R² = 36

⇒ R = √36

⇒ R = 6

∴ The correct answer is 6 cm.

Given:

Parallel sides = 22 and 10

Non-parallel sides = 13

Formula Used:

Height from right triangle = √(side² − base²)

Area of trapezium = (1 ÷ 2) × (sum of parallel sides) × height

Calculation:

⇒ Difference of bases = 22 − 10 = 12

⇒ Half difference = 12 ÷ 2 = 6

⇒ Height = √(13² − 6²)

⇒ Height = √(169 − 36)

⇒ Height = √133

⇒ Area = (1 ÷ 2) × (22 + 10) × √133

⇒ Area = (1 ÷ 2) × 32 × √133

⇒ Area = 16√133

∴ The correct answer is height = √133 cm and area = 16√133 cm².

Given:

Radius of hemisphere = 12.6

CSA : TSA of cylinder = 1 : 2

Formula Used:

Volume of hemisphere = (2 ÷ 3) × π × r³

Volume of cylinder = π × R² × h

CSA of cylinder = 2 × π × R × h

TSA of cylinder = 2 × π × R × (h + R)

Calculation:

⇒ CSA ÷ TSA = (2πRh) ÷ (2πR(h + R))

⇒ = h ÷ (h + R) = 1 ÷ 2

⇒ 2h = h + R

⇒ h = R

⇒ Volume of hemisphere = (2 ÷ 3) × π × (12.6)³

⇒ Volume of cylinder = π × R² × R = π × R³

⇒ (2 ÷ 3) × π × (12.6)³ = π × R³

⇒ (2 ÷ 3) × (12.6)³ = R³

⇒ (12.6)³ = 2000.376

⇒ R³ = (2 ÷ 3) × 2000.376

⇒ R³ ≈ 1333.584

⇒ R ≈ 11

∴ The correct answer is 11.

Given:

Investment ratio = 5 : 3 : 2

Total time = 12

Change after = 6

Total profit = 90000

Formula Used:

Profit ∝ Investment × Time

Calculation:

⇒ A investment = 5

⇒ First 6 months = 5 × 6 = 30

⇒ Next 6 months = 10 × 6 = 60

⇒ Total A = 30 + 60 = 90

⇒ B investment = 3

⇒ First 6 months = 3 × 6 = 18

⇒ Next 6 months = 4.5 × 6 = 27

⇒ Total B = 18 + 27 = 45

⇒ C investment = 2

⇒ First 6 months = 2 × 6 = 12

⇒ Next 6 months = 2 × 6 = 12

⇒ Total C = 12 + 12 = 24

⇒ Ratio = 90 : 45 : 24

⇒ Ratio = 30 : 15 : 8

⇒ Total parts = 30 + 15 + 8 = 53

⇒ B share = 90000 × 15 ÷ 53

⇒ B share ≈ 25471.7

∴ The correct answer is 25472.

Given:

X + Y = 5000

$\frac{5}{9}$ of X = $\frac{3}{7}$ of Y

Formula Used:

Equate ratios and solve linear equations

Calculation:

⇒ $\frac{5}{9}$X = $\frac{3}{7}$Y

⇒ 5 × 7 × X = 3 × 9 × Y

⇒ 35X = 27Y

⇒ X : Y = 27 : 35

⇒ Total ratio = 27 + 35 = 62

⇒ Y = 5000 × 35 ÷ 62

⇒ Y ≈ 2822.58

∴ The correct answer is 2822.58.

Shortcut Trick

For the trigonometric identity sin A = cos B to be true, the angles must be complementary.

Therefore, A + B = 90°.

Substituting the given values: 2x + (x + 30°) = 90°.

3x + 30° = 90° ⇒ 3x = 60° ⇒ x = 20°.

∴ The correct answer is 20°.

Alternate Method

Given: sin(2x) = cos(x + 30°)

Formula Used: sin θ = cos(90° − θ)

Applying the transformation to the Left Hand Side (LHS):

⇒ cos(90° − 2x) = cos(x + 30°)

By comparing the angles on both sides:

⇒ 90° − 2x = x + 30°

⇒ 90° − 30° = x + 2x

⇒ 60° = 3x

⇒ x = 60° ÷ 3

⇒ x = 20°

∴ The correct answer is 20°.

Additional Information

Trigonometric Complementary Angles

Two angles are complementary if their sum is 90°. Standard relations include: sin θ = cos(90° − θ), tan θ = cot(90° − θ), and sec θ = cosec(90° − θ).

Reciprocal Identities

Standard reciprocal relations: cosec θ = 1 ÷ sin θ, sec θ = 1 ÷ cos θ, and cot θ = 1 ÷ tan θ.

Pythagorean Identities

Fundamental relations between functions: sin²θ + cos²θ = 1 and 1 + tan²θ = sec²θ.

Given:

LCM(A, B) = B

LCM(B, C) = C

Formula Used:

If LCM(a, b) = b then a divides b

LCM of multiple numbers is the greatest among them if each divides the next

Calculation:

⇒ From LCM(A, B) = B ⇒ A divides B

⇒ From LCM(B, C) = C ⇒ B divides C

⇒ Therefore A divides B and B divides C ⇒ A divides C

⇒ So C is the largest multiple covering A and B

⇒ LCM(A, B, C) = C

∴ The correct answer is C.

Given:

Time = 5

Amount = $\frac{7}{5}$ × Principal

Formula Used:

Simple Interest = Principal × Rate × Time ÷ 100

Amount = Principal + Simple Interest

Calculation:

⇒ Amount = Principal + SI = $\frac{7}{5}$ × Principal

⇒ SI = $\frac{7}{5}$P - P

⇒ SI = $\frac{2}{5}$P

⇒ SI = P × R × 5 ÷ 100

⇒ $\frac{2}{5}$P = P × R × 5 ÷ 100

⇒ $\frac{2}{5}$ = R × 5 ÷ 100

⇒ R × 5 = 40

⇒ R = 8

∴ The correct answer is 8%.

Given:

Capacities ratio = 2 : 3 : 5

P ratio (A : W) = 1 : 1

Q ratio (A : W) = 2 : 1

R ratio (A : W) = 3 : 1

Formula Used:

Quantity of component = Total × (ratio part ÷ total ratio)

Calculation:

⇒ Let capacities = 2, 3, 5

⇒ In P: Alcohol = 2 × 1 ÷ 2 = 1

⇒ In P: Water = 2 × 1 ÷ 2 = 1

⇒ In Q: Alcohol = 3 × 2 ÷ 3 = 2

⇒ In Q: Water = 3 × 1 ÷ 3 = 1

⇒ In R: Alcohol = 5 × 3 ÷ 4 = 15 ÷ 4

⇒ In R: Water = 5 × 1 ÷ 4 = 5 ÷ 4

⇒ Total Alcohol = 1 + 2 + 15 ÷ 4

⇒ Total Alcohol = 3 + 15 ÷ 4 = 27 ÷ 4

⇒ Total Water = 1 + 1 + 5 ÷ 4

⇒ Total Water = 2 + 5 ÷ 4 = 13 ÷ 4

⇒ Ratio = (27 ÷ 4) : (13 ÷ 4)

⇒ Ratio = 27 : 13

∴ The correct answer is 27 : 13.

Given:

A = 20% more than B

B = 25% more than C

Formula Used:

If X is a% more than Y ⇒ X = Y × (1 + a ÷ 100)

Percentage increase = (Difference ÷ Original) × 100

Calculation:

⇒ Let C = 100

⇒ B = 100 × (1 + 25 ÷ 100) = 100 × 1.25 = 125

⇒ A = 125 × (1 + 20 ÷ 100) = 125 × 1.20 = 150

⇒ Increase from C to A = 150 - 100 = 50

⇒ Percentage increase = 50 ÷ 100 × 100

⇒ Percentage increase = 50%

∴ The correct answer is 50%.

Given:

$\frac{4}{23}, \frac{8}{17}, \frac{3}{5}, \frac{5}{21}$

Formula Used:

Compare fractions by converting into decimal values

Calculation:

⇒ $\frac{4}{23}$ ≈ 0.174

⇒ $\frac{8}{17}$ ≈ 0.471

⇒ $\frac{3}{5}$ = 0.6

⇒ $\frac{5}{21}$ ≈ 0.238

⇒ Descending order: $\frac{3}{5}$ > $\frac{8}{17}$ > $\frac{5}{21}$ > $\frac{4}{23}$

∴ The correct answer is $\frac{3}{5}$ > $\frac{8}{17}$ > $\frac{5}{21}$ > $\frac{4}{23}$.

Given:

$0.\overline{56}$

Options: 0.51, 0.59, 0.61, 0.57

Formula Used:

Convert recurring decimal to fraction

Calculation:

⇒ Let x = $0.\overline{56}$

⇒ 100x = $56.\overline{56}$

⇒ 100x - x = 56

⇒ 99x = 56

⇒ x = $\frac{56}{99}$

⇒ $\frac{56}{99}$ ≈ 0.5656

⇒ 0.51 < 0.5656

⇒ 0.59 > 0.5656

⇒ 0.61 > 0.5656

⇒ 0.57 > 0.5656

∴ The correct answer is $0 . \overline{51}$.

Given:

$\frac{\sqrt[3]{64}+\sqrt[4]{256}}{\sqrt{81}}$

Formula Used:

$\sqrt[n]{a^n} = a$

Calculation:

⇒ $\frac{\sqrt[3]{64}+\sqrt[4]{256}}{\sqrt{81}} = \frac{4+4}{9} = \frac{8}{9}$

∴ The correct answer is $\frac{8}{9}$.

Given:

$\sqrt{a} + \sqrt{b} = 10$

$\sqrt{a} - \sqrt{b} = 4$

Formula Used:

$(x+y)^2 + (x-y)^2 = 2(x^2 + y^2)$

Calculation:

⇒ $(\sqrt{a} + \sqrt{b})^2 + (\sqrt{a} - \sqrt{b})^2 = 2(a + b)$

⇒ $10^2 + 4^2 = 2(a + b)$

⇒ $100 + 16 = 2(a + b)$

⇒ $116 = 2(a + b)$

⇒ $a + b = 58$

∴ The correct answer is $58$.

Shortcut Trick

Interest for 1 year = 5% of ₹12000 = ₹600

Total Simple Interest (SI) required = ₹15600 − ₹12000 = ₹3600

Time = Total Interest ÷ Interest per year

⇒ Time = 3600 ÷ 600 = 6 years

∴ The correct answer is 6 years.

Alternate Method

Given:

Principal (P) = ₹12000

Amount (A) = ₹15600

Rate (R) = 5% per annum

Formula Used:

Simple Interest (SI) = A − P

SI = (P × R × T) ÷ 100

Calculations:

⇒ SI = 15600 − 12000 = ₹3600

⇒ 3600 = (12000 × 5 × T) ÷ 100

⇒ 3600 = 120 × 5 × T

⇒ 3600 = 600 × T

⇒ T = 3600 ÷ 600

⇒ T = 6 years

∴ The correct answer is 6 years.

Additional Information

Direct Amount Formula

The total amount in simple interest can be directly calculated using A = P(1 + (R × T) ÷ 100).

Simple Interest vs Compound Interest

Simple Interest remains constant every year, whereas Compound Interest increases as interest is calculated on the previous year's interest.

Effective Rate of Interest

The total interest percentage over 'T' years at 'R' rate is simply (R × T)%. In this case, 5% × 6 = 30%.

Given:

Group A students = 10

Average of A = 20

Group B students = 20

Average of B = x

Combined average = 34

Formula Used:

Total sum = Number × Average

Combined average = (Sum of all values) ÷ Total number

Calculation:

⇒ Sum of A = 10 × 20 = 200

⇒ Sum of B = 20 × x

⇒ Total students = 10 + 20 = 30

⇒ 34 = (200 + 20x) ÷ 30

⇒ 34 × 30 = 200 + 20x

⇒ 1020 = 200 + 20x

⇒ 20x = 820

⇒ x = 820 ÷ 20 = 41

∴ The correct answer is 41.

Given:

Selling price (SP) = 140% of the value of discount

Marked price (MP) = ?% of the value of discount

Formula Used:

SP = 140% of discount = (140 ÷ 100) × Discount

MP = SP + Discount

MP = ?% of Discount

Calculation:

Let the value of Discount = D.

⇒ SP = (140 ÷ 100) × D = 1.4D

⇒ MP = SP + Discount = 1.4D + D = 2.4D

⇒ MP = 240% of Discount

∴ The correct answer is 240 percent.

The correct answer is Shiva.

Key Points

• The Nayanars were a group of 63 Tamil saints who lived during the 6th to 9th centuries CE. They were ardent devotees of Lord Shiva and contributed significantly to Shaivism in South India.
• The Nayanars composed devotional hymns in praise of Lord Shiva, which are collectively known as the Tirumurai. These hymns are considered sacred scriptures in Shaivism.
• They played a crucial role in the Bhakti Movement in Tamil Nadu, which emphasized personal devotion to God over ritualistic practices or caste-based hierarchies.
• Prominent Nayanars like Sambandar, Appar, and Sundarar are revered for their poetic contributions and unwavering devotion to Lord Shiva.
• The teachings and lives of the Nayanars were instrumental in spreading the principles of Shaivism and countering the rise of Jainism and Buddhism in South India during their time.

Additional Information

• Nayanars and the Bhakti Movement:
• The Bhakti Movement emerged as a reformist movement focusing on personal devotion to God. The Nayanars were among the earliest proponents of this movement in South India.
• They rejected caste-based discrimination and emphasized equality before God, promoting a more inclusive form of worship.
• Prominent Nayanar Saints:
• Sambandar: Known for his poetic hymns in Tamil, Sambandar was a child prodigy who composed devotional songs dedicated to Lord Shiva.
• Appar: He is known for converting many Jains to Shaivism through his teachings and hymns.
• Sundarar: His compositions reflect a personal and emotional connection with Lord Shiva, often referring to him as a friend or benefactor.
• Tirumurai:
• The devotional hymns composed by the Nayanars are compiled in a collection known as the Tirumurai.
• The Thevaram, a part of the Tirumurai, is sung in Shaivite temples even today.
• Shaivism:
• Shaivism is one of the major traditions within Hinduism that worships Lord Shiva as the Supreme Being.
• It is widely practiced in South India, and the contributions of the Nayanars have been significant in its propagation.

Important Points

• The Nayanars are often associated with the Alvars, who were Vaishnavite saints devoted to Lord Vishnu. Together, they represent the Shaivite and Vaishnavite traditions of the Bhakti Movement.
• The Nayanars opposed the dominance of Jainism and Buddhism during their era and re-established the prominence of Shaivism in Tamil Nadu.
• Their lives and teachings are chronicled in the Periya Puranam, a 12th-century Tamil text written by Sekkizhar.
• Their influence is still visible in South Indian culture, especially in temple architecture, rituals, and Tamil literature.

The correct answer is Article 148.

Key Points

• Article 148 of the Indian Constitution mentions the establishment of the Comptroller and Auditor-General (CAG) of India.
• The CAG is responsible for auditing all receipts and expenditures of the Government of India and the state governments, including bodies and authorities substantially financed by the government.
• The CAG is considered the guardian of the public purse and ensures accountability and transparency in the financial administration of the country.
• The CAG is appointed by the President of India and holds office for a term of 6 years or until attaining the age of 65 years, whichever is earlier.
• Article 148 ensures the independence of the CAG by providing safeguards such as fixed tenure, removal procedure similar to that of a Supreme Court judge, and salary charged on the Consolidated Fund of India.

Additional Information

• Role of the Comptroller and Auditor-General (CAG):
• The CAG audits and reports on the accounts of the Union and State governments to ensure they are in compliance with laws and regulations.
• It examines whether expenditures were made for the intended purposes and whether the government’s financial transactions were conducted efficiently.
• The reports of the CAG are submitted to the President of India or the Governor of a state, who then table them in the respective legislature.
• Constitutional Provisions:
• Articles 149-151 of the Indian Constitution further elaborate on the duties, powers, and responsibilities of the CAG.
• Article 149: Specifies the duties and powers of the CAG.
• Article 150: Provides that the accounts of the Union and the States shall be kept in the format prescribed by the President on the advice of the CAG.
• Article 151: Stipulates that the reports of the CAG on the accounts of the Union and the States shall be laid before the Parliament or the State Legislature.
• Independence of the CAG:
• The CAG is independent of the executive, and its authority is protected under the Constitution.
• Its salary and other conditions of service cannot be varied to its disadvantage after appointment.
• The CAG is removed from office in the same manner as a judge of the Supreme Court, which ensures its independence.
• Examples of Reports by CAG:
• The CAG has been instrumental in uncovering several financial irregularities, such as the 2G spectrum case and the coal allocation scam.
• Such reports lead to corrective measures and reforms in governance.

Important Points

• Comparison with Other Articles:
• Article 142: Grants the Supreme Court the power to pass any decree or order necessary to ensure complete justice.
• Article 144: Mandates all authorities, civil and judicial, in India to act in aid of the Supreme Court.
• Article 146: Deals with the conditions of service of officers and employees of the Supreme Court.
• None of these articles pertain to the Comptroller and Auditor-General of India, which is specifically covered under Article 148.
• International Counterparts:
• Countries such as the United Kingdom have similar institutions like the National Audit Office (NAO).
• The United States has the Government Accountability Office (GAO), which performs similar auditing functions.

The correct answer is Directive Principles of State Policy.

Key Points

• The Directive Principles of State Policy (DPSP) are outlined in Part IV of the Indian Constitution, spanning from Articles 36 to 51. These principles serve as guidelines for the state to ensure socio-economic reforms and to establish a just society.
• The DPSP aim to promote economic equality, reduce the disparity between the rich and the poor, and provide for the welfare of citizens by ensuring access to resources, healthcare, education, and employment.
• These principles are non-justiciable, meaning they cannot be enforced by courts. However, they act as a guiding framework for the government to formulate laws and policies.
• Key provisions under DPSP include ensuring adequate means of livelihood, equitable distribution of wealth, equal pay for equal work, protection of children and youth, free legal aid, and promotion of education and public health.
• Some examples of socio-economic reforms influenced by DPSP include the implementation of the Right to Education Act (2009) and the establishment of schemes like MGNREGA and National Food Security Act.

Additional Information

• Fundamental Rights:
• These are outlined in Part III of the Indian Constitution and guarantee civil liberties to individuals, such as the right to equality, freedom, and protection against exploitation.
• They are justiciable and can be enforced through courts.
• Examples include Article 14 (Right to Equality) and Article 21 (Right to Life and Personal Liberty).
• Fundamental Duties:
• Added by the 42nd Amendment Act, 1976, and listed under Article 51A, these duties are non-justiciable and act as moral obligations for citizens.
• Examples include respecting the Constitution, promoting harmony, and protecting the environment.
• Separation of Powers:
• This principle ensures that the legislative, executive, and judiciary function independently to maintain a system of checks and balances.
• It is not explicitly mentioned in the Constitution but is derived from its provisions to prevent abuse of power.
• Directive Principles of State Policy (DPSP):
• They are inspired by the Irish Constitution and aim to establish economic democracy.
• Some specific articles include:
• Article 39(b): Distribution of material resources to subserve the common good.
• Article 41: Right to work, education, and public assistance in cases of unemployment, old age, or sickness.
• Article 47: Duty of the state to raise the level of nutrition and standard of living.

Important Points

• Relationship Between DPSP and Fundamental Rights:
• While Fundamental Rights ensure individual freedoms, the Directive Principles focus on the collective welfare of society.
• In cases of conflict, courts have attempted to harmonize both. For instance, the Kesavananda Bharati Case (1973) established that DPSPs cannot override Fundamental Rights but play a crucial role in governance.
• Implementation Challenges:
• The non-justiciable nature of DPSP makes their enforcement dependent on the political will of the government.
• Resource constraints and regional disparities often hinder their effective implementation.

The correct answer is Brazil.

Key Points

• The 17th BRICS Summit was held in July 2025 in Brazil. Hence, option 4 is correct.
• BRICS is a grouping of major emerging economies consisting of:
• Brazil
• Russia
• India
• China
• South Africa
• The summit focused on issues related to:
• Global economic cooperation
• Trade and investment
• Climate change
• Multilateral reforms
• Global South cooperation
• Brazil hosted the summit as part of the rotational chairmanship system followed by BRICS nations.
• Option-wise Analysis:
• South Africa – Hosted the 15th BRICS Summit in 2023.
• Russia – Hosted the 16th BRICS Summit in 2024.
• India – Not the host of the 2025 summit.
• Brazil – Hosted the 17th BRICS Summit in 2025. Correct.
• Hence, the correct answer is Brazil.

Additional Information

• BRICS was originally formed as BRIC in 2006, and South Africa joined the group in 2010.
• The term “BRIC” was coined by economist Jim O’Neill of Goldman Sachs in 2001.
• BRICS countries together account for a significant share of the world’s:
• Population
• GDP
• Natural resources
• The New Development Bank (NDB), established by BRICS in 2014, is headquartered in Shanghai, China.
• BRICS aims to strengthen cooperation among emerging economies and promote a more balanced global order.

Important Points

• BRICS Summits are held annually under the rotating presidency of member nations.
• Questions related to international organizations, global summits, multilateral groupings, and current affairs are frequently asked in competitive examinations.

The correct answer is 1966.

Key Points

• The Asian Development Bank (ADB) was established on 19 December 1966, with the objective of fostering economic growth and cooperation in the Asia-Pacific region.
• The founding members of ADB include 31 countries, with the headquarters located in Mandaluyong, Philippines.
• ADB focuses on poverty reduction, sustainable development, and regional integration through financial support, technical assistance, and policy consultation.
• Its initial capital was USD 1 billion, and it has since grown significantly, with more than 68 members as of now, including both regional and non-regional members.
• Japan and the United States are the largest contributors to ADB’s resources and play a crucial role in its governance and operations.

Additional Information

• Functions of ADB:
• ADB provides loans, grants, and equity investments to its member countries for development projects in sectors like infrastructure, education, health, and agriculture.
• It also offers technical assistance to help member nations design, implement, and improve development projects.
• ADB promotes regional cooperation by supporting cross-border projects and encouraging trade and investment partnerships among member nations.
• Key Milestones:
• ADB’s first President was Takeo Fukuda from Japan.
• It initiated its first loan project in 1968, providing funds for agriculture development in Thailand.
• Over the years, ADB has evolved to address challenges such as climate change, disaster management, and urbanization.
• Membership Details:
• ADB currently has 68 members, with 49 regional members and 19 non-regional members.
• Prominent members include India, China, Japan, Australia, and the United States.
• Funding Mechanism:
• ADB raises funds through capital contributions from member countries and by issuing bonds in international financial markets.
• It also mobilizes resources from other financial institutions for co-financing development projects.
• Important Reports:
• ADB publishes the Asian Development Outlook, an annual report analyzing economic trends and prospects for its member countries.
• The Key Indicators for Asia and the Pacific report provides statistical data to support regional development efforts.