SSC CHSL 2025 Tier-1 (Held On: 21 Nov, 2025 Shift 1) (Previous Year Paper)

The correct answer is option 1.

Key Points

To answer this question, let's break down each sentence to identify the grammatically and contextually correct ones:

• 1. Injured were taken to the hospital.
• This sentence describes injured people being taken to the hospital.
• The sentence is erroneous because it is missing the article "the" before "injured".
• The correct sentence would be: "The injured were taken to the hospital."
• 2. The baby laughed on seeing itself in the mirror.
• This sentence describes a baby laughing upon seeing its reflection.
• This sentence is grammatically and contextually correct.
• 3. Whose book is this?
• This sentence is used to ask about the ownership of a book.
• This sentence is grammatically and contextually correct.
• 4. Shakespeare was the most prolific writer that time has ever seen.
• This sentence describes Shakespeare's prolific writing nature.
• This sentence is grammatically and contextually correct.

The correct answer is 'with'.

 

Key Points

• The preposition "with" is used to indicate compatibility or suitability.
• The phrase "compatible with" is a standard collocation used in English grammar.
• Options 1, 2, and 4 are incorrect as they do not fit the context of the sentence.

Therefore, the correct answer is Option 3.

 

Complete Sentence: "The solution is not compatible with older versions of the software."

 

Additional Information

• Option 1: "for" is incorrect because "compatible for" is not a valid phrase in English.
• Option 2: "to" is incorrect because "compatible to" is not a standard collocation.
• Option 4: "at" is incorrect as it does not fit the sentence context.

The correct answer is 'puts down'.

 

Key Points

• The phrasal verb "puts down" means to attribute or assign something to a particular cause.
• In the context of the sentence, "puts down" is appropriate because it implies the act of blaming or attributing her failures to bad luck.
• Options 2, 3, and 4 are incorrect because they do not fit the meaning or context of the sentence:
• Option 2 (turns out): refers to a result or outcome and is not relevant here.
• Option 3 (breaks into): refers to entering a place forcefully and does not fit the context.
• Option 4 (boils down): refers to simplifying or summarizing, which does not match the intended meaning.

Therefore, the correct answer is Option 1.

 

Complete Sentence: "She always puts down her failures to bad luck rather than taking ownership."

 

Additional Information

• Option 2: "turns out" is incorrect because it implies a result or discovery, which does not align with the idea of attributing failures to bad luck.
• Option 3: "breaks into" is incorrect as it refers to entering a place forcefully, unrelated to the sentence's context.
• Option 4: "boils down" is incorrect as it refers to simplifying or summarizing, which is not relevant here.

The correct answer is option 1.

Key Points

The correctly spelt word is 'Quarantine'.

• The word 'Quarantine' is a noun and verb.
• As a noun, it means 'a state, period, or place of isolation in which people or animals that have arrived from elsewhere or been exposed to infectious or contagious diseases are placed.' (संक्रमण के कारण अलगाव)
• For Example -
• During the pandemic, many people had to stay in quarantine for safety reasons.

Therefore, the correct spelling is 'Quarantine'.

Additional Information

Let's understand why the other options are incorrect:

• Quarentine - This is a misspelling of the word 'Quarantine'.
• Quaranteen - This is an incorrect spelling and does not represent a valid word.
• Quarintine - This is another misspelling of the word 'Quarantine'.

The correct answer is: Option 1.

Key Points

• The word "date" in the context of the question refers to a romantic meeting or social outing. (डेट / मुलाकात)
• Example: They enjoyed their first date at the coffee shop.
• The word "date" in Option 1 refers to a specific day or time when something is scheduled or occurs. (तिथि)
• Example: The expiry date on the food package is clearly printed.
• Hence, the correct answer contains a homonym of the word "date" as it has a different meaning in Option 1.

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: They agreed to go on a second date after their coffee meeting. (डेट / मुलाकात)
• Example: They decided to plan their next date at a park.
• Option 3: He invited her to a dinner date at his favorite restaurant. (डेट / मुलाकात)
• Example: Their dinner date was filled with laughter and good food.
• Option 4: The movie was a great choice for a first date. (डेट / मुलाकात)
• Example: Watching a romantic movie on their first date was a memorable experience.

The correct answer is: Option 3.

Key Points

• The word "Amplify" means to increase the volume, intensity, or extent of something; it refers to making something more pronounced or stronger. (विस्तारित करना, बढ़ाना)
• Example: The teacher used a microphone to amplify her voice during the lecture.
• "Reduce" is the antonym of amplify, meaning to make something smaller or less in amount, degree, or intensity. (कम करना)
• Example: The company decided to reduce its expenses to improve profitability.
• Hence, we can infer that the opposite of 'Amplify' is 'Reduce'.

Therefore, the correct answer is: Option 3.

Additional Information

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

• Expand (विस्तारित करना): To make something larger or more extensive.
• Example: The company plans to expand its operations to new markets next year.
• Magnify (बड़ा करना): To enlarge something or make it appear larger, especially through a lens or microscope.
• Example: The scientist used a magnifying glass to study the tiny insect.
• Increase (बढ़ाना): To become greater in size, quantity, or degree.
• Example: The government aims to increase the budget for education next year.

The correct answer is 'to eat'.

 

Key Points

• The verb phrase "to eat" is correct because it properly follows the verb "gave" to describe the purpose of the action.
• The inclusion of "it" in Option 2 is unnecessary and redundant, as "cake" is already mentioned in the sentence.
• Options 3 and 4 are grammatically incorrect, as they do not properly align with the structure of the sentence.

Therefore, the correct answer is Option 1.

 

Complete Sentence: "My mother gave us some cake to eat."

 

Additional Information

• Option 2: "to eat it" is incorrect because "it" is redundant when "cake" is already specified.
• Option 3: "eating it" is incorrect because it disrupts the intended meaning and grammatical structure of the sentence.
• Option 4: "eat it" is incorrect because it does not properly follow "gave us" in the sentence.

The correct answer is Option 2.

 

Key Points

• Indirect Speech: She said that she could go there the following morning if her mother did not want her to go for shopping.
• Key Conversions:
• "I can come here tomorrow morning" becomes "She could go there the following morning"
• Pronoun "I" is replaced by "she" as per the subject.
• Modal verb "can" changes to its past form "could" in reported speech.
• Adverb "here" is changed to "there" to indicate a shift in place.
• Adverb "tomorrow morning" is converted to "the following morning" to reflect the time change.
• "if my mother does not want me to go" becomes "if her mother did not want her to go"
• Pronoun "my" is changed to "her" to match the subject.
• Verb "does not want" is converted to "did not want" to maintain past tense in reported speech.
• Pronoun "me" is replaced by "her" as per the subject.
• Punctuation and Format:
• The reporting verb "said" is used without quotation marks in indirect speech.
• The sentence structure is adjusted to maintain proper grammar and flow in indirect speech.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "She said that she could go there the following morning if her mother did not want her to go for shopping."

 

Additional Information

• Option 1: "She said that she can go there the next morning if her mother did not want her to go for shopping."
• Incorrect because "can" is not changed to "could" in reported speech.
• Option 3: "She said that she could go there the following morning if her mother does not want her to go for shopping."
• Incorrect because "does not" is not changed to "did not" in reported speech.
• Option 4: "She said that she went there the following morning if her mother does not want her to go for shopping."
• Incorrect because "went" is an incorrect conversion of "can come" and alters the meaning of the sentence.

The correct answer is Option 2.

 

Key Points

• Indirect Speech: The students asked the teacher what was the proper way to write a report when there was no details mentioned in the question.
• Key Conversions:
• "What is the proper way" becomes "what was the proper way"
• The reporting verb changes from present to past tense.
• The verb "is" is converted to "was" to match the sequence of tense.
• "there is no details" becomes "there was no details"
• The present tense "is" is changed to past tense "was" to maintain tense consistency.
• Punctuation and Format:
• The question in direct speech is converted into a statement in indirect speech.
• The quotation marks are removed, and the sentence is restructured.
• The reporting verb "said" is changed to "asked" to reflect the interrogative nature of the original sentence.

Therefore, the correct answer is Option 2.

 

Correct Sentence: The students asked the teacher what was the proper way to write a report when there was no details mentioned in the question.

 

Additional Information

• Option 1: "The students asked the teacher what had been the proper way to write a report when there was no details mentioned in the question."
• Incorrect usage of "had been" as it changes the meaning unnecessarily to past perfect tense.
• Option 3: "The students asked the teacher what had to be the proper way to write a report when there was no details mentioned in the question."
• Incorrect usage of "had to be" as it implies obligation, which is not present in the original sentence.
• Option 4: "The students asked the teacher what was being the proper way to write a report when there was no details mentioned in the question."
• Incorrect structure: "was being" is grammatically incorrect in this context.

The correct answer is Option 2.

 

Key Points

• Active voice structure: The subject performs the action, while the object receives it.
• In the passive sentence, "It has been determined that the ancient artifact is authentic," the subject (experts) is not explicitly mentioned.
• To convert to active voice, reintroduce the subject (experts) as the doer of the action.
• The verb "has been determined" is changed to "have determined" to match the active voice structure.
• The object, "the ancient artifact is authentic," remains unchanged in the active voice.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "Experts have determined that the ancient artifact is authentic."

 

Additional Information

• Option 1: "The ancient artifact is authentic." – This is a statement, not a conversion to active voice.
• Option 3: "It was determined that the ancient artifact is authentic." – This is still in passive voice.
• Option 4: "The authenticity of the ancient artifact has been determined." – This is also in passive voice.

The correct answer is Option 2.

 

Key Points

• Indirect Speech: She exclaimed with disgust that the food tasted terrible.
• Key Conversions:
• "She exclaimed with disgust" becomes "Ugh!"
• The expression "Ugh!" conveys the disgust mentioned in the indirect speech.
• "the food tasted terrible" becomes "How terrible this food tastes!"
• The phrase is converted into a direct exclamation to match the tone and meaning.
• The verb tense is adjusted for direct speech.
• Punctuation and Format:
• Direct speech is enclosed in quotation marks.
• Starts with an exclamation "Ugh!" followed by a complete sentence expressing disgust.
• Maintains the tone and meaning of the original indirect speech.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "She said, "Ugh! How terrible this food tastes!"

 

Additional Information

• Option 1: "Alas! This food tastes terrible."
• The word "Alas" expresses sadness rather than disgust, altering the tone.
• Option 3: "Oh no! This food tastes terrible."
• The phrase "Oh no" conveys surprise or concern, which doesn't match the disgust in the original sentence.
• Option 4: "What terrible-tasting food!"
• Although it conveys disgust, the sentence structure is different and doesn't match the original sentence fully.

The correct answer is option 4.

Key Points

The correctly spelled word is 'maintenance'.

• Maintenance refers to the process of preserving a condition or situation, or the state of being preserved.
• In the given context, it implies regular upkeep or servicing of machinery to ensure smooth and efficient functioning.
• For Example: Regular maintenance of the air conditioning system will prevent unnecessary repairs.

Therefore, the correct answer is 'maintenance'.

Additional Information

Explanation of the incorrect options:

• Option 1 - 'maintainance': Incorrect spelling of the word.
• Option 2 - 'maintanence': Incorrect spelling of the word.
• Option 3 - 'maintanance': Incorrect spelling of the word.

The correct answer is Option 3.

 

Key Points

• Active voice structure: The subject performs the action, while in passive voice, the subject is acted upon.
• The sentence "Let no stone be left unturned in the search for the missing documents" is in the passive form.
• To convert to active voice: Use the imperative structure to directly instruct the action.
• The phrase "Let no stone be left unturned" becomes "Leave no stone unturned."
• This ensures the meaning remains the same while converting the sentence to the active voice.

Therefore, the correct answer is Option 3.

 

Correct Sentence: "Leave no stone unturned in the search for the missing documents."

 

Additional Information

• Option 1: "Don't leave a stone unturned in the search for the missing documents." – Incorrect structure with "Don't."
• Option 2: "No stone should be left unturned in the search for the missing documents." – Passive voice, not active.
• Option 4: "Leave every stone unturned in the search for the missing documents." – Changes the meaning of the sentence.

The correct answer is option 3.

Key Points

The misspelled word is 'Refridgerator'.

• The correct spelling would be 'Refrigerator'.
• The word 'Refrigerator' is a noun which means 'an appliance or compartment that is artificially kept cool and used to store food and drink'. (रेफ्रिजरेटर)
• For Example -
• He opened the refrigerator to grab a bottle of water.

Therefore, the correct answer is 'Refridgerator'.

Additional Information

Let's understand the meanings of the other correctly spelled words - 

• Bureaucracy - a system of government in which most of the important decisions are made by state officials rather than by elected representatives (नौकरशाही)
• Garrulous - excessively talkative, especially on trivial matters (वाचाल)
• Acquiesce - accept something reluctantly but without protest (मौन स्वीकृति देना)

The correct answer is option 2.

Key Points

The misspelled word is 'aquire'.

• The correct spelling is 'acquire'.
• The word 'acquire' is a verb which means 'to gain or obtain something, often through effort or experience'.
• For Example -
• He worked hard to acquire the skills necessary for his job.

Therefore, the correct answer would be 'aquire'.

Additional Information

Let's understand the meanings of the other relevant words in the context - 

• Hierarchy - a system in which people or things are arranged according to their importance or rank.
• Responsibilities - duties or tasks that one is required or expected to carry out.

The correct answer is Option 1.

 

Key Points

• Indirect Speech: My mother lovingly asked me if I was going to the party that night.
• Key Conversions:
• "if I was going" becomes "Are you going"
• Indirect question "if I was going" is converted to direct question "Are you going."
• Pronoun "I" is changed to "you" to match direct speech.
• Verb "was going" is changed to "are going" to match the present tense in direct questions.
• "that night" becomes "tonight"
• Time expression "that night" is converted to "tonight" to reflect the perspective of the speaker.
• Reporting verb:
• Indirect: "lovingly asked"
• Converted to: "asked" while maintaining the context.
• Punctuation and Format:
• Direct speech is enclosed in quotation marks.
• Starts with a capital letter "Are" and ends with a question mark "?".
• Reporting clause precedes the quoted speech, ending with a comma.

Therefore, the correct answer is Option 1.

 

Correct Sentence: "My mother asked me, ‘Are you going to the party tonight?’"

 

Additional Information

• Option 2: "My mother said to me, ‘Were you going to the party that night?’"
• Incorrect tense: "were you" changes the context to past instead of present.
• Option 3: "My mother said to me, Were you going to the party that night?"
• Does not include proper punctuation for direct speech (missing quotation marks).
• Option 4: "My mother asked, ‘you going to the party that night?’"
• Lacks the auxiliary verb "Are" to form a correct question.

The correct answer is Option 3.

 

Key Points

• Indirect Speech: The coach told the athletes that they had been training hard all season and deserved a break.
• Key Conversions:
• "they had been training hard" becomes "You have been training hard"
• Pronoun "they" is changed to "you" to match the direct address.
• Verb tense "had been training" is converted to "have been training" to fit the direct speech context.
• "deserved a break" remains unchanged.
• Maintains the same idea while fitting into the direct speech format.
• Reporting verb:
• Indirect: "told"
• Converted to: "told the athletes" to preserve the clarity of the speaker and audience in direct speech.
• Punctuation and Format:
• Direct speech is enclosed in quotation marks.
• Starts with a capital letter "You" and ends with a period ".".
• Reporting clause follows the quoted speech, starting with a lowercase letter after the comma.

Therefore, the correct answer is Option 3.

 

Correct Sentence: "“The coach said to the athletes, "You have been training hard all season and deserved a break."

 

Additional Information

• Option 1: "The coach said, ‘You were training hard all season and deserved a break.’"
• Incorrect tense: "were training" instead of "have been training" changes the meaning.
• Option 2: "The coach told the athletes, ‘You had been training hard all season and deserved a break.’"
• Incorrect tense: "had been training" does not match the implied present relevance of the speech.
• Option 4: "The coach told the athletes, ‘They had been training hard all season and deserved a break.’"
• Incorrect pronoun: "They" does not reflect direct speech addressing the athletes directly as "You."

The correct answer is Option 1.

 

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 government is to launch an extensive investigation into the alleged financial irregularities."
• To convert to passive voice: Place the object "an extensive investigation" at the beginning.
• Change the active verb form "is to launch" to "is to be launched" (future passive structure).
• Add the preposition "by" followed by the original subject "the government."

Therefore, the correct answer is Option 1.

 

Correct Sentence: "An extensive investigation is to be launched into the alleged financial irregularities by the government."

 

Additional Information

• Option 2: "The alleged financial irregularities are to be extensively investigated by the government." – Incorrect structure as it changes the focus of the sentence.
• Option 3: "An extensive investigation will be launched into the alleged financial irregularities by the government." – Incorrect tense (future simple instead of "is to be").
• Option 4: "It is intended by the government to launch an extensive investigation into the alleged financial irregularities." – Incorrect transformation, as it alters the original meaning.

The correct answer is Option 4 i.e 'If implemented effectively, the NEP could reshape India's educational landscape'.

 

Key Points

• The sentence "If implemented effectively, the NEP could reshape India's educational landscape" contains the modal verb "could" which is used to express possibility.
• Modal verbs such as would, could, may, and might are often used to indicate possibility, permission, or ability.

Therefore, the correct answer is- Option 4.

 

Additional Information

• Option 1: The sentence does not contain a modal verb.
• Option 2: The sentence does not contain a modal verb.
• Option 3: While "will" is a modal verb, it is expressing a definite future event rather than possibility.

The correct answer is Option 2 i.e 'Learning'.

 

Key Points

• A gerund is a verb form ending in "-ing" that functions as a noun.
• In the passage, the word "learning" is used as a noun, making it a gerund.

Therefore, the correct answer is- Option 2.

 

Additional Information

• Option 1: "Reshape" is a verb and not a gerund.
• Option 3: "Emphasis" is a noun and not a gerund.
• Option 4: "Replace" is a verb and not a gerund.

The correct answer is: Option 3 i.e. Considering all parts as interconnected and complete.

Key Points

• The word "holistic" means considering the entire system, including all parts, rather than focusing on individual components. It involves an approach that takes into account the whole picture and sees the interconnections between various elements. (समग्र)
• Example: A holistic approach to education involves integrating various subjects and considering students' overall well-being and development.
• "Limited to academic learning only" is not correct as it refers to a narrow focus solely on academic aspects without considering other factors. (केवल शैक्षणिक शिक्षण तक सीमित)
• Example: The curriculum that is limited to academic learning only may not address students' social and emotional needs.
• "Related to health and medicine" is not correct as it refers to something specifically connected to these fields. (स्वास्थ्य और चिकित्सा से संबंधित)
• Example: Holistic medicine aims to treat the whole person, including physical, mental, and emotional aspects.
• "Focused only on one subject" is not correct as it implies a narrow focus on a single discipline. (केवल एक विषय पर ध्यान केंद्रित)
• Example: A curriculum focused only on one subject may neglect the importance of cross-disciplinary learning.

Therefore, the correct answer is: Option 3 i.e. Considering all parts as interconnected and complete.

Additional Information

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

• Related to health and medicine (स्वास्थ्य और चिकित्सा से संबंधित): Connected specifically to healthcare fields.
• Example: The conference focused on topics related to health and medicine, including recent advancements in treatments.
• Limited to academic learning only (केवल शैक्षणिक शिक्षण तक सीमित): Confined solely to academic aspects.
• Example: The traditional education system was limited to academic learning only, often overlooking practical skills.
• Focused only on one subject (केवल एक विषय पर ध्यान केंद्रित): Paying attention solely to a single discipline.
• Example: A research project that is focused only on one subject may miss interdisciplinary insights.

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

Key Points

• The word "flexible" means capable of bending easily without breaking, or being adaptable and willing to change. (लचीला)
• Example: The flexible schedule allows employees to work from home when necessary.
• "Rigid" is an antonym for flexible as it means not able to be bent or easily changed; stiff and unyielding. (कठोर)
• Example: The rigid rules made it difficult for employees to take leave when needed.
• "Adjustable" is not correct as it means capable of being changed or adapted. It is close in meaning to flexible. (समायोज्य)
• Example: The chair is adjustable to suit people of different heights.
• "Easy" is not correct as it means not difficult. It is not directly related as an opposite of flexible. (आसान)
• Example: The task was easy to complete.
• "Clear" is not correct as it means easy to understand or free from ambiguity. (स्पष्ट)
• Example: The instructions were clear and easy to follow.

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

Additional Information

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

• Adjustable (समायोज्य): Capable of being changed.
• Example: The adjustable straps on the bag make it convenient for people of different sizes.
• Easy (आसान): Not difficult.
• Example: The new software is easy to use even for beginners.
• Clear (स्पष्ट): Easy to understand.
• Example: The teacher's explanation was clear and concise.

The correct answer is Option 3 i.e 'To encourage practical and creative learning'.

 

Key Points

• The passage states that the NEP promotes vocational education, digital literacy, and interdisciplinary studies, and aims to reduce rote learning and exams-centric approaches by encouraging practical knowledge and creativity.
• The emphasis is on fostering practical and creative learning rather than rote memorization.

Therefore, the correct answer is- Option 3.

 

Additional Information

• Option 1: The passage emphasizes the use of mother tongue or regional language at the primary level, not the removal of regional languages from schools.
• Option 2: The NEP aims to reduce rote learning, not increase it.
• Option 4: The passage does not suggest focusing only on English; it discusses the emphasis on mother tongue or regional language at the primary level.

The correct answer is 'mockery'.

 

Key Points

• The word "sarcasm" refers to a form of mockery or ironic remark often intended to ridicule or criticize someone.
• Among the given options, the word "mockery" most closely aligns with the meaning of sarcasm.
• Options 1, 3, and 4 are incorrect because they do not convey the same meaning as sarcasm.

Therefore, the correct answer is Option 2.

 

Complete Sentence: "The stranger's eyes sparkled with a mixture of challenge and mockery."

 

Additional Information

• Option 1: "Kindness" is incorrect because sarcasm is not related to kindness.
• Option 3: "Encouragement" is incorrect because sarcasm does not imply encouragement.
• Option 4: "Compliment" is incorrect because sarcasm is often used to mock rather than compliment.

The correct answer is: Option 2: Poise.

Key Points

• The word "Poise" refers to graceful and balanced behavior or a state of composure, particularly in stressful situations. (संतुलन, आत्मसंयम)
• Example: Despite the chaos around her, she managed to maintain her poise and address the audience confidently.
• It reflects a sense of elegance and a calm demeanor, often associated with confidence and control.
• Hence, the word 'Poise' perfectly matches the definition of graceful and balanced behavior.

Therefore, the correct answer is: Option 2: Poise.

Additional Information

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

• Clumsy (असावधान/भद्दा): Lacking grace or skill in movement or action.
• Example: He was clumsy and accidentally knocked over the vase.
• Grit (धैर्य): Courage and determination in the face of challenges.
• Example: Her grit and hard work helped her achieve success against all odds.
• Frenzy (उन्माद): A state of uncontrolled excitement or wild behavior.
• Example: The fans went into a frenzy when the actor arrived at the event.

Given: You're giving a presentation, and a few students in the back are yawning, looking at the ceiling, and occasionally checking their phones.

Qualities Projected in this situation: Observation skills, adaptability and Audience engagement. 

Hence, "Option 2" is the correct answer

Key Points

Checklist for attempting SRT questions:

1. Read the question and options carefully.

2. Look for options that are realistic, optimistic, and reflect officer-like qualities.

3. Do not skip any situation.

4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.

5. React quickly and be logical

Additional Information

Officer qualities:

Given:

Length of tunnel = 200 m

Length of train = 100 m

Time taken = 10 s

Formula used:

Speed = Distance ÷ Time

Calculations:

Total distance covered

⇒ Length of train + Length of tunnel

⇒ 100 + 200

⇒ 300 m

Speed

⇒ 300 ÷ 10

⇒ 30 m/s

∴ Speed of the train = 30 m/s.

According to the question:

P's rank from the left → 7th

Q's rank from the right → 12th

After interchange, P's rank from the left → 22nd

Total number of people = P's rank from the left + After interchange, P's rank from the left - 1

Total number of people = 12 + 22 - 1 → 33

Hence, "Option 3" is the correct answer.

According to the question:

A's rank from the left → 12th

B's rank from the right → 15th

Number of students between A and B → 7

The maximum number of students in the row → A's rank from the left + B's rank from the right + The maximum number of students in the row

→ 12 + 15 + 7 = 34​

Hence, the correct answer is "Option 3"

Given:

Total students = 30

Sneha position from left = 12

Priya position from right = 15

So, the students are between Sneha and Priya  = Total students - ( Position of Sneha + Position of Priya )

= 30 − ( 12 + 15 )

= 30 − 27 

= 3

∴ Number of students between Sneha and Priya = 3.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

(I) All planets are galaxies → Follow (As all planets are stars and all stars are galaxies. As whole planets comes in stars which whole comes in galaxies, therefore it is true.)

(II) All galaxies are planets → Does not follow (As all planets are stars and all stars are galaxies. So it is possible but not definite.)

∴ Here, Only conclusion I follows.​

Hence, the correct answer is "Option 1"

Given Statement:

The government has announced a new policy to reduce carbon emissions by 50% in the next 10 years.

Check the Inferences:

I. The government is taking steps to combat climate change.

Reducing carbon emissions is a major action to fight climate change.

⇒ This inference follows. ✔

II. The new policy will have no impact on the environment.

The statement only says emissions will be reduced, which normally affects the environment positively.

⇒ Saying no impact is not supported.

⇒ This inference does not follow. ✘

III. The government is not interested in reducing carbon emissions.

The statement clearly says the government wants to reduce emissions by 50%.

⇒ This is the opposite of the statement.

⇒ This inference does not follow. ✘

∴ Only Inference I follows.

Logic used here:

Stages of plant growth

Seed → initial stage

Sprout → seed begins to grow

Sapling → young plant

Next stage → Tree (fully grown plant)

∴ The next word is Tree.

Odometer : Distance :: ? : Humidity

Instrument : What it measures

Odometer → measures Distance

Similarly, the instrument that measures Humidity is → Hygrometer

Hence Hygrometer : Humidity

∴ The correct answer is Hygrometer.

The logic followed here is:

Logic: The second word is what the first word measures.

Here,

Ammeter : Electric current → Ammeter measures Electric current.

Similarly,

Spectrophotometer : Light Intensity → Spectrophotometer measures Light Intensity.

Hence, the correct answer is "Option 1 ".

The logic followed here is.

For PEN : QGQ

For INK : ?

The resulting letters are JPN.

Hence, the correct answer is "Option 1".

The logic followed here is: (Fruits that belong to the stone fruit / drupe family)

Apple → Has a core with seeds, belongs to pome fruit family

Nectarine → Has a hard stone/pit inside, belongs to stone fruit family

Apricot → Has a hard stone/pit inside, belongs to stone fruit family

Cherry → Has a hard stone/pit inside, belongs to stone fruit family

Three (Nectarine, Apricot, Cherry) are all stone fruits with a hard pit inside, while Apple is a pome fruit with seeds in a core.

Thus, Apple is different from the others.

Hence, the correct answer is " Option 1 ".

The logic followed here is :

•  TOTAL : YSWCM 

Similarly,

•  MINUS :?

Thus, the term at the place of ? will be " RMQWT ".

Hence, the correct answer is " Option 4 "

The logic followed here is :

Numerators follow the pattern of odd numbers squared → 1², 3², 5², 7², 9²

Missing numerator = 5² = 25

Thus, the missing number in the series is " 25/2 "

Hence, the correct answer is "Option 2"

The logic followed here is :

Numerators follow the pattern of consecutive numbers cubed → 3³, 4³, 5³, 6³, 7³

Missing numerator = 7³ = 343

Thus, the missing term from the given series is " 343/2 ".

Hence, the correct answer is "Option 4".

The correct order of words as they would appear in the English dictionary is:

3. Wabash

5. Wackily

2. Wagged

4. Waggon

1. Wagnor

The correct order is '3, 5, 2, 4, 1'.

Hence, the correct answer is "Option 4 ".

Given: Anil is 18th from the left end and 20th from the right end.

**Formula used :**Total = Left rank + Right rank − 1

⇒ 18 + 20 − 1 = 37

So, the total number of students in the row is 37.

Hence, the correct answer is "Option 1".

Given: Total boys = 25, Rakesh is 10th from the top.

Formula used : Position from bottom = Total − Rank from top + 1

⇒ 25 − 10 + 1 = 16

So, Rakesh's position from the bottom is 16th.

Hence, the correct answer is "Option 2".

Given: Sam's rank from top = 9th, Sam's rank from bottom  

Formula used : Total students = Rank from top + Rank from bottom − 1 

                         

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⇒ Total students = 9 + 38 − 1

⇒ Total students = 46

So, there are 46 students in the class.

Hence, The correct answer is " Option 2 "

Given series: P, H, D, B, ?

The logic followed here is:

16 ÷ 2 = 8 ÷ 2 = 4 ÷ 2 = 2 ÷ 2 = 1

Position 1 = A

Thus, the missing term in the series is A

Hence, the correct answer is "Option 1"

Given Reference: Bengaluru: 15th Aug.ust, 2025

Compare each option with the given Reference:

So, the statement that exactly matches the Given Reference is option (1).

Hence, the correct answer is "Option (1)".

Given: You're a judge and the accused is proven guilty but also mentally unstable. 

Let's check all the options:

(1) Maximum sentence ⇒ It is not appropriate (  Ignores the mental instability completely, punishment without proper evaluation is unjust. )

(2) Immediate release ⇒  It is not appropriate (  Accused is proven guilty, releasing immediately ignores the crime committed. )

(3) Refer to psychiatric evaluation before sentencing ⇒ It is the most appropriate verdict. (  Balances both facts — guilty verdict AND mental instability. Law requires mental state to be considered before sentencing )

(4) Ignore mental state ⇒ It is not appropriate. ( Mental instability is a legally relevant factor, ignoring it is against judicial principles )

Hence, the correct answer is "Option 3"

Given: A government bans single-use plastic, claiming it will reduce ocean pollution.

Let's check all the options:

(1) Most plastic waste in oceans comes from fishing nets and industrial waste ⇒ It does not support the decision ( This weakens the decision as it shifts blame away from single-use plastic.)

(2) Citizens are unaware of recycling methods ⇒It does not support the decision. (  This is irrelevant to the ban on single-use plastic )

(3) A majority of coastal waste is composed of single-use plastic items ⇒ It best supports the decision. (  Directly proves that banning single-use plastic will reduce ocean pollution. )

(4) Plastic alternatives are more expensive and less durable ⇒ It does not support the decision. (  This weakens the decision as it shows the ban may not be practical.)

Hence, the correct answer is "Option 3"

Given word: IDENTIFICATION

By checking all the options:

Available letters: I, D, E, N, T, I, F, I, C, A, T, I, O, N

(1) CONFIDENT ⇒ It can be formed 

(2) DICTATION ⇒ It can be formed. 

(3) INACTION ⇒  It can be formed.

So, All the words can be formed using the letters only once.

Hence, the correct answer is " Option 4 ".

Given: 6 persons.

F is not at the right end. D is not at any end.

From clues, E is immediate left of B, and C is immediate Neighbour of both A and E 

Remaining D and F go to the left 

So, 2nd to the right of F = A

So, the person sitting second to the right of F is 'A'.

Hence, the correct answer is "Option 3".

Given:

Option 1: 1/4

Option 2: 1/17

Option 3: 1/10

Option 4: 1/8

Formula Used:

A fraction results in a non-terminating repeating decimal if its denominator (in simplest form) has prime factors other than 2 or 5.

Calculation:

⇒ For 1/4: Denominator = 4 = 2² (prime factor is 2 only, so terminates).

⇒ For 1/17: Denominator = 17 (prime number other than 2 or 5, so non-terminating repeating).

⇒ For 1/10: Denominator = 10 = 2 × 5 (prime factors are 2 and 5, so terminates).

⇒ For 1/8: Denominator = 8 = 2³ (prime factor is 2 only, so terminates).

∴ The correct answer is Option 2.

Shortcut Trick

Profit per dozen = (Selling Price per piece × 12) − Cost Price per dozen

⇒ Profit per dozen = (110 × 12) − 1200 = 1320 − 1200 = ₹120

Total items in dozens = Total Profit ÷ Profit per dozen = 360 ÷ 120 = 3 dozens

Total number of calculators = 3 × 12 = 36

∴ The correct answer is 36 calculators.

Alternate Method

Given:

Cost Price (CP) of 1 dozen (12 calculators) = ₹1,200

Selling Price (SP) of 1 calculator = ₹110

Total Profit = ₹360

Formula Used:

1. Profit per unit = Selling Price per unit − Cost Price per unit
2. Number of units = Total Profit ÷ Profit per unit

Calculations:

⇒ Cost Price (CP) of 1 calculator = 1200 ÷ 12 = ₹100

⇒ Selling Price (SP) of 1 calculator = ₹110

⇒ Profit on 1 calculator = 110 − 100 = ₹10

⇒ Number of calculators bought = 360 ÷ 10

⇒ Number of calculators = 36

∴ The correct answer is 36 calculators.

Additional Information

Profit Percentage Formula

Profit % = (Profit ÷ Cost Price) × 100. In this case, Profit % = (10 ÷ 100) × 100 = 10%.

Selling Price Calculation

SP = CP × (100 + Profit %) ÷ 100. This is used to find the Selling Price when CP and profit percentage are known.

Unitary Method in Profit and Loss

Always convert given quantities (like dozens, gross, or score) into single units to simplify the calculation of profit or loss per item.

Shortcut Trick

Volume of sphere = Volume of water displaced in the cylindrical container.

(4/3) × r³ = R² × h (Since π cancels out from both sides)

(4/3) × r³ = 10² × 1.5

r³ = (150 × 3) ÷ 4 = 112.5

r = √³(112.5) ≈ 4.8 cm

∴ The correct answer is 4.8 cm.

Alternate Method

Given:

Diameter of the cylindrical container = 20 cm

Rise in the water level (h) = 1.5 cm

Formula Used:

Volume of Cylinder = πR²h

Volume of Sphere = (4/3)πr³

Calculations:

⇒ Radius of cylinder (R) = 20 ÷ 2 = 10 cm

⇒ Volume of water raised = Volume of cylinder with height 1.5 cm

⇒ Volume of water raised = π × (10)² × 1.5

⇒ Volume of water raised = 150π cm³

⇒ According to Archimedes' Principle, Volume of sphere = Volume of displaced water

⇒ (4/3) × π × r³ = 150π

⇒ 4 × r³ = 150 × 3

⇒ 4 × r³ = 450

⇒ r³ = 450 ÷ 4 = 112.5

⇒ r = √³(112.5)

⇒ r ≈ 4.827 cm

∴ The correct answer is 4.8 cm.

Additional Information

Archimedes' Principle

When an object is fully or partially submerged in a fluid, the volume of the fluid displaced is equal to the volume of the submerged part of the object.

Volume of a Sphere

The volume (V) of a sphere with radius (r) is given by the formula V = (4/3)πr³. The surface area is 4πr².

Volume of a Cylinder

The volume (V) of a cylinder with base radius (R) and height (h) is V = πR²h. The curved surface area is 2πRh.

Given:

Marked price of cupboard = ₹3,200

Marked price is 25% above cost price.

Discount on marked price = 10%

Formula Used:

Cost price = Marked price ÷ (1 + Markup percentage)

Selling price = Marked price × (1 - Discount percentage)

Profit percentage = [(Selling price - Cost price) ÷ Cost price] × 100

Calculation:

⇒ Cost price = ₹3,200 ÷ (1 + 25/100)

⇒ Cost price = ₹3,200 ÷ 1.25

⇒ Cost price = ₹2,560

⇒ Selling price = ₹3,200 × (1 - 10/100)

⇒ Selling price = ₹3,200 × 0.9

⇒ Selling price = ₹2,880

⇒ Profit percentage = [(₹2,880 - ₹2,560) ÷ ₹2,560] × 100

⇒ Profit percentage = [₹320 ÷ ₹2,560] × 100

⇒ Profit percentage = 12.5%

∴ The correct answer is 12.5%.

Given:

Average age of 30 students = 18 years

Total number of students initially = 30

Number of students who left = 5

Number of students who joined = 5

New average age = 17.2 years

Average age of 5 students who left = 20.4 years

Formula Used:

Total age = Average age × Number of students

Total age of new group = Total age of remaining students + Total age of new students

Calculation:

⇒ Total age of initial 30 students = 18 × 30 = 540 years

⇒ Total age of 5 students who left = 20.4 × 5 = 102 years

⇒ Total age of remaining 25 students = 540 − 102 = 438 years

⇒ Total age of new group = 17.2 × 30 = 516 years

⇒ Total age of 5 students who joined = 516 − 438 = 78 years

⇒ Average age of 5 students who joined = 78 ÷ 5 = 15.6 years

∴ The correct answer is 15.6 years.

Given:

Defect rate₁ = 1.8%

Defect rate₂ = 2.4%

Defect rate₃ = 1.6%

Total defective units (all 4) = 4.12

Defective units of 4th machine = 0.92

Total production of each machine = same

Formula Used:

Defective units = Production × Defect% ÷ 100

Total defective = Sum of individual defectives

Calculation:

⇒ Defective units from first three = 4.12 − 0.92

⇒ Defective units from first three = 3.20

⇒ Let production of each machine = P

⇒ P × (1.8 + 2.4 + 1.6) ÷ 100 = 3.20

⇒ P × 5.8 ÷ 100 = 3.20

⇒ P = 3.20 × 100 ÷ 5.8

⇒ P = 320 ÷ 5.8

⇒ P = 55.1724

⇒ Defect% of 4th = 0.92 × 100 ÷ 55.1724

⇒ Defect% of 4th ≈ 1.67%

∴ The correct answer is approximately 1.67%.

Shortcut Trick

Sum of averages of pairs containing the target variable (Test 2) minus the average of the pair without it.

Score in Test 2 = (Avg of 1 & 2) + (Avg of 2 & 3) − (Avg of 1 & 3)

Score in Test 2 = 82.6 + 84.2 − 80.4 = 166.8 − 80.4 = 86.4

∴ The correct answer is 86.4.

Alternate Method

Given:

Average of Test 1 (T₁) and Test 2 (T₂) = 82.6

Average of Test 2 (T₂) and Test 3 (T₃) = 84.2

Average of Test 1 (T₁) and Test 3 (T₃) = 80.4

Formula Used:

Sum = Average × Number of observations

Calculations:

⇒ T₁ + T₂ = 82.6 × 2 = 165.2 — (Eq. 1)

⇒ T₂ + T₃ = 84.2 × 2 = 168.4 — (Eq. 2)

⇒ T₁ + T₃ = 80.4 × 2 = 160.8 — (Eq. 3)

⇒ Adding all equations: 2(T₁ + T₂ + T₃) = 165.2 + 168.4 + 160.8 = 494.4

⇒ T₁ + T₂ + T₃ = 494.4 ÷ 2 = 247.2

⇒ T₂ = (T₁ + T₂ + T₃) − (T₁ + T₃)

⇒ T₂ = 247.2 − 160.8 = 86.4

∴ The correct answer is 86.4.

Additional Information

Cyclic Average Property

In a system of three variables where averages of pairs (A,B), (B,C), and (C,A) are given as x, y, and z, the individual values are A = x+z−y, B = x+y−z, and C = y+z−x.

Combined Average

The average of all three items together is simply the average of the three pairwise averages: (82.6 + 84.2 + 80.4) ÷ 3 = 82.4.

Weighted Average

If the number of items in each group is different, use the formula: Average_total = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Given:

A's investment = ₹20,000

B's investment = ₹30,000

C's investment = ₹50,000

Total profit = ₹50,000

Formula Used:

Profit share ratio = Investment of A : Investment of B : Investment of C

Individual share of profit = (Individual ratio × Total profit) ÷ Total ratio

Calculation:

⇒ Profit share ratio = 20,000 : 30,000 : 50,000

⇒ Profit share ratio = 2 : 3 : 5

⇒ Total ratio = 2 + 3 + 5 = 10

⇒ A's share of profit = (2 × 50,000) ÷ 10

⇒ A's share of profit = 100,000 ÷ 10

⇒ A's share of profit = ₹10,000

∴ The correct answer is ₹10,000.

Given:

First day height = 1.2 cm

Daily increase = 0.3 cm

Day number = 10

Formula Used:

n^th term of AP = a + (n − 1)d

Calculation:

⇒ a = 1.2

⇒ d = 0.3

⇒ n = 10

⇒ Height on 10th day = 1.2 + (10 − 1) × 0.3

⇒ Height on 10th day = 1.2 + 9 × 0.3

⇒ Height on 10th day = 1.2 + 2.7

⇒ Height on 10th day = 3.9 cm

∴ The correct answer is 3.9 cm.

Given:

Sides = 16, 30, 34

Formula Used:

If a² + b² = c², triangle is right angled

Radius of circumcircle of right triangle = Hypotenuse ÷ 2

Calculation:

⇒ 16² + 30² = 256 + 900 = 1156

⇒ 34² = 1156

⇒ Triangle is right angled

⇒ Radius = 34 ÷ 2

⇒ Radius = 17

∴ The correct answer is 17 units.

Given:

Amount after 5 years = 180% of Principal

Time₁ = 5 years

Principal₂ = 2500

Time₂ = 2 years

Formula Used:

Amount = Principal × (1 + r × t ÷ 100)

Simple Interest = Principal × r × t ÷ 100

Calculation:

⇒ 1 + r × 5 ÷ 100 = 180 ÷ 100

⇒ 1 + 5r ÷ 100 = 1.8

⇒ 5r ÷ 100 = 0.8

⇒ 5r = 80

⇒ r = 16%

⇒ Interest = 2500 × 16 × 2 ÷ 100

⇒ Interest = 2500 × 32 ÷ 100

⇒ Interest = 800

∴ The correct answer is 800.

Given:

80% of total money distributed

Ratio = 3 : 5

Rate₁ = 9%

Rate₂ = 6%

Time = 6 years

Difference in interest = 2592

Formula Used:

Simple Interest = Principal × Rate × Time ÷ 100

Percentage method (Assume total = 100)

Calculation:

⇒ Let total money = 100

⇒ Distributed amount = 80

⇒ Kavya = 3 ÷ 8 × 80 = 30

⇒ Aryan = 5 ÷ 8 × 80 = 50

⇒ Interest of Kavya = 30 × 9 × 6 ÷ 100 = 16.2

⇒ Interest of Aryan = 50 × 6 × 6 ÷ 100 = 18

⇒ Difference = 18 − 16.2 = 1.8

⇒ 1.8 corresponds to 2592

⇒ 100 corresponds to 2592 ÷ 1.8 × 100

⇒ Total money = 144000

∴ The correct answer is 144000.

Given:

tanθ = 5 ÷ 12

Length of ladder = 13 m

Formula Used:

tanθ = Perpendicular ÷ Base

Hypotenuse² = Perpendicular² + Base²

Calculation:

⇒ Perpendicular : Base = 5 : 12

⇒ Hypotenuse = √(5² + 12²)

⇒ Hypotenuse = √(25 + 144)

⇒ Hypotenuse = √169 = 13

⇒ Scale factor = 13 ÷ 13 = 1

⇒ Height = 5 × 1 = 5 m

∴ The correct answer is 5 m.

Given:

Principal₁ = 6400

Amount₁ after 8 years = 8100

Time₁ = 8 years

Principal₂ = 2240

Time₂ = 4 years

Formula Used:

Amount = Principal × (1 + r)ⁿ

Calculation:

⇒ 8100 = 6400 × (1 + r)⁸

⇒ (1 + r)⁸ = 8100 ÷ 6400

⇒ (1 + r)⁸ = 81 ÷ 64

⇒ (1 + r) = (81 ÷ 64)^{1 ÷ 8}

⇒ 81 = 3⁴ and 64 = 2⁶

⇒ (81 ÷ 64)^{1 ÷ 8} = (3⁴ ÷ 2⁶)^{1 ÷ 8}

⇒ (1 + r) = 3^{1 ÷ 2} ÷ 2^{3 ÷ 4}

⇒ (1 + r)⁴ = (81 ÷ 64)^{1 ÷ 2}

⇒ (1 + r)⁴ = 9 ÷ 8

⇒ Required amount = 2240 × 9 ÷ 8

⇒ Required amount = 2240 × 1.125

⇒ Required amount = 2520

∴ The correct answer is 2520.

Given:

Ratio of son and mother's age = 1:3

After 5 years, ratio of their age = 3:7

Formula Used:

Present age = Ratio constant × Ratio value

Future age = Present age + 5

Calculation:

Let the present ages of son and mother be 1x and 3x respectively.

After 5 years:

⇒ (1x + 5) ÷ (3x + 5) = 3 ÷ 7

Cross multiplying:

⇒ 7(1x + 5) = 3(3x + 5)

⇒ 7x + 35 = 9x + 15

⇒ 35 - 15 = 9x - 7x

⇒ 20 = 2x

⇒ x = 10

Son's age = 1x = 10

Mother's age = 3x = 30

∴ The correct answer is 10, 30.

Given:

∠ACB = 75°

Angle between tangent at A and chord AC = 40°

Formula Used:

Angle between tangent and chord = Angle in opposite arc

Angle at center = 2 × Angle at circumference

Calculation:

⇒ Angle between tangent and chord AC = Angle in opposite arc

⇒ ∠ABC = 40°

⇒ In △ABC:

⇒ ∠BAC = 180° − (75° + 40°)

⇒ ∠BAC = 180° − 115°

⇒ ∠BAC = 65°

⇒ Minor arc AC subtends ∠ABC at circumference

⇒ ∠ABC = 40°

⇒ Angle at center = 2 × 40°

⇒ Angle at center = 80°

∴ The correct answer is 80°.

Given:

Speed ratio (Car : Bus) = 5 : 3

Distance = 360 km

Time taken by bus = 6 hours

Formula Used:

Speed = Distance ÷ Time

Time = Distance ÷ Speed

Calculation:

⇒ Speed of bus = 360 ÷ 6

⇒ Speed of bus = 60 km/hour

⇒ 3 parts = 60

⇒ 1 part = 20

⇒ Speed of car = 5 × 20

⇒ Speed of car = 100 km/hour

⇒ Time taken by car = 360 ÷ 100

⇒ Time taken by car = 3.6 hours

∴ The correct answer is 3.6 hours.

Shortcut Trick

Pass % of boys = 100% − 20% = 80%

Pass % of girls = 100% − 40% = 60%

Required Ratio = (5 × 80%) : (3 × 60%)

⇒ 400 : 180 = 20 : 9

∴ The correct answer is 20:9.

Alternate Method

Given:

Ratio of Boys : Girls = 5 : 3

Fail % of Boys = 20% | Fail % of Girls = 40%

Calculations:

Let the number of boys be 500 and girls be 300.

⇒ Number of boys who passed = 80% of 500

⇒ Passed boys = (80 ÷ 100) × 500 = 400

⇒ Number of girls who passed = 60% of 300

⇒ Passed girls = (60 ÷ 100) × 300 = 180

⇒ Required Ratio = 400 : 180

⇒ Divide both by 20: (400 ÷ 20) : (180 ÷ 20) = 20 : 9

∴ The correct answer is 20:9.

Additional Information

Complementary Percentages

The sum of passing percentage and failing percentage is always 100%. If x% fail, then (100 − x)% pass.

Ratio Scaling Property

Multiplying or dividing both terms of a ratio by the same non-zero constant (e.g., multiplying 5:3 by 100 to get 500:300) does not change the value of the ratio.

Base of Percentage

Always ensure the percentage is applied to the correct base. Here, 20% is of boys (5 units) and 40% is of girls (3 units).

Given:

$\sec(\theta) = \csc(42^\circ)$

Formula Used:

$\sec\theta = \frac{1}{\cos\theta}$

$\csc\alpha = \frac{1}{\sin\alpha}$

$\sin(90^\circ - \alpha) = \cos\alpha$

Calculation:

⇒ $\frac{1}{\cos\theta} = \frac{1}{\sin42^\circ}$

⇒ $\cos\theta = \sin42^\circ$

⇒ $\sin42^\circ = \cos(90^\circ - 42^\circ)$

⇒ $\sin42^\circ = \cos48^\circ$

⇒ $\cos\theta = \cos48^\circ$

⇒ $\theta = 48^\circ$

∴ The correct answer is $\theta = 48^\circ$.

Given:

$(\sqrt{3})^5 × 9^2 = 3^n × 3\sqrt{3}$

Formula Used:

$\sqrt{a} = a^{1/2}$

$(a^m)^n = a^{mn}$

$a^m × a^n = a^{m+n}$

Calculation:

⇒ $(\sqrt{3})^5 × 9^2 = (3^{1/2})^5 × (3^2)^2 = 3^{5/2} × 3^4 = 3^{5/2 + 4} = 3^{13/2}$

⇒ $3^n × 3\sqrt{3} = 3^n × 3 × 3^{1/2} = 3^n × 3^{3/2} = 3^{n + 3/2}$

⇒ $3^{13/2} = 3^{n + 3/2} ⇒ \frac{13}{2} = n + \frac{3}{2} ⇒ n = \frac{10}{2} = 5$

∴ The correct answer is $5$.

Given:

$y = 3 - \sqrt{8}$

Formula Used:

$\frac{1}{a - b} = \frac{a + b}{a^2 - b^2}$

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

Calculation:

⇒ $\frac{1}{y} = \frac{1}{3 - \sqrt{8}} = \frac{3 + \sqrt{8}}{9 - 8} = 3 + \sqrt{8}$

⇒ $y + \frac{1}{y} = (3 - \sqrt{8}) + (3 + \sqrt{8}) = 6$

∴ The correct answer is $6$.

Given:

$Area_1 = 5 \text{ cm}^2$

$Area_2 = 45 \text{ cm}^2$

Side of smaller triangle = 2 cm

Formula Used:

$\frac{Area_2}{Area_1} = \left(\frac{Side_2}{Side_1}\right)^2$

Calculation:

⇒ $\frac{45}{5} = \left(\frac{Side_2}{2}\right)^2$

⇒ $9 = \left(\frac{Side_2}{2}\right)^2$

⇒ $\frac{Side_2}{2} = 3$

⇒ $Side_2 = 6$

∴ The correct answer is 6 cm.

Shortcut Trick

Ratio of heights of smaller triangle to larger triangle = 1 : 3.

Ratio of their areas = (1)² : (3)² = 1 : 9.

Area of the trapezoid = Area of larger triangle − Area of smaller triangle = 9 − 1 = 8 units.

Required ratio = Area of trapezoid : Area of larger triangle = 8 : 9.

∴ The correct answer is 8:9.

Alternate Method

Given:

Height of smaller triangle (h) = 1/3 × Height of larger triangle (H)

⇒ h/H = 1/3

Formula Used:

For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding heights or sides.

⇒ Area_small / Area_large = (h/H)²

Calculations:

⇒ Area_small / Area_large = (1/3)²

⇒ Area_small / Area_large = 1/9

⇒ Area_small = (1/9) × Area_large

⇒ Area_trapezoid = Area_large − Area_small

⇒ Area_trapezoid = Area_large − (1/9) × Area_large

⇒ Area_trapezoid = (8/9) × Area_large

⇒ Area_trapezoid / Area_large = 8/9

∴ The correct answer is 8:9.

Additional Information

Similarity Property of Areas

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of any two corresponding linear dimensions (sides, medians, altitudes, or perimeters).

Area of a Trapezoid

The area of a trapezoid formed by a parallel cut in a triangle can always be calculated as the difference between the areas of the original triangle and the smaller triangle removed from the top.

Midsegment Theorem Case

If the cut is made at the midpoints (h = 1/2 H), the area of the smaller triangle is 1/4 of the larger, and the trapezoid is 3/4 of the larger triangle area.

Given:

$x + y = 7$

$xy = 12$

Formula Used:

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

Calculation:

⇒ $(x + y)^2 = 7^2 = 49$

⇒ $x^2 + y^2 + 2xy = 49$

⇒ $x^2 + y^2 + 2(12) = 49$

⇒ $x^2 + y^2 + 24 = 49$

⇒ $x^2 + y^2 = 49 - 24 = 25$

∴ The correct answer is $25$.

Given:

$x + y = 12$

$x - y = 4$

Formula Used:

$x^3 + y^3 = (x + y)^3 - 3xy(x + y)$

$xy = \frac{(x + y)^2 - (x - y)^2}{4}$

Calculation:

⇒ $xy = \frac{12^2 - 4^2}{4} = \frac{144 - 16}{4} = \frac{128}{4} = 32$

⇒ $x^3 + y^3 = 12^3 - 3 × 32 × 12 = 1728 - 1152 = 576$

⇒ $\frac{x^3 + y^3}{x + y} = \frac{576}{12} = 48$

∴ The correct answer is $48$.

The correct answer is Fundamental Rights.

Key Points

• Fundamental Rights in the Indian Constitution are inspired by the Bill of Rights in the US Constitution. The Indian Constitution guarantees these rights under Part III, ensuring basic freedoms and equality to all citizens.
• The American Bill of Rights, added as the first ten amendments to the US Constitution in 1791, serves as a source of inspiration for ensuring civil liberties such as freedom of speech, religion, and equality before law.
• Indian Fundamental Rights include rights like the Right to Equality (Articles 14-18), Right to Freedom (Articles 19-22), and Right to Constitutional Remedies (Article 32), among others.
• Dr. B.R. Ambedkar, the chief architect of the Indian Constitution, emphasized the importance of Fundamental Rights in ensuring the protection of individual freedoms and societal equality.
• Although inspired by the US Constitution, the Indian Fundamental Rights are adapted to align with the socio-political conditions of India, allowing for reasonable restrictions and aligning with the principle of parliamentary sovereignty.

Additional Information

• Centrifugal form of federalism:
• The concept of a strong central government in India is not borrowed from the US; instead, it is influenced by the Government of India Act, 1935. This system centralizes power, contrary to the US model of federalism, which emphasizes state sovereignty.
• Indian federalism is described as quasi-federal, with a strong unitary bias, especially during emergencies.
• Concept of Concurrent List:
• The concept of the Concurrent List is borrowed from the Australian Constitution, not the US. This list allows both the Centre and states to legislate on subjects of common interest.
• Examples of subjects in the Concurrent List include education, marriage, and bankruptcy.
• Single Citizenship:
• The concept of single citizenship in India is derived from the British Constitution, ensuring that all Indians are citizens of India, irrespective of their state of residence.
• This contrasts with the US, where individuals have dual citizenship—one for their state and one for the federal nation.
• Additional Features Borrowed from the US Constitution:
• The Indian Constitution also draws inspiration from the US Constitution for features like judicial review, the independence of the judiciary, and the impeachment process of the President.
• Other influences include the concept of a written Constitution and the division of powers among the legislature, executive, and judiciary.

Important Points

• Fundamental Rights:
• Fundamental Rights in India are enforceable by courts. Citizens can approach the Supreme Court under Article 32 or High Courts under Article 226 for their enforcement.
• These rights aim to abolish discrimination, ensure equality, and protect individual liberty.
• Adaptations to Indian Context:
• Unlike the US Bill of Rights, Indian Fundamental Rights include the concept of reasonable restrictions to balance individual liberty with societal interests.
• For example, freedom of speech (Article 19) in India is subject to restrictions based on sovereignty, public order, and morality.