SSC CHSL 2025 Tier-1 (Held On: 14 Nov, 2025 Shift 1) (Previous Year Paper)

The correct answer is '1' i.e. I can't hardly .

Key Points

• The phrase "I can't hardly" is grammatically incorrect because it is an example of a double negative.
• The word "can't" is already negative, and adding the word "hardly", which also has a negative connotation, creates redundancy.
• In standard English grammar, double negatives are avoided as they can create confusion or alter the intended meaning of the sentence.

Correct sentence: I can hardly believe that he managed to finish the marathon.

Additional Information

• Double negatives occur when two negative words are used in the same clause. They often confuse the meaning or make the sentence informal.
• For example:
• Incorrect: I don't need no help.
• Correct: I don't need any help.
• It's important to revise the sentence structure to eliminate such errors and maintain clarity and formality.

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

Key Points

• To make the sentence meaningful, the phrase that fits correctly is "halfway", which implies reaching a compromise or middle ground.
• The sentence indicates that negotiations failed because neither side agreed to compromise.
• The other options do not logically fit the context of the statement.

Correct sentence: Negotiations broke down when both sides refused to meet halfway.

Additional Information

• Contextual Usage of Phrases:
• With open arms: Refers to warmly welcoming someone, which does not fit the scenario.
• Half the battle: Refers to achieving a significant part of a task, which is unrelated to negotiation breakdowns.
• In the same breath: Refers to saying two things simultaneously, which does not relate to compromise.
• Halfway: Refers to meeting in the middle or compromising, which correctly fits the context of the sentence.

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

Key Points

• The word "Glib" refers to being fluent or smooth in speech but often in an insincere or superficial manner.
• The synonym for "glib" that best matches its meaning is "articulate", as it conveys the idea of being fluent and expressive in speech.
• Other options such as "sincere" and "forthright" do not match the nuanced meaning of "glib," which often carries a negative connotation of insincerity.
• Option 4, "Dispassionate," means unemotional or impartial, which is unrelated to the meaning of "glib."

Correct sentence: The synonym for the word "glib" is articulate.

Additional Information

• Contextual Meaning: While "glib" can mean fluent, it often implies a lack of sincerity, which should be considered when choosing its synonym.
• Example Usage: The politician’s glib answers during the debate impressed some but left others questioning his sincerity.

The correct answer is '2' i.e. keep her nose to the grindstone .

Key Points

• The idiom keep her nose to the grindstone means to work hard and stay focused on a task despite challenges or setbacks.
• In the given sentence, the subject continues to remain optimistic and work hard despite difficulties, which aligns perfectly with the meaning of the idiom.
• The other options are not appropriate in this context:
• Option 1: Turn over a new leaf: Refers to starting fresh or making a change in behavior, which does not fit the context of persistence.
• Option 3: Throw caution to the wind: Means to act recklessly, which contradicts the sense of optimism and hard work.
• Option 4: Pull the plug: Refers to stopping or discontinuing something, which is the opposite of continuing to work hard.

Correct sentence: Despite numerous setbacks, she remained optimistic and continued to keep her nose to the grindstone.

Additional Information

• Idioms are expressions that convey a figurative meaning different from their literal meaning.
• Choosing the correct idiom depends on the context of the sentence and the intended meaning.

The correct answer is '3' i.e. The baby started to tire of playing with the same toy .

Key Points

• The word "tire" in the given sentence means to become bored or exhausted by something.
• In Option 3, the sentence "The baby started to tire of playing with the same toy" uses the word "tire" in the same sense, meaning to grow bored or weary.
• Options 1, 2, and 4 refer to "tire" as a part of a vehicle (e.g., a bicycle or car tire), which is a completely different meaning.

Correct sentence: The baby started to tire of playing with the same toy.

Additional Information

• Homonyms: Words that are spelled and pronounced the same but have different meanings. In this case, "tire" can mean:
• To grow weary or bored (e.g., "I am starting to tire of this long journey").
• A rubber covering for wheels (e.g., "My bicycle has a flat tire").
• Always focus on the context of the sentence to determine the correct meaning.

The correct answer is Option 2.

 

Key Points

• The passage clearly states that movies are a powerful storytelling medium that significantly influence society.
• Films help in shaping cultural norms, meaning they influence the traditions, behaviour, and social practices of people.
• Movies also affect public opinion and individual perspectives by presenting ideas, social issues, and narratives that audiences engage with.
• Through their emotional and visual impact, films can introduce new ideas and challenge existing prejudices, thereby influencing societal thinking.

Therefore, the correct answer is Option 2.

 

Additional Information

• Option 1 – Incorrect because the passage clearly mentions that films influence societal values and perceptions, not merely entertainment.
• Option 3 – Incorrect as the passage does not mention advertising; it focuses on the social and cultural impact of movies.
• Option 4 – Incorrect because the passage explains that movies address real social issues and ideas, not only fantasy or escapism.

The correct answer is Option 2.

 

Key Points

• The passage explicitly states: "Movies can introduce new ideas, challenge old prejudices, and initiate serious discussions on social issues."
• It explains that the "pictorial and emotional power" of film creates a "special kind of empathy," which helps viewers understand different experiences and expand their horizons.
• While the text warns that movies can reinforce stereotypes, it presents the introduction of new ideas and social discussion as the specific means by which they challenge existing prejudices.
• Therefore, Option 2 is the only choice that reflects the positive, transformative role of cinema described in the text.

Therefore, the correct answer is Option 2.

 

Correct Sentence from Text: "Movies can introduce new ideas, challenge old prejudices, and initiate serious discussions on social issues."

 

Additional Information

• Option 1: Incorrect. The text lists reinforcing stereotypes as a negative outcome or a misuse of film's power, not as a way to challenge prejudice.
• Option 3: Incorrect. The author clarifies that films are "more than a form of entertainment," serving as a "mirror to the collective consciousness."
• Option 4: Incorrect. The text suggests movies do the opposite by initiating "serious discussions on social issues," which often involves tackling controversial topics.

The correct answer is Option 2.

 

Key Points

• The text highlights that the "pictorial and emotional power of film" is what creates a "special kind of empathy" in the audience.
• This empathy is achieved by "taking viewers into other worlds and experiences," which allows them to understand perspectives different from their own.
• The passage suggests that this immersion is what leads to "expanding horizons" and a deeper understanding of the collective consciousness.
• Option 2 directly paraphrases the text's explanation of how film generates empathy, while the other options focus on specific genres or technical elements not emphasized in this context.

Therefore, the correct answer is Option 2.

 

Correct Sentence from Text: "The pictorial and emotional power of film provides a special kind of empathy, taking viewers into other worlds and experiences, hence understanding and expanding horizons."

 

Additional Information

• Option 1: Incorrect. While humor is a common movie element, the text identifies "pictorial and emotional power" as the source of empathy, not specifically humor.
• Option 3: Incorrect. The text mentions "unrealized versions of life" as a potential negative responsibility, rather than the primary driver of empathy.
• Option 4: Incorrect. Although movies use visuals, the text focuses on the emotional result of the "pictorial power" rather than just the technical "action scenes."

The correct answer is Option 4.

 

Key Points

• The passage concludes by noting that because movies have the power to influence society, there is a significant "responsibility" attached to them.
• It mentions that because films can reinforce stereotypes or spread harmful ideologies, there is "all the more reason to embrace critical interaction with the narratives we watch."
• This implies that the responsibility lies in the critical examination and mindful consumption of film narratives to mitigate potential negative effects.
• Option 4 accurately reflects the author's call for "critical interaction," which is the core responsibility suggested for handling the medium's power.

Therefore, the correct answer is Option 4.

 

Correct Sentence from Text: "Still, this power has responsibility... and all the more reason to embrace critical interaction with the narratives we watch."

 

Additional Information

• Option 1: Incorrect. The text explicitly states that movies have a "tremendous influence on society," so entertaining without influencing is not the described reality or responsibility.
• Option 2: Incorrect. While the text says movies can do this, it is presented as a risk or negative potential, not a desirable responsibility.
• Option 3: Incorrect. The text advocates for the opposite—challenging prejudices and initiating serious discussions—rather than avoiding them.

The correct answer is Option 2.

 

Key Points

• The author acknowledges that while film is a powerful tool for good, it also carries potential risks: "movies can reinforce stereotypes, help spread harmful ideologies, or offer unrealized versions of life."
• These negative outcomes are the reason the text advocates for "critical interaction" with the media we consume.
• The passage suggests that the same "pictorial and emotional power" that builds empathy can also be misused to promote harmful narratives or social biases.
• Option 2 directly lists the negative consequences mentioned in the final sentence of the passage.

Therefore, the correct answer is Option 2.

 

Correct Sentence from Text: "Still, this power has responsibility; movies can reinforce stereotypes, help spread harmful ideologies, or offer unrealized versions of life..."

 

Additional Information

• Option 1: Incorrect. The text states that movies have a "tremendous influence on society."
• Option 3: Incorrect. The text mentions that movies can offer "unrealized versions of life," implying they are not always accurate representations of reality.
• Option 4: Incorrect. The passage argues that movies influence "cultural norms, public opinion, and individual opinions," showing they have vast societal influence beyond just emotional appeal.

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

Key Points

• The word Evanescence means the process of vanishing or fading away.
• Among the given options, Evanescence is the correct spelling.
• The other options are misspelled forms of the word.

Correct usage: The beauty of the sunset had a sense of evanescence, fading quickly as the night approached.

Additional Information

• Etymology: The word "evanescence" originates from the Latin word "evanescere," meaning "to vanish."
• Usage: Commonly used in literature or poetry to describe something fleeting or temporary.

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

Key Points

• The word 'Voluptuous' is correctly spelled, meaning full of luxury, sensual pleasure, or indulgence.
• Other options like 'Voluptous,' 'Voloptuous,' and 'Volaptuous' are incorrect spellings and do not exist in standard English.

Correct spelling: Voluptuous, which refers to something sensuous or luxurious.

Additional Information

• Tips for Spelling:
• Break down the word into syllables: Vo-lup-tu-ous.
• Pay attention to the correct arrangement of vowels and consonants.
• Common Usage:
• She wore a voluptuous gown that was the highlight of the evening.
• The artist painted a voluptuous landscape filled with vibrant colors.

The correct answer is '1' i.e. Things that are opposites or completely different .

Key Points

• The idiom "Chalk and cheese" is used to describe two things that are completely different or opposites in nature.
• The idiom emphasizes the idea that the two things being compared have nothing in common, just like chalk and cheese, which are unrelated and dissimilar substances.

Correct sentence: The two brothers are as different as chalk and cheese; one is outgoing while the other is reserved.

Additional Information

• Idioms to Compare Similar Things:
• Like two peas in a pod: Used to describe two things or people that are very similar.
• Cut from the same cloth: Indicates that two people or things are alike in character or behavior.
• Idioms for Opposites:
• As different as night and day: Highlights the complete difference between two things or people.

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

Key Points

• The word Bankrupt refers to a person who is legally declared unable to pay their debts.
• While Debtor is someone who owes money, it does not necessarily imply legal insolvency.
• Pauper denotes a very poor person, but it does not directly refer to the specific status of being unable to pay debts.
• Lender refers to an individual or a financial institution that makes funds available to another.

Correct sentence: The correct one-word substitute for a person who is unable to pay their debts is Bankrupt.

Additional Information

• Bankrupt:
• Legally declared unable to pay debts.
• Often involves a legal process to resolve financial obligations.
• Debtor:
• A person who owes money.
• Does not necessarily imply financial insolvency.
• Pauper:
• A very poor person.
• Does not directly mean inability to pay debts.
• Lender:
• A person or organization that lends money.
• Expects the borrowed amount to be repaid, usually with interest.

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

Key Points

• The word ignorance refers to the lack of knowledge or awareness about a particular subject or situation.
• Among the given options, knowledge is the most appropriate antonym as it directly refers to having information, understanding, or awareness about something.
• The other options, such as wisdom, awareness, and understanding, are related to knowledge but do not directly serve as the opposite of ignorance in the most literal sense.

Correct sentence: The antonym of ignorance is knowledge.

Additional Information

• Wisdom: While it involves knowledge, it specifically refers to the ability to apply knowledge and experience for sound judgment and decision-making.
• Awareness: Refers to being conscious or informed about something, but it does not directly contradict ignorance.
• Understanding: Refers to comprehending something, which is related to knowledge but not a direct antonym of ignorance.

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

Key Points

• The word Iconoclast refers to a person who challenges or opposes established beliefs, customs, or institutions.
• An antonym for Iconoclast would describe someone who adheres to or conforms to established norms and beliefs.
• Among the options provided:
• Critic: Refers to someone who evaluates or finds faults, not the opposite of Iconoclast.
• Rebel: Someone who opposes authority, similar to Iconoclast.
• Conformist: Someone who follows established customs or norms, which is the opposite of Iconoclast.
• Dissenter: Someone who disagrees with majority opinions, similar to Iconoclast.

Correct antonym: Conformist.

Additional Information

• Synonyms for Iconoclast: Rebel, Dissenter, Nonconformist.
• Other Antonyms for Iconoclast: Traditionalist, Conventionalist.

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

Key Points

• A fatalist is a person who believes that all events in life are predetermined by fate and cannot be changed.
• The word Fatalist is derived from "fate," which signifies destiny or predetermined events.
• Other options do not align with the meaning of the word:
• Realist: A person who accepts a situation as it is and deals with it practically.
• Idealist: A person who is guided by ideals rather than practical considerations.
• Pragmatist: A person who is practical and focused on reaching goals.

Correct sentence: A fatalist believes that everything in life is determined by fate.

Additional Information

• It is important to understand the meaning of each word in the options to select the correct one-word substitute.
• Word substitution questions often test vocabulary and comprehension skills.

The correct answer is '1' i.e. Why did the child break the window?

Key Points

• The given sentence is written in the Passive Voice.
• The question asks to change it into the Active Voice.
• In the passive voice sentence, the subject (the child) is receiving the action, and the object (the window) is being acted upon.
• In the active voice, we need to make the subject (the child) perform the action (break the window).
• The correct transformation is: "Why did the child break the window?"

Correct sentence: Why did the child break the window?

Additional Information

• Active Voice:
• In the active voice, the subject performs the action.
• Example: The child broke the window.
• Passive Voice:
• In the passive voice, the subject receives the action.
• Example: The window was broken by the child.

The correct answer is '1' i.e. He told her that if she could solve that puzzle, he would give her the prize that he had been planning to give away all along. .

Key Points

• Pronoun Logic: The pronouns must align with the reporter's perspective. "You" becomes "she" and "I" becomes "he".
• Tense Backshift: Since the reporting verb "said" is in the past, all verbs in the quoted speech must shift one step back into the past.
• Can becomes Could.
• Will becomes Would.
• Was planning (Past Continuous) becomes Had been planning (Past Perfect Continuous).
• Distance Shift: Words showing nearness in time or place (e.g., "this") are changed to words showing distance ("that").
• The Indirect Sentence: He told her that if she could solve that puzzle, he would give her the prize that he had been planning to give away all along.

Additional Information

• Type 1 Conditionals: In indirect speech, Type 1 conditional sentences (If + Present, Will + Verb) usually shift to Type 2 (If + Past, Would + Verb).
• Continuous Tenses: Note that "was planning" doesn't just stay in the past; it moves to the Past Perfect Continuous to indicate the action was ongoing before the conversation took place.

The correct answer is '1' i.e. The few clothes.

Key Points

• The word "clothes" is a plural noun. Therefore, the use of "less clothes" in the given sentence is incorrect because "less" is used for uncountable nouns.
• The correct quantifier to use with plural countable nouns like "clothes" is "few."
• Among the options provided, "The few clothes" is the most suitable replacement for the highlighted part of the sentence.
• It conveys the idea that the small number of clothes made for the wedding have gone out of style.

Correct sentence: The few clothes that I made for the wedding have gone out of style.

Additional Information

• Usage of Quantifiers:
• Few: Used with plural countable nouns to indicate a small number (e.g., "few apples").
• Less: Used with uncountable nouns to indicate a smaller amount (e.g., "less water").
• Little: Used with uncountable nouns to indicate a small amount (e.g., "little time").
• Fewer: Used with plural countable nouns to compare two quantities (e.g., "fewer books").

The correct answer is '3' i.e. The armed forces publicly challenged a notification issued by the .

Key Points

• The given sentence refers to a completed action in the past. Hence, the verb should be in the past tense.
• Option 3 correctly uses the past tense verb "challenged", making it grammatically appropriate.
• Options 1, 2, and 4 use incorrect verb forms or structures, which do not align with the sentence's context.

Correct sentence: In an act of brazen defiance and indiscipline, the armed forces publicly challenged a notification issued by the prime minister’s office to deal with the leak of information, on a report in the respected Dawn newspaper..

Additional Information

• Past Tense: Used to describe actions that have already been completed.
• Correct Usage: "challenged" is the appropriate verb form to match the past tense narrative of the sentence.

The correct answer is '1' i.e. A new book is bought by her every month.

Key Points

• The given sentence is in the active voice, stating that "She buys a new book every month."
• To transform this sentence into the passive voice, the object of the active sentence ("a new book") becomes the subject of the passive sentence.
• The verb "buys" is in the present simple tense. When changing to passive voice, the correct form is "is + past participle," resulting in "is bought."
• The phrase "by her" is added to indicate the doer of the action in the passive construction.

Correct passive sentence: A new book is bought by her every month.

Additional Information

• Active vs Passive Voice:
• In the active voice, the subject performs the action (e.g., "She buys a book").
• In the passive voice, the subject receives the action (e.g., "A book is bought by her").
• Passive voice is formed using the verb "to be" + past participle.
• Examples:
• Active: He writes a letter. → Passive: A letter is written by him.
• Active: They clean the room. → Passive: The room is cleaned by them.

The correct answer is '4' i.e. The detective asked the suspect, "How can you have committed the crime without leaving any evidence when the security cameras have been recording all night?" .

Key Points

• To convert Indirect Speech to Direct Speech, we must reverse the tense back-shifting that occurred during reporting.
• The modal "could" in indirect speech generally shifts back to "can" in direct speech to maintain the original perspective of the speaker.
• The past perfect continuous tense "had been recording" in indirect speech typically originates from the present perfect continuous "have been recording" in direct speech.
• Pronouns also shift: the third-person "he" (referring to the suspect) must be changed to the second-person "you" as the detective is addressing the suspect directly.

Correct sentence: The detective asked the suspect, "How can you have committed the crime without leaving any evidence when the security cameras have been recording all night?"

Additional Information

• Direct to Indirect Tense Shifting:
• Present Perfect Continuous (have been recording) becomes Past Perfect Continuous (had been recording).
• Can becomes Could.
• Present Perfect (have committed) becomes Past Perfect (had committed/could have committed in modal context).
• Reporting Interrogative Sentences:
• In "Wh-" questions, the question word (how, what, where) acts as the connector.
• The sentence structure changes from interrogative (Verb + Subject) in direct speech to assertive (Subject + Verb) in indirect speech.

The correct answer is '1' i.e. P, Q, R, S .

Key Points

• To form a meaningful and grammatically correct paragraph, the sequence of the sentences must follow a logical flow of events.
• The paragraph starts with P, where the subject is getting ready for shopping by taking his keys and preparing a shopping list.
• Next, Q describes the shopping activity in the crowded aisles, logically following P.
• R comes next, where the subject pays for the items at the register, which naturally comes after shopping.
• Finally, S concludes the paragraph with the subject reaching home and preparing for the week, completing the sequence.

Correct sequence: P, Q, R, S.

Additional Information

• While rearranging sentences, identify the context and logical order of the events.
• Look for clues such as connectors, pronouns, or transitions that indicate the flow of ideas.
• Ensure that the paragraph is coherent and grammatically correct after rearranging the parts.

The correct answer is '2' i.e. Q, R, P, S .

Key Points

• The paragraph revolves around the emergence and philosophy of existentialism in the 20th20th

century, emphasizing the human condition, freedom, responsibility, and its psychological effects.

• The correct order of sentences is determined by their logical flow and coherence.
• Q: The paragraph begins with introducing the topic of existentialist philosophers and their focus on the human condition in a world without inherent meaning.
• R: The next sentence explains the context or background, highlighting how existentialism was a response to the moral vacuum left by two world wars.
• P: The idea of individual freedom and responsibility is then introduced as a key aspect of existentialist thought.
• S: Finally, the paragraph concludes with the emotional consequence of this radical freedom—anxiety and dread.

Correct sentence order: Q, R, P, S.

Additional Information

• Existentialism: A philosophical movement that emphasizes individual freedom, choice, and responsibility in a world lacking inherent meaning.
• Anxiety and Dread: Existentialist concepts referring to the emotional burden of recognizing one's freedom and responsibility.

Given:

The logic followed here is that each letter is shifted by 3 positions forward (+3 pattern) in the alphabetical series.

For LEARNERS : OHDUQHUV

Applying the same logic to TEACHERS : ?

The resulting code is WHDFKHUV.

Hence, the correct answer is "Option 1".

Given:

The logic followed here is that each letter is shifted to its immediate next letter in the alphabetical series (+1 pattern).

For ENCYCLOPEDIA : FODZDMPQFEJB

 

For DICTIONARY : EJDUJPOBSZ

 

Applying the same logic to THESAURUS : ?

 

The resulting code is UIFTBVSVT.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: Each letter is replaced by its alphabetical position number.

TELESCOPE is coded as 20-5-12-5-19-3-15-16-5

T → 20

E → 5

L → 12

E → 5

S → 19

C → 3

O → 15

P → 16

E → 5

MICROSCOPE is coded as 13-9-3-18-15-19-3-15-16-5

M → 13

I → 9

C → 3

R → 18

O → 15

S → 19

C → 3

O → 15

P → 16

E → 5

Similarly, STETHOSCOPE is coded as:

S → 19

T → 20

E → 5

T → 20

H → 8

O → 15

S → 19

C → 3

O → 15

P → 16

E → 5

So, STETHOSCOPE will be coded as

19-20-5-20-8-15-19-3-15-16-5

Hence, the correct option is Option 1

Solution

Tourism can harm the very sites it seeks to promote - True (The statement mentions that the surge in visitors has caused damage to ancient monuments and local ecosystems, which means tourism can harm heritage sites).

All tourists intentionally damage heritage sites - False (The statement does not mention that all tourists intentionally cause damage; it only refers to damage due to increased visitors).

Authorities are taking steps to reduce the negative impact of tourism - True (It is clearly stated that authorities are limiting access and introducing conservation fees).

hence the correct option is Option 2.

Train hard anyway – False, Ignoring the doctor’s advice can worsen the injury and delay proper recovery.

Follow gradual recovery plan – True, Gradually resuming training as advised by the doctor ensures safe and steady recovery.

Quit sports altogether – False, There is no need to quit since light training is allowed.

Take painkillers and push through –False This may hide pain and cause further serious damage.

Hence, the correct option is Option 2.

BODMAS Rule:

According to the question, the symbols denote the following operations:

Now, given the expression: 11 % 2 # 6 @ 15 = ?

After substituting the specified symbols, the new equation is:

11 × 2 ÷ 6 − 15

⇒ 11 × (2 ÷ 6) − 15

⇒ 11 × (1/3) − 15 = $-\frac{34}{3}$​

The value of the expression is $-\frac{34}{3}$

Hence, the correct answer is "Option 2".

Check option: 

Privately praise their insights and invite them to share, offering support – True, This builds confidence and creates a safe environment for them to express their ideas.

Take credit for their ideas to boost confidence – false ,This is unethical and may damage trust.

Ignore and let them remain quiet – false, This does not help them grow or overcome their fear.

Publicly ask them to speak up in a meeting without prior notice – false, This may increase their anxiety instead of encouraging them.

Hence, the correct option is, Option 1.

Total students = 35

Karan is 9^th from the left.

Arjun is 15^th from the right.

Position of Arjun from the left = 35 − 15 + 1 = 21^st

Now positions are:

Karan → 9^th

Arjun → 21^st

Number of students between them = 21 − 9 − 1 = 11

Hence, the correct answer is Option 2.

Given

Golden diya is 8^th from the left end.

Silver diya is 10^th from the right end.

Position of silver diya from left = 30 − 10 + 1 = 21^st

So, diyas between golden and silver diya = 21 − 8 − 1 = 12.

So, there are '12' diyas between them.

Hence, the correct answer is Option 4.

Course of action I: Increase the number of ambulances and ensure GPS tracking for quick response – Follows, Since there are complaints about delays, increasing ambulances and improving tracking directly addresses the problem and helps improve response time.

Course of action II: Close all emergency services until better management is implemented – Does not follow Closing emergency services would worsen the situation and is not a practical or logical solution.

Hence, the correct option is Option 1

Argument I: Yes, it will improve enrollment – Strong, It gives a clear, practical reason supporting the proposal. Tax benefits can motivate parents to choose government schools, which may increase enrollment.

Argument II: No, it discriminates against private school students – Strong, This is also a valid concern. Providing tax benefits only to parents of government school students may create inequality and raise fairness issues.

Since both arguments present logical and relevant points from different perspectives, both are strong arguments.

Hence, the correct answer is Option 2.

The logic followed here is:

Thus, the missing letter in the series is W.

Hence, the correct answer is "Option 4".

The logic followed here is:

Thus, the missing letter in the series is Z.

Hence, the correct answer is "Option 1".

Launch the AI without restrictions – Inappropriate,This could lead to misuse, fraud, and serious ethical concerns.

Keep the AI a company secret – Inappropriate While it prevents misuse, it also limits positive and responsible innovation.

Release the AI with strict ethical guidelines and detection tools – Most appropriate This balances innovation with safety by reducing the risk of misuse through proper safeguards.

Sell it to the highest bidder – Inappropriate Profit-focused decision without considering ethical consequences.

Hence the correct option is Option 3.

Given Word: COMMUNICATION

NATION → Can be formed

UNISON → Cannot be formed (Because the letter 'S' is not in the given word)

ACTION → Can be formed

UNION → Can be formed

Hence, the correct answer is "Option 2".

Charge high fees for water – Inappropriate, This may create inequality and does not immediately solve the shortage problem.

Start rationing permanently – Inappropriate,  Permanent rationing is not justified without assessing long-term conditions.

Ignore and hope rain comes – Inappropriate, This is irresponsible and does not address the crisis.

Deploy tankers temporarily while fixing main pipeline –  appropriate This provides immediate relief while corrective measures are taken to restore regular supply.

Hence, the correct answer is Option 4.

The logic followed here:

AZ : ZA

Here, the letters are reversed.

A Z → Z A

Now apply the same pattern to BY:

B Y → Y B

Hence, the correct answer is Option 1.

The logic followed here is:

For BA : EZ

Applying the same logic to CO : ?

The resulting pair is FN.

Hence, the correct answer is "Option 2".

The logic followed here is:

Thus, the missing term in the series is 340.

Hence, the correct answer is "Option 2";

The logic followed here is:

Thus, the missing term in the series is 220.

Hence, the correct answer is "Option 1";

The logic followed here is:

Thus, the missing term in the series is 1368.

Hence, the correct answer is "Option 1";

Given:

8 @ 4 ~ 2 ~ 6 = ?

By using the BODMAS rule:

By decoding the given symbols we get:

Substituting the given operators in the expression:

⇒ 8 @ 4 ~ 2 ~ 6

⇒ 8 - (4 ÷ 2) ÷ 6

⇒ 8 - 2 ÷ 6

⇒ 8 - 1/3

⇒ (24 - 1) / 3

⇒ 23/3 

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: 1^st number + 11 = 2^nd number.

Now, let's check the options:

For, 55 : 66

⇒ 55 + 11 = 66. (Follows pattern)

For, 77 : 88

⇒ 77 + 11 = 88. (Follows pattern)

For, 33 : 44

⇒ 33 + 11 = 44. (Follows pattern)

Similarly, for 22 : 39

⇒ 22 + 11 = 33 ≠ 39.

Hence, the correct answer is "Option 1".

The arrangement of the given words in the order in which they appear in an English dictionary is as shown below :

1. Galaxy

3. Garage

2. Garden

4. General

5. Gentle

6. Golden

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

The arrangement of the given words in the order in which they appear in an English dictionary is as shown below:

2. Retroactive

5. Retrograde

3. Retrogression

4. Retrospection

1. Retrospective

Hence, the correct answer is 2, 5, 3, 4, 1

Given:

A invested = Rs. 75,000 (for 3 years)

B invested = Rs. 1,00,000 (after 1 year withdrew Rs. 20,000, so remaining Rs. 80,000 for next 2 years)

C invested = Rs. 1,50,000 (for 3 years)

Total profit = Rs. 4,50,000

Formula used: 

Profit sharing ratio = Capital × Time

Calculations:

A’s capital-time = 75,000 × 3 = 2,25,000

B’s capital-time:

First year = 1,00,000 × 1 = 1,00,000

Next 2 years = 80,000 × 2 = 1,60,000

Total = 1,00,000 + 1,60,000 = 2,60,000

C’s capital-time = 1,50,000 × 3 = 4,50,000

Profit sharing ratio:

2,25,000 : 2,60,000 : 4,50,000

Divide by 5,000 to simplify:

45 : 52 : 90

Total parts = 45 + 52 + 90 = 187

C’s share = (90 / 187) × 4,50,000

= 4,05,00,000 / 187

≈ Rs. 2,16,577.54

∴ The correct answer is “Option 4.”

Given:

Sin A = 3/5

Cos B = 5/13

We know that: Sin A Cos B + Cos A Sin B = Sin (A + B)

So, first we need to find Cos A and Sin B.

Since, Sin A = 3/5

Formula used: 

Sin²A + Cos²A = 1

Sin²B + Cos²B = 1

Calculations:

Sin²A + Cos²A = 1

Cos A = √(1 − (3/5)²)

= √(1 − 9/25)

= √(16/25)

= 4/5

Sin²B + Cos²B = 1

Sin B = √(1 − (5/13)²)

= √(1 − 25/169)

= √(144/169)

= 12/13

Sin A Cos B + Cos A Sin B

= (3/5 × 5/13) + (4/5 × 12/13)

= (15/65) + (48/65)

= 63/65

∴ The correct answer is “Option 1.”

Given:

Difference between Selling Price (SP) and Cost Price (CP) = ₹500

Profit percentage = 25%

Since SP − CP = Profit,

Profit = ₹500

Formula used: Profit % = (Profit / CP) × 100

Calculations:

25 = (500 / CP) × 100

25 = 50000 / CP

CP = 50000 / 25

CP = ₹2000

Now, SP = CP + Profit

SP = 2000 + 500

SP = ₹2500

∴ The correct answer is “Option 2.”

Shortcut Trick

Convert percentage to fraction: 20% = 1/5.

Since the number of cars is 20% more, let trucks = 5 units.

Then cars = 5 + 1 = 6 units.

The ratio of trucks to cars = 5 : 6.

∴ The correct answer is 5:6.

Alternate Method

Given:

Number of cars is 20% more than the number of trucks.

Formula Used:

Ratio = Value₁ : Value₂

Calculations:

Let the number of trucks be 100.

⇒ Number of cars = 100 + 20% of 100

⇒ Number of cars = 100 + 20 = 120

⇒ Ratio of trucks to cars = 100 : 120

⇒ Ratio = 100/20 : 120/20

⇒ Ratio = 5 : 6

∴ The correct answer is 5:6.

Additional Information

Percentage to Ratio Conversion

To convert a percentage increase to a ratio, use the base 100. An x% increase results in a ratio of 100 : (100 + x).

Inverse Percentage Relation

If A is 20% more than B, then B is [20/(100+20)] × 100 = 16.67% less than A.

Ratio Basics

A ratio is a comparison of two similar quantities. The order of terms is crucial; the ratio of A to B (A:B) is different from B to A (B:A).

∴ The correct answer is 5:6.

Given:

Amount doubles in 7 years (under compound interest)

We need to find the time required for the amount to become 16 times.

Formula used:

If amount doubles in T years, then

Final amount after n such periods = Principal × (2ⁿ)

Calculations:

Since, amount doubles in 7 years:

After 7 years → 2 times

After 14 years → 4 times

After 21 years → 8 times

After 28 years → 16 times

Because: 16 = 2⁴

So, number of doubling periods needed = 4

Each doubling takes 7 years:

Total time = 4 × 7

Total time = 28 years

∴ The correct answer is “Option 2.”

Shortcut Trick

Ratio of number of students in groups = 20 : 30 : 50 = 2 : 3 : 5.

Let the assumed average be 60 marks.

Net deviation = [2 × (50 − 60) + 3 × (60 − 60) + 5 × (70 − 60)] ÷ (2 + 3 + 5)

Net deviation = [−20 + 0 + 50] ÷ 10 = 30 ÷ 10 = 3.

Combined Average = Assumed Average + Net deviation = 60 + 3 = 63.

∴ The correct answer is 63.

Alternate Method

Given:

Number of students (n₁, n₂, n₃) = 20, 30, 50

Average marks (A₁, A₂, A₃) = 50, 60, 70

Formula Used:

Combined Average = (n₁A₁ + n₂A₂ + n₃A₃) ÷ (n₁ + n₂ + n₃)

⇒ Total Marks = (20 × 50) + (30 × 60) + (50 × 70)

⇒ Total Marks = 1000 + 1800 + 3500

⇒ Total Marks = 6300

⇒ Total Students = 20 + 30 + 50 = 100

⇒ Combined Average = 6300 ÷ 100 = 63

∴ The correct answer is 63.

Additional Information

Weighted Average Formula

The formula for weighted average is ∑(w_i × x_i) ÷ ∑w_i, where w is the weight (quantity) and x is the value (average).

Combined Average with N Groups

If multiple groups join, the combined mean is the sum of all individual sums divided by the total count: A_avg = (n₁A₁ + n₂A₂ + ... + n_kA_k) ÷ (n₁ + n₂ + ... + n_k).

Effect of Constant Addition

If every observation in a data set is increased by a constant k, the mean of the data set also increases by exactly k.

Given:

When a number is divided by 45, remainder = 27

When the same number is divided by 27, remainder = 9

Let the number be N.

From the first condition:

N = 45a + 27

From the second condition:

N = 27b + 9

Formula used:

If N leaves remainder r when divided by d, then

N − r is divisible by d.

Calculations:

From first condition:

N − 27 is divisible by 45

From second condition:

N − 9 is divisible by 27

Now check options:

Option 1: 189

189 ÷ 45 = remainder 9 (not 27) 

Option 2: 117

117 ÷ 45 = remainder 27 

117 ÷ 27 = remainder 9 

So, 117 satisfies both conditions.

∴ The correct answer is “Option 2.”

Given:

Ravi scores 40% marks and fails by 30 marks.

Sohan scores 50% marks and gets 20 marks more than the pass marks.

Let the maximum marks = M

Let the pass marks = P

Formula used: 

Marks obtained = (Percentage × Maximum marks) / 100

Calculations:

Ravi’s marks = 40% of M

= 40M / 100

= 0.4M

Since he fails by 30 marks:

0.4M = P − 30 …… (1)

Sohan’s marks = 50% of M

= 50M / 100

= 0.5M

He gets 20 marks more than pass marks:

0.5M = P + 20 …… (2)

Now subtract equation (1) from equation (2):

0.5M − 0.4M = (P + 20) − (P − 30)

0.1M = 50

M = 50 / 0.1

M = 500

∴ The correct answer is “Option 3.”

Given:

Distance from Gurugram to Jaipur = 240 km

Speed = 60 km/h

Distance from Jaipur to Ajmer = 130 km

Speed = 50 km/h

Break time = 1 hour

Formula used: Average Speed = Total Distance / Total Time

Calculations:

Step 1: Time taken from Gurugram to Jaipur

Time = Distance / Speed

Time = 240 / 60 = 4 hours

Step 2: Time taken from Jaipur to Ajmer

Time = 130 / 50 = 2.6 hours

Step 3: Total distance

Total distance = 240 + 130 = 370 km

Step 4: Total time (including break)

Total time = 4 + 1 + 2.6

Total time = 7.6 hours

Step 5: Average speed

Average speed = 370 / 7.6

Average speed ≈ 48.68 km/h

∴ The correct answer is “Option 1.”

Given:

A can complete the whole work in 30 days.

Number of days given = 6

Formula used:

Work done = (Number of days worked / Total days required) × Total work

Since, total work = 1 (complete work),

Calculations:

Work done in 6 days = 6 / 30 = 1 / 5 = 0.2

To express in percentage: 0.2 × 100 = 20%

So, A will complete

1/5 of the work (or 20% of the work) in 6 days.

∴ The correct answer is “Option 3.”

Given:

Marked Price (MP) is 20% more than Cost Price (CP).

Discount offered = 10% on Marked Price.

Let CP = 100 (assumption method for easy calculation)

Formula used:

Marked Price = CP + 20% of CP

Selling Price = MP − 10% of MP

Profit % = (Profit / CP) × 100

Calculations:

Step 1: CP = 100

Step 2: MP = 100 + 20% of 100

MP = 100 + 20

MP = 120

Step 3: Discount = 10% of 120 = 12

Selling Price (SP) = 120 − 12

SP = 108

Step 4: Profit = SP − CP

Profit = 108 − 100

Profit = 8

Profit % = (8 / 100) × 100

Profit % = 8%

∴ The correct answer is “Option 2.”

Given:

Rate of interest (R) = 8% per annum

Time (T₁) = 3 years

Simple Interest (SI₁) = ₹2400

Formula used: Simple Interest = (Principal × Rate × Time) / 100

Calculations:

2400 = (P × 8 × 3) / 100

2400 = (24P) / 100

2400 = 0.24P

P = 2400 / 0.24

P = 10,000

Now find the amount after 5 years.

Simple Interest for 5 years:

SI₂ = (10000 × 8 × 5) / 100

= (10000 × 40) / 100 = 400000 / 100 = 4000

Amount after 5 years = Principal + Interest

= 10000 + 4000 = ₹14,000

So, the required amount is ₹14,000

∴ The correct answer is “Option 3.”

Given:

x² + y² = 58

x + y = 10

We need to find: xy

Formula used: (x + y)² = x² + y² + 2xy

Calculations:

Step 1:(x + y)² = 10² = 100

Step 2: Using the formula: 100 = 58 + 2xy

Step 3: 100 − 58 = 2xy

42 = 2xy

Step 4:

xy = 42 / 2

xy = 21

∴ The correct answer is “Option 1.”

Given:

Number = 7744

Formula used: If a × a = N, then √N = a

Calculations:

Check by multiplication:

88 × 88 = 88 × (80 + 8)

= (88 × 80) + (88 × 8)

= 7040 + 704

= 7744

Since 88 × 88 = 7744

Therefore, √7744 = 88

∴ The correct answer is “Option 2.”

Shortcut Trick

Initial ratio of Milk : Water = 2 : 1 (Total = 3 units).

Target ratio = 1 : 2. Since Milk quantity is constant, multiply target ratio by 2 → 2 : 4.

Increase in Water units = 4 − 1 = 3 units.

Initial total mixture = 3 units = 75 litres.

Water to be added = 3 units = 75 litres.

∴ The correct answer is 75 litres.

Alternate Method

Given:

Initial volume = 75 litres | Initial ratio (Milk:Water) = 2 : 1 | Final ratio = 1 : 2

Calculations:

⇒ Quantity of Milk = (2/3) × 75 = 50 litres

⇒ Quantity of Water = (1/3) × 75 = 25 litres

⇒ Let x litres of water be added.

⇒ New Ratio = Milk ÷ (Water + x) = 1 ÷ 2

⇒ 50 ÷ (25 + x) = 1 ÷ 2

⇒ 100 = 25 + x

⇒ x = 100 − 25 = 75 litres

∴ The correct answer is 75 litres.

Additional Information

Constant Component Rule

In mixture problems where only one component is added or removed, the absolute quantity of the other component remains unchanged. Use this to equate the ratios.

Alligation Method

Ratio of quantities = (Value₂ − Mean Value) : (Mean Value − Value₁). Here, added water is 100% water concentration.

Percentage Change in Mixture

Initial Mixture × Initial % of Constant Part = Final Mixture × Final % of Constant Part.

Shortcut Trick

When a larger solid sphere is melted to form smaller identical spheres, the number of spheres (n) is the ratio of their volumes.

Shortcut formula: n = (Radius of larger sphere ÷ Radius of smaller sphere)³

n = (12 ÷ 2)³ = 6³

n = 216

∴ The correct answer is 216.

Alternate Method

Given:

Radius of the large metal sphere (R) = 12 cm

Radius of each small sphere (r) = 2 cm

Formula Used:

Volume of a sphere = (4/3) × π × radius³

Calculations:

⇒ Volume of the large sphere = (4/3) × π × (12)³

⇒ Volume of one small sphere = (4/3) × π × (2)³

⇒ Let the number of smaller spheres be n.

⇒ Total volume of n small spheres = Volume of the large sphere

⇒ n × (4/3) × π × (2)³ = (4/3) × π × (12)³

⇒ n × 2³ = 12³

⇒ n × 8 = 1728

⇒ n = 1728 ÷ 8

⇒ n = 216

∴ The correct answer is 216.

Additional Information

Conservation of Volume

When a solid is melted and recast into other shapes, its total volume remains unchanged, provided there is no wastage of material.

Volume of a Sphere

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

Surface Area of a Sphere

The total surface area (A) of a sphere is 4πr². Unlike other solids, a sphere only has a curved surface area which is equal to its total surface area.

Hemisphere Properties

A hemisphere is half of a sphere. Its volume is (2/3)πr³ and its total surface area is 3πr².

Given:

Inner radius of hemispherical tank (r) = 3 m

Rate of filling = 1800π liters per minute

1 m³ = 1000 liters

We need to find the time required to fill the tank completely.

Formula used:

Volume of hemisphere = (2/3) π r³

Time = Volume / Rate

Calculations:

Step 1:Volume of hemisphere

= (2/3) π (3)³

= (2/3) π × 27

= 18π m³

Step 2:Convert volume into liters

18π m³ = 18π × 1000 liters

= 18000π liters

Step 3:Time required

Time = Volume / Rate

= 18000π / 1800π

π cancels out

= 18000 / 1800

= 10 minutes

∴ The correct answer is “Option 2.”

Given:

Recurring decimal = 0.454545…

Let, x = 0.454545…

Formula used:

For a recurring decimal with two repeating digits (ab),

If x = 0.ababab…, then

100x − x removes the repeating part.

Calculations:

x = 0.454545…

Multiply both sides by 100:

100x = 45.454545…

Now subtract: 100x − x

45.454545…

− 0.454545…

= 45

So, 99x = 45

x = 45 / 99

Simplify: Divide numerator and denominator by 9

45 ÷ 9 = 5

99 ÷ 9 = 11

x = 5 / 11

∴ The correct answer is “Option 2.”

Given:

Circumference of the circular sheet = 352 cm

Two identical circular plates of maximum size are cut from it.

Formula used:

Circumference of circle = 2πR

When two identical maximum circles are cut from a larger circle,

Diameter of each small circle = Radius of the large circle

Calculations:

Step 1: Find radius of the large circular sheet

2πR = 352

Using π = 22/7

2 × (22/7) × R = 352

(44/7)R = 352

R = 352 × 7 / 44

R = 8 × 7

R = 56 cm

Step 2: Diameter of each small plate = Radius of large circle

So, diameter of small circle = 56 cm

Radius of small circle = 56 / 2 = 28 cm

Step 3:Circumference of each small plate

= 2πr

= 2 × (22/7) × 28

= 44 × 4

= 176 cm

∴ The correct answer is “Option 1.”

Given:

$343 × (\sqrt{7})^n = 49^4$

Formula Used:

aⁿ × a^m = a^{n + m}

Calculation:

$343 × (\sqrt{7})^n = 49^4$

⇒ (7)³ + × (7)^n/2 = (7²)⁴

⇒ (7)^{3 + n/2} = (7)⁸

On equating, we get

3 + n/2 = 8

⇒ n/2 = 8 - 3

⇒ n/2 = 5

⇒ n = 10

Hence, the correct answer is option (2).

Given:

Slope of the line (m) = −5

Point through which the line passes = (2, 3)

Formula used:

Point–slope form of a line:

y − y₁ = m(x − x₁)

Calculations:

Step 1: Substitute the given values in the formula:

y − 3 = −5(x − 2)

Step 2: Simplify the equation:

y − 3 = −5x + 10

Step 3: Bring 3 to the right-hand side:

y = −5x + 13

∴ The correct answer is “Option 4.”

Shortcut Trick

Direct formula for the sum of squares: 2(a² + b²) = (a + b)² + (a − b)²

Direct formula for the product: 4ab = (a + b)² − (a − b)²

Given (a + b)² = 17 and (a − b)² = 1

⇒ a² + b² = (17 + 1) ÷ 2 = 9 and ab = (17 − 1) ÷ 4 = 4

Required value = (a² + b²) / ab = 9/4

∴ The correct answer is 9/4.

Alternate Method

Given:

a + b = √17

a − b = √1 = 1

Formula Used:

(a + b)² = a² + b² + 2ab

(a − b)² = a² + b² − 2ab

Calculations:

Squaring both given equations:

⇒ (a + b)² = (√17)² = 17

⇒ (a − b)² = (1)² = 1

Adding the two squared equations:

⇒ (a + b)² + (a − b)² = 2(a² + b²)

⇒ 17 + 1 = 2(a² + b²)

⇒ 18 = 2(a² + b²)

⇒ a² + b² = 9

Subtracting the two squared equations:

⇒ (a + b)² − (a − b)² = 4ab

⇒ 17 − 1 = 4ab

⇒ 16 = 4ab

⇒ ab = 4

Now, find the ratio:

⇒ (a² + b²) / ab = 9 / 4

∴ The correct answer is 9/4.

Additional Information

Standard Algebraic Identities

Useful relations include (a + b)² + (a − b)² = 2(a² + b²) and (a + b)² − (a − b)² = 4ab.

Sum and Product Relation

If the Sum (S) and Difference (D) of two numbers are known, then a² + b² = (S² + D²) ÷ 2 and ab = (S² − D²) ÷ 4.

Quadratic Roots

For a quadratic equation x² − (a+b)x + ab = 0, the values of a and b are the roots of the equation.

Given:

1 + sin(x) / 1 − cos(x) + 1 − sin(x) / 1 + cos(x)

Formula used:

sin²x + cos²x = 1

Rationalization using conjugate: (a / b) × (b / b)

Calculations:

(1 + sin x) / (1 − cos x)

Multiply numerator and denominator by (1 + cos x):

= (1 + sin x)(1 + cos x) / (1 − cos x)(1 + cos x)

= (1 + sin x)(1 + cos x) / (1 − cos²x)

Using identity: 1 − cos²x = sin²x

= (1 + sin x)(1 + cos x) / sin²x

Second term: (1 − sin x) / (1 + cos x)

Multiply numerator and denominator by (1 − cos x):

= (1 − sin x)(1 − cos x) / (1 + cos x)(1 − cos x)

= (1 − sin x)(1 − cos x) / (1 − cos²x)

= (1 − sin x)(1 − cos x) / sin²x

Now add both terms:

= [ (1 + sin x)(1 + cos x) + (1 − sin x)(1 − cos x) ] / sin²x

Expand both:

(1 + sin x)(1 + cos x)

= 1 + cos x + sin x + sin x cos x

(1 − sin x)(1 − cos x)

= 1 − cos x − sin x + sin x cos x

Now add:

= (1 + cos x + sin x + sin x cos x)

(1 − cos x − sin x + sin x cos x)

= 2 + 2 sin x cos x

So expression becomes:

= (2 + 2 sin x cos x) / sin²x

= 2(1 + sin x cos x) / sin²x

∴ The correct answer is “Option 2.”

Given:

tan(θ) = 12/5

Formula used:

tan(θ) = Perpendicular / Base

Hypotenuse² = Perpendicular² + Base² (Pythagoras Theorem)

Calculations:

tan(θ) = 12/5

So, Perpendicular = 12 units

Base = 5 units

Now using Pythagoras Theorem:

Hypotenuse² = 12² + 5²

Hypotenuse² = 144 + 25

Hypotenuse² = 169

Hypotenuse = √169

Hypotenuse = 13

∴ The correct answer is “Option 1.”

Shortcut Trick

Identify the Pythagorean Triplet: The set (5, 12, 13) satisfies the condition 5² + 12² = 13².

Given cos A = Base/Hypotenuse = 12/13, we directly identify Base = 12 and Hypotenuse = 13.

The Perpendicular must be 5 based on the triplet.

sin A = Perpendicular/Hypotenuse = 5/13 and cot A = Base/Perpendicular = 12/5.

∴ The correct answer is 5/13 and 12/5.

Alternate Method

Given: cos A = 12/13

Formula Used: sin A = Perpendicular (p) / Hypotenuse (h); cot A = Base (b) / Perpendicular (p); h² = p² + b²

⇒ In ΔABC, let Base (AB) = 12 and Hypotenuse (AC) = 13.

⇒ Using Pythagoras Theorem: AC² = AB² + BC²

⇒ 13² = 12² + BC²

⇒ 169 = 144 + BC²

⇒ BC² = 169 − 144 = 25

⇒ Perpendicular (BC) = √25 = 5

⇒ sin A = BC / AC = 5/13

⇒ cot A = AB / BC = 12/5

∴ The correct answer is 5/13 and 12/5.

Additional Information

Pythagorean Theorem

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: h² = p² + b².

Trigonometric Ratios

Basic ratios include sin θ = P/H, cos θ = B/H, tan θ = P/B, and their reciprocals cosec θ, sec θ, and cot θ = B/P.

Pythagorean Triplets

Common triplets used in exams include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

The correct answer is C. V. Raman.

Key Points

• National Science Day is celebrated on February 28 every year in India to commemorate the discovery of the Raman Effect by Sir C. V. Raman on this day in 1928.
• Raman was awarded the Nobel Prize in Physics in 1930 for his groundbreaking work on the scattering of light, which came to be known as the Raman Effect.
• The Raman Effect is a phenomenon in which light changes its wavelength when it passes through a transparent medium, leading to the discovery of molecular energy levels.
• The celebration of National Science Day is aimed at spreading awareness about the importance of science, technology, and innovation in daily life and encouraging the younger generation to pursue scientific careers.
• Every year, National Science Day is celebrated with a specific theme. For example, in 2023, the theme was "Global Science for Global Wellbeing."

Additional Information

• C. V. Raman:
• Born on November 7, 1888, in Tiruchirappalli, Tamil Nadu, India.
• He completed his education at Presidency College, Madras, and was a brilliant student in physics.
• In 1928, he discovered the Raman Effect, which became a cornerstone of modern physics and spectroscopy.
• He was the first Indian to win a Nobel Prize in Physics, establishing India's global reputation in scientific research.
• He was also awarded the Bharat Ratna, India’s highest civilian honor, in 1954.
• Raman Effect:
• The Raman Effect explains the scattering of light when it traverses a material medium and undergoes a change in energy and wavelength.
• This discovery opened up new avenues for studying molecular structures and has applications in fields such as chemistry, material science, and biology.
• The Raman Spectroscopy technique is widely used in various industries, including pharmaceuticals and environmental science.
• Other Notable Scientists Mentioned in the Options:
• Homi J. Bhabha: Known as the Father of India’s Nuclear Program; he was instrumental in establishing the Bhabha Atomic Research Centre (BARC).
• Vikram Sarabhai: Known as the Father of the Indian Space Program; he played a pivotal role in establishing ISRO (Indian Space Research Organisation).
• A. P. J. Abdul Kalam: Known as the Missile Man of India for his work on ballistic missile technology; he also served as the 11^th President of India.

Important Points

• National Science Day:
• Started in 1986 upon the recommendation of the National Council for Science and Technology Communication (NCSTC).
• It is an occasion to honor the contributions of Indian scientists and promote the importance of scientific research.
• Applications of Raman Effect:
• Used in chemical analysis to determine the composition of substances.
• Applied in forensic science for crime scene investigations.
• Widely utilized in astronomy to study the composition of distant celestial bodies.