SSC CHSL 2025 Tier-1 (Held On: 14 Nov, 2025 Shift 2) (Previous Year Paper)

The correct answer is 'had arrived'.

Key Points

• The sentence uses two actions in the past:
• The train leaving the station happened first.
• Our arrival happened later.
• The action that happened first should be in past perfect tense ("had left"), while the later action should be in simple past tense.
• Therefore, "had arrived" is incorrect and should be replaced with "arrived".
• Hence, the grammatical error is in Part D.

Therefore, the correct answer is Option 4.

Correct Sentence: "The train had left the station before we arrived."

Additional Information

• Past perfect tense is used for the action completed earlier in the past.
• Simple past tense is generally used for the later past action.
• Example: "She had eaten before I arrived."

The correct answer is: Option 2.

Key Points

• The idiom "stabbed him in the back" means to betray someone who trusts you. (पीठ में छुरा घोंपना)
• Example: She trusted her colleague, but he stabbed her in the back by taking credit for her work.
• "Showed her true colors" means to reveal one's real personality or intentions, often negative ones. (असली रूप दिखाना)
• Example: After months of pretending to be kind, she finally showed her true colors and betrayed her friends.
• The sentence implies that the person pretended for months but eventually betrayed someone. Hence, "stabbed him in the back" fits best.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Option 1: Played her cards right (अपने पत्ते सही से खेलना): To act cleverly and make the right decisions to achieve success. (समझदारी से काम लेना)
• Example: If you play your cards right, you might get promoted soon.
• Option 3: Took the bull by the horns (सांड को सींग से पकड़ना): To face a difficult situation directly and with courage. (किसी मुश्किल स्थिति का साहस के साथ सामना करना)
• Example: Instead of avoiding the issue, he took the bull by the horns and resolved it.
• Option 4: Burned the midnight oil (आधी रात तक काम करना): To work late into the night, usually studying or working hard. (रात देर तक काम करना)
• Example: She burned the midnight oil to prepare for her final exams.

The correct answer is: Meticulous.

Key Points

• The word "Fastidious" means showing or demanding excessive care or attention to detail; being very particular and hard to please. (अत्यधिक चुस्त, सूक्ष्म और कठिन-से-प्रसन्न)
• Example: She was fastidious about the cleanliness of her home, making sure every corner was spotless.
• "Meticulous" refers to showing great attention to detail; being very careful and precise. (बहुत सावधानीपूर्वक और बारीकी से काम करने वाला)
• Example: The artist was meticulous in his work, spending hours perfecting every detail of the painting.
• Since both "Fastidious" and "Meticulous" emphasize attention to detail and care, "Meticulous" is the correct synonym for "Fastidious".

Therefore, the correct answer is: Meticulous.

Additional Information

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

• Easygoing (निश्चिंत, आसान): Relaxed and unconcerned about rules or details.
• Example: He has an easygoing attitude and never gets stressed about deadlines.
• Indulgent (सहिष्णु, उदार): Being overly lenient or permissive, often to satisfy someone's desires.
• Example: The indulgent grandparents spoiled their grandchildren with sweets and toys.
• Careless (लापरवाह): Not giving sufficient attention or thought to avoiding harm or errors.
• Example: His careless mistake cost the team an important project.

The correct answer is: Option 3 (red herring).

Key Points

• The word "red herring" refers to something that misleads or distracts from the actual issue. (गुमराह करने वाला या ध्यान भटकाने वाला)
• Example: The politician introduced a red herring by discussing unrelated matters to avoid answering the tough question.
• In the context of the sentence, the CEO’s personal reasons were a distraction from the real reasons for his resignation.

Therefore, the correct answer is: Option 3 (red herring).

Additional Information

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

• Can of worms (मुसीबतों का पिटारा): Refers to a complicated or problematic situation that could lead to trouble.
• Example: Trying to change the law might open a can of worms for the government.
• Slip of the tongue (जुबान फिसलना): Refers to an unintentional mistake in speech.
• Example: His slip of the tongue revealed the surprise party plan.
• Feather in the cap (सम्मान की बात): Refers to an achievement or honor that adds prestige.
• Example: Winning the championship was a feather in his cap.

The correct answer is Option 2: To communicate a specific message or concept through visuals

 

Key Points

• The primary purpose of graphic design is to communicate a specific message or concept through visuals, making it a powerful tool for effective communication.
• While aesthetics are important, the focus of graphic design lies in delivering the intended message clearly and effectively.
• Design choices such as color, typography, and layout are made to support the message or idea being conveyed.
• Thus, the main goal of graphic design is not just to make designs look modern or follow trends, but to ensure that the message is communicated in a visually engaging and impactful way.

Therefore, the correct answer is Option 2.

 

Correct Explanation: Graphic design is a discipline that blends creativity and purpose. The design elements are intentionally chosen to communicate specific ideas, messages, or emotions to the target audience, ensuring clarity and engagement.

 

Additional Information

• Option 1: Creating aesthetically pleasing visuals is a part of graphic design, but it is secondary to the primary purpose of communication.
• Option 3: Making designs look modern is not the primary goal of graphic design; it is merely a style choice.
• Option 4: Following industry trends can enhance a design's relevance but is not the main objective of graphic design.

The correct answer is Option 1: Typography, color, images, and layout.

 

Key Points

• Graphic designers combine various elements to create visually appealing and effective messages.
• These elements include typography, color, images, and layout, which are essential for designing visual communication.
• Typography involves the style and arrangement of text to make it readable and visually engaging.
• Color is used to evoke emotions, create emphasis, and establish a visual hierarchy.
• Images, including illustrations and photography, add visual interest and convey meaning.
• The layout organizes these elements cohesively to guide the viewer's attention and ensure clarity.

Therefore, the correct answer is Option 1.

 

Correct Explanation: Graphic designers use typography, color, images, and layout to effectively communicate ideas and messages visually.

 

Additional Information

• Option 2: While videos, music, and text are used in multimedia design, they are not the primary elements of graphic design.
• Option 3: Design software is a tool for creating designs, but it is not an element of graphic design itself.
• Option 4: Photography, videos, and music are relevant to multimedia but do not encompass all essential elements of graphic design.

The correct answer is Option 3: To influence understanding, marketing, and branding.

 

Key Points

• Graphic design is a powerful tool used to influence understanding, marketing, and branding in everyday life.
• It helps in creating visually compelling messages that convey ideas and information effectively.
• Through logos, advertisements, product packaging, and digital content, graphic design plays a vital role in shaping consumer perceptions and behaviors.
• It connects businesses with their audiences by building a strong and recognizable brand identity.

Therefore, the correct answer is Option 3.

 

Correct Explanation: Graphic design is not just about aesthetics; it involves strategic visual communication to achieve specific goals such as marketing, branding, and influencing understanding.

 

Additional Information

• Option 1: While graphic design is used to entertain audiences and promote entertainment services, this is only one of its many applications.
• Option 2: Creating visual appeal without any specific function is not the primary purpose of graphic design. It is inherently functional and goal-oriented.
• Option 4: Improving aesthetic quality is a part of graphic design, but its scope extends far beyond just aesthetics.

The correct answer is Option 1: Fine eye for detail, good design principles comprehension, expertise in design tools.

 

Key Points

• A fine eye for detail is essential in graphic design to ensure precision and accuracy in designs.
• Good comprehension of design principles, such as balance, contrast, alignment, and hierarchy, is critical for creating visually appealing work.
• Expertise in design tools like Adobe Photoshop, Illustrator, and InDesign is necessary for executing creative ideas effectively.
• These skills are foundational for success in graphic design, making Option 1 the correct choice.

Therefore, the correct answer is Option 1.

 

Correct Explanation: Option 1 highlights the fundamental skills required for a successful graphic design career, focusing on attention to detail, design principles, and tool expertise.

 

Additional Information

• Option 2: While managing teams and writing compelling texts are valuable skills, they are not core to graphic design.
• Option 3: Knowledge of web coding, photography, and motion graphics is useful for specialized roles but not essential for all graphic designers.
• Option 4: Advanced software coding and web development fall outside the primary scope of graphic design.

The correct answer is Option 1: Combining creativity with visual communication to address real-world problems.

 

Key Points

• The job of a graphic designer fundamentally involves combining creativity with visual communication to address real-world problems.
• This means using design principles, tools, and skills to create visuals that effectively communicate ideas and solve specific challenges.
• Option 2 (Creating new art for art's sake) is incorrect because graphic design is purpose-driven and not solely about personal expression.
• Option 3 (Organizing visuals for minimalistic designs) is a subset of graphic design but does not encompass its broader scope.
• Option 4 (Following predefined rules) is incorrect because graphic design often requires flexibility and innovation.

Therefore, the correct answer is Option 1.

 

Correct Explanation: Graphic design is a discipline that blends creativity with strategic visual communication to solve problems and convey messages effectively across various mediums.

 

Additional Information

• Creativity: Graphic designers use their creative abilities to craft visually appealing and effective designs.
• Purpose-driven: Unlike art for personal expression, graphic design focuses on addressing specific communication goals and problems.
• Tools and Skills: Designers use software like Adobe Photoshop, Illustrator, and Figma to create their work.
• Flexibility: While design principles exist, graphic designers often need to adapt and innovate based on project requirements.

The correct answer is: Option 2.

Key Points

• The word "rose" in the provided sentence refers to a type of flower, specifically a red rose. (गुलाब)
• Example: He gave her a bouquet of roses for her birthday.
• In Option 2, the word "rose" is used with the same meaning, referring to a flower. (गुलाब)
• Example: The smell of the freshly cut rose filled the room.
• Hence, the correct answer is Option 2.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Option 1: "The water level rose quickly after the heavy rain." (बढ़ गया) — Here, "rose" is used to mean "increased" or "went up."

• Example: The temperature rose sharply during the summer months.

• Option 3: "Prices for gasoline rose sharply over the weekend." (बढ़ गया) — In this context, "rose" refers to the increase in prices.

• Example: The stock market rose significantly after the announcement of the new policy.

• Option 4: "The sun rose just as we were finishing our hike." (उगना) — Here, "rose" refers to the rising of the sun in the sky.

• Example: The sun rose early in the morning, spreading warmth across the valley.

The correct answer is option 1.

Key Points

The correctly spelled word is 'Delusion'.

• Delusion is a noun which means 'a false belief or opinion, often as a result of deception'. (भ्रम)
• For Example -
• She was under the delusion that she could finish the project in one day.

Therefore, the correct answer is 'Delusion'.

Additional Information

Let's understand why the other options are incorrect - 

• Dilusion - This is a misspelling of 'Delusion'.
• Delussion - This is also a misspelling of 'Delusion'.
• Delusian - This is an incorrect form of the word 'Delusion'.

The correct answer is option 2.

Key Points

The misspelled words are:

• Milenium instead of Millennium
• Millenniam instead of Millennium
• Millenium instead of Millennium

The correct spelling is 'Millennium'.

• Millennium is a noun that means 'a period of a thousand years'.
• For Example -
• The year 2000 marked the beginning of a new millennium.

Therefore, the correct answer is option 2: Millennium.

Additional Information

Key Spelling Tip:

• The word 'Millennium' is derived from the Latin word 'mille', meaning 'thousand', and 'annus', meaning 'year'.
• It has two 'l's and two 'n's, which are often misspelled.

The correct answer is: Option 1 i.e. "Increased and decreased".

Key Points

• The idiom "Waxed and waned" refers to something that alternately increases and decreases in size, strength, or intensity over a period of time. (बढ़ना और घटना)
• Example: His interest in the project waxed and waned over the years.
• "Increased and decreased" means a fluctuation between growing and diminishing, which is the exact meaning of the idiom "waxed and waned." (बढ़ा और घटा)
• Example: The company's sales figures waxed and waned with the changing market trends.

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: Grown steadily (लगातार बढ़ना): Refers to continuous or consistent growth without any decline.
• Example: His confidence has grown steadily since he started his new job.
• Option 3: Expanded and contracted rapidly (तेजी से फैलना और सिकुड़ना): Refers to something that increases and decreases quickly in size or volume.
• Example: The balloon expanded and contracted rapidly due to the air pressure changes.
• Option 4: Became fixed and stable (स्थिर और स्थायी हो गया): Refers to something becoming steady and unchanging.
• Example: After years of instability, his life finally became fixed and stable.

The correct answer is: Calligraphy.

Key Points

• The word "Calligraphy" refers to the art of beautiful handwriting, often created using special pens or brushes. (सुंदर लिखावट की कला)
• Example: She practiced calligraphy every day to perfect her skills for creating elegant wedding invitations.
• Calligraphy is a specialized skill that involves creating visually appealing text and is often used in decorative designs or artistic expressions. (सुंदर अक्षर लिखने की कला)
• Example: The museum displayed ancient calligraphy scrolls that showcased beautiful script styles.
• Hence, we can conclude that the art of beautiful handwriting is known as "Calligraphy".

Therefore, the correct answer is: Calligraphy.

Additional Information

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

• Orthography (वर्तनी): The conventional spelling system of a language.
• Example: The English orthography can be challenging for non-native speakers due to its irregularities.
• Lexicography (शब्दकोश निर्माण): The practice of compiling dictionaries.
• Example: He studied lexicography to understand how dictionaries are made.
• Etymology (शब्दों की उत्पत्ति का अध्ययन): The study of the origin and history of words.
• Example: Learning the etymology of a word can help you remember its meaning and origin.

The correct answer is: Option 1 (Corrupt).

Key Points

• The word "Upright" refers to a person who is honest, moral, and holds a high ethical standard. (ईमानदार, सच्चा, या नैतिक)
• Example: The upright judge was respected for his fairness and integrity in all cases.
• The word "Corrupt" is the antonym of upright and refers to someone or something that is dishonest, immoral, or engages in unethical practices. (भ्रष्ट)
• Example: The official was removed from his post due to his corrupt practices.
• Hence, the opposite of "Upright" is "Corrupt".

Therefore, the correct answer is: Option 1 (Corrupt).

Additional Information

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

• Honest (ईमानदार): Being truthful and sincere in one’s actions and words.
• Example: An honest person never hides the truth, even if it is inconvenient.
• Ethical (नैतिक): Following moral principles and doing what is right.
• Example: The company’s ethical policies ensured fair treatment of all employees.
• Noble (महान): Having or showing fine personal qualities or high moral principles.
• Example: The noble act of donating to charity inspired many people.

The correct answer is: Cataclysm.

Key Points

• The word "Cataclysm" means a sudden and violent event that causes great destruction or change. (प्रलय)
• Example: The earthquake was a cataclysm that devastated the entire region.
• The word "Cataclysm" signifies a disaster or upheaval of massive proportions, often leading to destruction and chaos. (प्रलय)
• Example: The volcanic eruption was a cataclysm that reshaped the landscape forever.
• Hence, we can infer that the correct one-word substitute for "A sudden and violent event causing great destruction" is "Cataclysm".

Therefore, the correct answer is: Cataclysm.

Additional Information

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

• Earthquake (भूकंप): A sudden shaking of the ground caused by movements within the earth's crust or volcanic action.
• Example: The earthquake destroyed many buildings in the city.
• Tsunami (सुनामी): A long high sea wave caused by an earthquake, submarine landslide, or other disturbances.
• Example: The tsunami swept away entire villages along the coast.
• Outbreak (प्रकोप): A sudden occurrence of something unwelcome, such as war or disease.
• Example: The outbreak of the epidemic spread fear among the population.

The correct answer is: Option 2 (Solitary).

Key Points

• The word "Gregarious" refers to someone who enjoys the company of others and is sociable. (सामाजिक)
• Example: John is gregarious and loves spending time with his friends at social gatherings.
• The word "Solitary" means someone who prefers to be alone, avoiding social interactions. (एकाकी)
• Example: After a long day at work, Sarah enjoys a solitary walk in the park to clear her mind.
• Hence, the opposite of "Gregarious" is "Solitary."

Therefore, the correct answer is: Option 2 (Solitary).

Additional Information

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

• Sociable (मिलनसार): Someone who enjoys being around people and is friendly in nature.
• Example: Emma is very sociable and can easily strike up a conversation with anyone.
• Friendly (मित्रवत): Someone who is kind, pleasant, and helpful.
• Example: The new neighbor is very friendly and always greets everyone with a smile.
• Outgoing (बहिर्मुखी): Someone who is extroverted and enjoys interacting with others.
• Example: Being outgoing, Alex finds it easy to make new friends wherever he goes.

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.
• Active voice structure: The subject of the sentence performs the action on the object.
• In the given passive sentence: "Why had the highly sensitive company report been rejected by the board of directors?"
• To convert this into active voice, the subject "the board of directors" must perform the action "rejected" on the object "the highly sensitive company report."
• The correct active voice sentence is: "Why had the board of directors rejected the highly sensitive company report?"

Therefore, the correct answer is Option 1.

 

Correct Sentence: "Why had the board of directors rejected the highly sensitive company report?"

 

Additional Information

• Option 2: "Why the board of directors had rejected the highly sensitive company report?" – Incorrect word order.
• Option 3: "The board of directors had rejected the highly sensitive company report, why?" – Incorrect structure and punctuation.
• Option 4: "Why did the board of directors reject the highly sensitive company report?" – Incorrect tense (simple past instead of past perfect).

The correct answer is Option 2.

 

Key Points

• Indirect Speech: The captain said that they had been sailing in those choppy waters for two days, and they expected that the storm, which was then on the horizon, would hit them in a few hours.
• Key Conversions:
• Pronoun Changes:
• "We" becomes "they" to match the third person in reported speech.
• "these" becomes "those" to reflect the change in perspective.
• Tense Changes:
• Present perfect "have been sailing" changes to past perfect "had been sailing" in reported speech.
• Present simple "expect" changes to past simple "expected."
• Future "will hit" changes to conditional "would hit" in reported speech.
• Present "is now" changes to past "was then" to reflect the past timeline.
• Reporting Verb:
• The reporting verb "said" is used to introduce the indirect speech without altering the tone.
• Punctuation and Format:
• Quotation marks are removed in indirect speech.
• The sentence structure is adjusted for grammatical correctness in reported speech.

Therefore, the correct answer is Option 2.

 

Correct Sentence: The captain said that they had been sailing in those choppy waters for two days, and they expected that the storm, which was then on the horizon, would hit them in a few hours.

 

Additional Information

• Option 1: The captain said that they have been sailing in these choppy waters for two days, and they expect that the storm, which is now on the horizon, will hit them in a few hours.
• Incorrect tense usage: "have been sailing" should change to "had been sailing," and "expect" should change to "expected."
• Words "these" and "is now" are not adjusted to "those" and "was then."
• Option 3: The captain said that they had been sailing in these choppy waters for two days, and they expected that the storm, which was then on the horizon, would hit them in a few hours.
• Incorrect usage of "these" instead of "those" for reported speech.
• Option 4: The captain said that they had been sailing in those choppy waters for two days, and they expected that the storm, which is now on the horizon, will hit them in a few hours.
• Incorrect tense usage: "is now" should change to "was then," and "will hit" should change to "would hit."

The correct answer is 'in a green dress, walked the dog'.

 

Key Points

• The placement of the phrase "in a green dress" is crucial for the correct sentence structure and clarity.
• Option 3: "in a green dress, walked the dog" correctly places the modifying phrase "in a green dress" near the subject "The girl," ensuring the sentence is unambiguous.
• Options 1, 2, and 4 are incorrect as they either imply the dog is wearing the dress or create an awkward sentence structure.

Therefore, the correct answer is Option 3.

 

Complete Sentence: "The girl, in a green dress, walked the dog."

 

Additional Information

• Option 1: "walk the dog, in a green dress" is incorrect as it suggests the dog is wearing the dress.
• Option 2: "walking the dog, in a green dress" is incorrect as it changes the tense and meaning of the sentence.
• Option 4: "in a green dress, walking the dog" is incorrect as it creates an incomplete and unclear sentence structure.

The correct answer is 'Of norms'.

 

Key Points

• The phrase "of norms" is the most appropriate replacement for "normal" in the sentence, as it accurately conveys the intended meaning of the relaxation being applied to the rules or regulations in question.
• Option 1 ("To norms") is incorrect because "to" does not fit the context of the sentence.
• Option 2 ("In normal") is incorrect because "normal" is not the correct word to describe the context of rules or regulations.
• Option 4 ("By normal") is incorrect as it does not convey the intended meaning of relaxation in rules.

Therefore, the correct answer is Option 3.

 

Complete Sentence: "The next stage for the banking sector has been set up, with proposed relaxation of norms for foreign direct investment."

 

Additional Information

• Option 1: "To norms" is incorrect as "to" does not suit the context of the sentence.
• Option 2: "In normal" is incorrect because "normal" cannot replace "norms" in this context.
• Option 4: "By normal" is incorrect as it misrepresents the intended meaning of the relaxation in question.

The correct answer is Option 2.

 

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the active voice, the sentence is: "The chef had prepared the special dish."
• To convert to passive voice: Place the object "the special dish" at the beginning.
• Change the active verb form "had prepared" to "had been prepared" (past perfect passive).
• Add the preposition "by" followed by the original subject "the chef."

Therefore, the correct answer is Option 2.

 

Correct Sentence: "The special dish had been prepared by the chef."

 

Additional Information

• Option 1: "The special dish was prepared by the chef." – Incorrect tense (past simple passive).
• Option 3: "The special dish has been prepared by the chef." – Incorrect tense (present perfect passive).
• Option 4: "The special dish is being prepared by the chef." – Incorrect tense (present continuous passive).

The correct answer is Option 1.

 

Key Points

• Indirect Speech: The scientist announced that the new compound would react violently if it came into contact with water, and that they had been observing its properties for months.
• Key Conversions:
• "The new compound would react violently" becomes "The new compound will react violently"
• The modal verb "would" is converted to "will" to reflect direct speech.
• The tense is changed to match the direct speech.
• "if it came into contact" becomes "if it comes into contact"
• The verb "came" is converted to "comes" to align with the direct speech present tense.
• "they had been observing" becomes "we have been observing"
• The pronoun "they" is changed to "we" to reflect the first person in direct speech.
• The past perfect continuous "had been observing" is converted to present perfect continuous "have been observing" in direct speech.
• Punctuation and Format:
• Direct speech is enclosed in quotation marks.
• Starts with a capital letter "The" and ends with a period ".".
• Reporting clause precedes the quoted speech, followed by a comma.

Therefore, the correct answer is Option 1.

 

Correct Sentence: "The scientist announced, ‘The new compound will react violently if it comes into contact with water, and we have been observing its properties for months.’"

 

Additional Information

• Option 2: "The scientist announced, 'The new compound will react violently if it came into contact with water, and we have been observing its properties for months.'"
• The clause "if it came into contact" is incorrect as it uses the past tense instead of the present tense in direct speech.
• Option 3: "The scientist announced, 'The new compound would react violently if it came into contact with water, and we were observing its properties for months.'"
• The modal verb "would" and the tense "we were observing" are incorrect as they do not match the direct speech format.
• Option 4: "The scientist announced, 'The new compound will react violently if it comes into contact with water, and we had been observing its properties for months.'"
• The tense "we had been observing" is incorrect as it does not match the present perfect continuous tense in direct speech.

The correct answer is Option 3.

Key Points

• The paragraph describes the step-by-step approach a director takes to bring a play to life.
• Sentence P is the first sentence as it introduces the initial step of casting the actors for the play:
• "She selected the ideal candidate for each character by casting the actors."
• Sentence Q follows as it elaborates on how the director helps the actors during the rehearsal process:
• "She helped them discover their voices and goals while guiding them through the rehearsal process."
• Sentence R is the third sentence because it explains how the director collaborates with set and lighting designers to create the desired atmosphere:
• "She collaborated with the set and lighting designers to achieve the ideal ambience."
• Sentence S is the final sentence as it concludes the paragraph by describing the culmination of the director's efforts on opening night:
• "She witnessed her actors realise her vision in front of an audience on opening night."
• The correct sequence is P, Q, R, S.

Coherent paragraph after rearrangement:

"She selected the ideal candidate for each character by casting the actors. She helped them discover their voices and goals while guiding them through the rehearsal process. She collaborated with the set and lighting designers to achieve the ideal ambience. She witnessed her actors realise her vision in front of an audience on opening night."

The correct answer is Option 1.

Key Points

• The paragraph begins with Sentence Q as it introduces the invention of the telegraph and its significance in history.
• Sentence Q is the first sentence because it sets the context for the importance of the telegraph:
• "The invention of the telegraph was one of the most remarkable technological advances of the 19^th century."
• Sentence P follows as it explains how the telegraph became important for long-distance communication:
• "It soon became a very important tool for long-distance information communication."
• Sentence R comes next because it describes how the telegraph connected cities and continents, influencing daily life:
• "In linking cities and even continents with its cable and signal networks, it transformed the rhythm of life."
• Sentence S concludes by elaborating on how the telegraph revolutionized politics, business, and warfare:
• "This rate of communication had a revolutionary effect on the conduct of politics, business, and warfare."
• The correct sequence is Q, P, R, S.

Coherent paragraph after rearrangement:

"The invention of the telegraph was one of the most remarkable technological advances of the 19^th century. It soon became a very important tool for long-distance information communication. In linking cities and even continents with its cable and signal networks, it transformed the rhythm of life. This rate of communication had a revolutionary effect on the conduct of politics, business, and warfare."

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

For MEASURE : PHDVXUH

Similarly, applying the same logic to CULTURE:

 

 The resulting code is FXOWXUH.

Hence, the correct answer is "Option 1".

Given:

The logic followed here is:

For REFRIGERATOR : SFGSJHFSBUPS

For MICROWAVE : NJDSPXBWF

Similarly, for DISHWASHER:

The resulting code is EJTIXBTIFS.

Hence, the correct answer is "Option 1".

The logic followed here is:

Given word: MATHEMATICS

Code pattern: Each letter is shifted +1 in the alphabet (A → B, B → C, …).

Option 1) NBUIFNBUJDT

→ M→N, A→B, T→U, H→I, E→F, M→N, A→B, T→U, I→J, C→D, S→T → Matches the pattern → Correct

Option 2) NBUJFNBUHDT

→ Last few letters do not match the +1 shift → Incorrect

Option 3) NBUJFNBUJFT

→ Last letters incorrect (S→T, not F) → Incorrect

Option 4) NBUJFMBJDT

→ Middle letters do not match the pattern → Incorrect

Hence, the correct answer is "Option 1".

Given Statement:

Urban air pollution has reached alarming levels in several metropolitan cities, prompting governments to implement stricter vehicle emission standards. While electric vehicle adoption is increasing gradually, many consumers still hesitate due to concerns about charging infrastructure and higher upfront costs. Industrial emissions also contribute significantly to air quality deterioration, requiring comprehensive policy reforms beyond just transportation sector changes.

Conclusions:

(I) Vehicle emissions are the primary cause of urban air pollution – False (The statement mentions vehicle emissions and industrial emissions, so we cannot say vehicle emissions are the primary cause).

(II) Electric vehicle adoption faces practical barriers despite environmental benefits – True (The statement mentions hesitation due to charging infrastructure and higher costs).

(III) Solving air pollution requires multi-sectoral policy interventions – True (The statement mentions industrial emissions and need for policy reforms beyond transportation).

So, Both conclusions II and III follow.

Hence, the correct answer is "Option 3".

Given: A man finds a lost wallet in the park with cash and an ID card.

Now,

The most ethical action is to use the ID to contact the owner or report it to the authorities, ensuring the wallet is returned to its rightful owner.

Hence, the correct answer is Option 3.

BODMAS Table: 

Given equation: 11 # 14 * 10 $ 9 = ?

Now, ‘*’ stands for ‘÷’, ‘%’ stands for ‘+’, ‘#’ stands for ‘−’and ‘$’ stands for ‘×’

So, the expression becomes:

⇒ 11 − 14 ÷ 10 × 9 = ?

Now apply BODMAS:

⇒ 11 − (14 ÷ 10 × 9)

⇒ 11 − (7/5 × 9)

⇒ 11 − (63/5)

⇒ (55 - 63)/5 = -8/5

Hence, the correct answer is -8/5.

BODMAS Table: 

Given equation: 3 % 14 & 5 @ 12 = ?

Now, ‘@’ stands for ‘+’,‘%’ stands for ‘−’,‘?’ stands for ‘×’ and ‘&’ stands for ‘÷’

So, the expression becomes:

⇒ 3 − 14 ÷ 5 + 12 = ?

Now apply BODMAS:

⇒ 3 − (14 ÷ 5) + 12

⇒ 3 − 14/5 + 12

Convert 3 and 12 into fraction form:

⇒ 15/5 − 14/5 + 60/5

⇒ (15 − 14 + 60) / 5

⇒ 61/5

Hence, the correct answer is "Option 3".

Given:

A classmate is being excluded from group study due to a rumor.

The socially responsible action is to act with empathy, fairness, and maturity.

1. Ignore the situation entirely — This avoids responsibility and allows unfair treatment to continue.
2. Join in excluding them to fit in — This supports bullying and unethical behavior.
3. Spread a counter-rumor — This worsens the situation and promotes more negativity.
4. Check with the classmate privately and include them while discouraging rumor spreading — This shows empathy, verifies facts, supports inclusion, and discourages harmful behavior.

Hence, the correct answer is "Option 4".

Given: Total players = 28

Player X is 11^th from the start.

Player Y is 7^th from the end.

So, position of Y from the start = 28 − 7 + 1

= 22

Now, players between X and Y = 22 − 11 − 1

= 10

So, there are '10' players standing between X and Y.

Hence, the correct answer is "Option 2".

Given: Total bulbs = 20

Red bulb is 5^th from the left.

Blue bulb is 8^th from the right.

So, position of blue bulb from the left = 20 − 8 + 1

= 13

Now, bulbs between red and blue = 13 − 5 − 1

= 7

So, there are '7' bulbs between red and blue.

Hence, the correct answer is "Option 3".

Given:

Statement: Should plastic bottles be completely banned?

Now, Arguments:

I. Yes, they pollute the environment – True (This is a strong argument as banning plastic bottles would directly address environmental pollution caused by plastics).

II. No, people still need an affordable container option – True (This is also a strong argument as it considers practical implications and the need for alternatives before banning).

So, Both arguments I and II are strong.

Hence, the correct answer is "Option 3".

Given:

Statement: Should social media platforms be strictly regulated to curb misinformation?

Now, Arguments:

I. Yes, misinformation spreads quickly and can cause harm to society – True (This is a strong argument as regulating platforms can help prevent societal harm caused by false information).

II. No, strict regulation may violate freedom of speech – True (This is also a strong argument as it considers the important legal and ethical implications of regulating speech).

So, Both arguments I and II are strong.

Hence, the correct answer is "Option 3".

The logic followed here is:

So, 'W' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

The logic followed here is:

So, 'T' will replace the question mark in the given series.

Hence, the correct answer is "Option 2".

Given:

A local government is planning to develop a public park in a densely populated urban area. However, the land proposed is currently used by street vendors and hawkers for their livelihood.

Judgement:

Option 1) Cancel the park project entirely – Weak (This ignores the public benefit of a park).

Option 2) Evict the vendors immediately and start construction – Weak (This disregards the livelihoods of the vendors and may cause social unrest).

Option 3) Relocate vendors to an alternative space and proceed with the park development – Strong (This balances public interest with the rights and livelihood of the vendors).

Option 4) Build a wall around the area to separate the park from the vendors – Weak (This does not address the issue of land use and vendor livelihoods effectively).

Hence, the correct answer is "Option 3".

Given word: PORTFOLIO

Check each option:

Option 1) FORT

→ Letters F, O, R, T are in PORTFOLIO → Can be formed

Option 2) PORTICO

→ Letters P, O, R, T, I, C, O → Letter C is not in PORTFOLIO → Cannot be formed

Option 3) RIFT

→ Letters R, I, F, T are in PORTFOLIO → Can be formed

Option 4) ROOF

→ Letters R, O, O, F are in PORTFOLIO → Can be formed

Hence, the correct answer is "Option 2".

Given: An NGO’s volunteers have overlapping roles, causing confusion.

Now,

The best way to resolve this problem is to define clear responsibilities using a simple responsibility matrix.

This approach clarifies who does what, reduces confusion, and improves efficiency.

Continuously replacing volunteers or leaving it to volunteers to decide can create more disorder, and doing nothing accepts inefficiency.

Hence, the correct answer is Option 1.

The logic followed here is:

Logic: In the first pair, the first letter increases by +2 and the second letter decreases by −2 in the English alphabetical order.

Here, AZ : CX

Similarly, BY : ?

So, BY becomes DW.

Hence, the correct answer is "Option 4.".

The logic followed here is:

Logic: In the first pair, the first letter decreases by −1, while the second letter remains the same.

Here, DE : CE

E → E (no change)

Similarly, FG : ?

G → G (no change)

So, FG becomes EG.

Hence, the correct answer is "Option 1."

The logic followed here is:

Thus, "214" will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

The logic followed here is:

Thus, "136" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

The logic followed here is:

thus, "2301" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

The logic followed here is:

Each pair consists of two consecutive perfect cubes, where the numbers follow the pattern n³ : (n+1)³.

1. 8 : 27 → 2³ : 3³ (Follows the pattern)

2. 1 : 8 → 1³ : 2³ (Follows the pattern)

3. 27 : 64 → 3³ : 4³ (Follows the pattern)

Whereas,

3. 8 : 26 → 2³ : 26. Since 26 is not a perfect cube (it should be 27), this pair does not follow the pattern.

So, 8 : 26 is the odd pair from the given options.

Hence, the correct answer is "Option 3".

Correct Option – 2

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

Enterprise → 2

Entertainment → 1

Entitlement → 3

Entrepreneurial → 4

Environment → 5

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

Hence, the correct answer is "Option (2)".

Correct Option – 2

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

Language → 2

Lawyer → 1

Leather → 3

Liberty → 4

Listen → 5

Little → 6

The correct order is '2, 1, 3, 4, 5, 6'.

Hence, the correct answer is "Option (2)".

Given:

P, Q, and R started a business.

P’s monthly salary = 2000

P’s annual salary = 2000 × 12 = 24000

Investments:

P = 50000

Q = 60000

R = 70000

Total earning of P at the end of the year = 40000

Formula used:

Total earning of P = Salary + Share from remaining profit

Calculations:

P’s total earning = 40000

Salary received by P = 24000

Therefore, Share of P from remaining profit = 40000 − 24000

= 16000

Now, remaining profit is divided in the ratio of investments.

Investment ratio:

50000 : 60000 : 70000

= 5 : 6 : 7

Total ratio = 5 + 6 + 7 = 18

P’s share = 5/18 of remaining profit

So, 5/18 × Remaining Profit = 16000

Remaining Profit = 16000 × 18 / 5

= 16000 × 3.6

= 57600

Now, Total Profit = Salary paid to P + Remaining Profit

= 24000 + 57600

= 81600

∴ The correct answer is “Option 3.”

Given:

cosA = $\frac{5}{13}$

sinB = $\frac{12}{13}$

Formula used:

sinA cosB + cosA sinB = $\sin(A+B)$

Where, sinA = $\sqrt{1-\cos^2A}$

cosB = $\sqrt{1-\sin^2B}$

Calculations:

sinA = $\sqrt{1-\left(\frac{5}{13}\right)^2}$

⇒ sinA = $\sqrt{1-\frac{25}{169}}$

⇒ sinA = $\sqrt{\frac{144}{169}}$

⇒ sinA = $\frac{12}{13}$

cosB = $\sqrt{1-\left(\frac{12}{13}\right)^2}$

⇒ cosB = $\sqrt{1-\frac{144}{169}}$

⇒ cosB = $\sqrt{\frac{25}{169}}$

⇒ cosB = $\frac{5}{13}$

sinA cosB + cosA sinB = $\frac{12}{13} \times \frac{5}{13} + \frac{5}{13} \times \frac{12}{13}$

⇒ $\frac{60}{169} + \frac{60}{169}$

⇒ $\frac{120}{169}$

∴ The correct answer is option (1).

Given:

Selling price of first sugar (SP₁) = ₹40 per kg

Profit on first sugar = 25%

Selling price of second sugar (SP₂) = ₹30 per kg

Loss on second sugar = 25%

Equal quantities are mixed.

Selling price of mixture = ₹36 per kg

Formula used:

SP = CP × (1 + Profit%)

SP = CP × (1 − Loss%)

Profit% or Loss% = (Profit or Loss / Total CP) × 100

Calculations:

Step 1: Find Cost Price (CP) of first sugar

SP₁ = CP₁ × (1 + 25/100)

40 = CP₁ × (125/100)

40 = CP₁ × 1.25

CP₁ = 40 / 1.25

CP₁ = 32

So, CP₁ = ₹32 per kg

Step 2: Find Cost Price (CP) of second sugar

SP₂ = CP₂ × (1 − 25/100)

30 = CP₂ × (75/100)

30 = CP₂ × 0.75

CP₂ = 30 / 0.75

CP₂ = 40

So, CP₂ = ₹40 per kg

Step 3: Since equal quantities are mixed

Average CP of mixture

= (32 + 40) / 2

= 72 / 2

= ₹36 per kg

Step 4: Compare with selling price of mixture

SP of mixture = ₹36 per kg

CP of mixture = ₹36 per kg

Profit/Loss = SP − CP

= 36 − 36

= 0

Profit/Loss percentage

= (0 / 36) × 100

= 0%

∴ The correct answer is “Option 3.”

Given:

Amount at the end of 2^nd year (A₂) = ₹4232

Amount at the end of 3^rd year (A₃) = ₹4655.20

Formula used:

In Compound Interest, A₃ = A₂ (1 + r/100)

Calculations:

4655.20 = 4232 (1 + r/100)

Divide both sides by 4232:

4655.20 / 4232 = 1 + r/100

1.10 = 1 + r/100

r/100 = 1.10 − 1

r/100 = 0.10

r = 10%

∴ The correct answer is “Option 4.”

Given:

Sum of three numbers = 180

Ratio of first to second = 3 : 5

Ratio of second to third = 4 : 7

Formula used:

If ratios are given separately, make the common term (second number) equal and then form a single ratio.

Calculations:

First : Second = 3 : 5

Second : Third = 4 : 7

Make the second term same in both ratios.

LCM of 5 and 4 = 20

Multiply first ratio by 4:

3 × 4 : 5 × 4 = 12 : 20

Multiply second ratio by 5:

4 × 5 : 7 × 5 = 20 : 35

Now combined ratio:

First : Second : Third = 12 : 20 : 35

Total parts = 12 + 20 + 35 = 67

Let each part = x

Then, 67x = 180

x = 180 / 67

x ≈ 2.686

Second number = 20x

= 20 × 2.686

≈ 53.73

∴ The correct answer is “Option 2.”

Given:

Total students = 7

Boys = 4, Girls = 3

Average spending of all = ₹120

Average spending of boys = ₹150

Formula used:

Total spending = Average × Total students

Spending of girls = Total spending - Spending of boys

Average spending of girls = Spending of girls ÷ Number of girls

Calculation:

Total spending = 120 × 7

⇒ Total spending = ₹840

Spending of boys = 150 × 4

⇒ Spending of boys = ₹600

Spending of girls = 840 - 600

⇒ Spending of girls = ₹240

Average spending of girls = 240 ÷ 3

⇒ Average spending of girls = ₹80

∴ The correct answer is option (3).

Given:

Length of courtyard = 3.78 m

Breadth of courtyard = 5.25 m

Tiles are square and of same size.

To find: Largest size of the tile.

Formula used:

Largest size of square tile = HCF of length and breadth (in same units)

Calculations:

Step 1: Convert meters to centimeters

Length = 3.78 m = 378 cm

Breadth = 5.25 m = 525 cm

Step 2: Find HCF of 378 and 525

Using Euclid’s method:

525 ÷ 378 = 1 remainder 147

378 ÷ 147 = 2 remainder 84 → Wait let's check carefully:

Actually, 378 ÷ 147 = 2 × 147 = 294, remainder 378 − 294 = 84 

147 ÷ 84 = 1 remainder 63

84 ÷ 63 = 1 remainder 21

63 ÷ 21 = 3 remainder 0 

So, HCF = 21 cm

∴ The correct answer is “Option 2.”

Given:

Initial Value (P) = ₹80,000

Depreciation Rate (r) = 10%

Time (t) = 3 years

Formula used:

A = P × (1 - r/100)^t

Calculations:

A = 80,000 × (1 - 10/100)³

⇒ A = 80,000 × (1 - 0.1)³

⇒ A = 80,000 × 0.9³

⇒ A = 80,000 × 0.729

⇒ A = ₹58,320

∴ The correct answer is option (2).

Given:

A completes work in = 12 days

B completes work in = 24 days

Both work together for = 4 days

Calculation:

LCM of 12 and 24 = 24 units (Total work)

Efficiency of A = 24 ÷ 12 = 2 units/day

Efficiency of B = 24 ÷ 24 = 1 unit/day

Combined efficiency = 2 + 1 = 3 units/day

Work done in 4 days = 3 × 4 = 12 units

Remaining work = 24 − 12 = 12 units

Now B alone works = Efficiency of B = 1 unit/day

Time to finish remaining work = 12 ÷ 1 = 12 days

∴ B will finish the job in 12 more days.

Given:

Marked Price (MP) = 140% of Cost Price (CP)

Discount = 15%

Calculations:

SP = MP × (1 - Discount)

⇒ SP = 140 × (1 - 0.15)

⇒ SP = 140 × 0.85

⇒ SP = 119% of CP

Profit Percentage = $\frac{\text{SP} - \text{CP}}{\text{CP}}$ × 100

⇒ Profit Percentage = $\frac{119 - 100}{100}$ × 100

⇒ Profit Percentage = 19%

∴ The correct answer is option (2).

Given:

Total investment = 25000

Rate A = 4%

Rate B = 6.5%

Time = 3 years

Total interest = 3975

Formula used:

SI = P × R × T ÷ 100

Calculation:

Let amount in A = x

Then amount in B = 25000 − x

Interest from A ⇒ x × 4 × 3 ÷ 100 = 12x ÷ 100

Interest from B ⇒ (25000 − x) × 6.5 × 3 ÷ 100

⇒ (25000 − x) × 19.5 ÷ 100

Total interest ⇒ 12x ÷ 100 + 19.5(25000 − x) ÷ 100 = 3975

Multiply by 100

⇒ 12x + 19.5(25000 − x) = 397500

⇒ 12x + 487500 − 19.5x = 397500

⇒ −7.5x + 487500 = 397500

⇒ −7.5x = −90000

⇒ x = 12000

∴ Amount invested in Account A = ₹12000.

Given:

x + y + z = 16

xy + yz + zx = 75

Formula used:

(x + y + z)² =x²+y²+z²+2(xy + yz + zx)

Calculations:

2(xy + yz + zx) = 2 × 75 = 150

$x^2 + y^2 + z^2 = (x + y + z)^2 - 2(xy + yz + zx)$

$x^2 + y^2 + z^2 = 256 - 150$

x²+ y² + z² = 106

∴ The correct answer is “Option 1.”

Shortcut Trick

The smallest number divisible by both 16 and 36 is their Least Common Multiple (LCM).

LCM of 16 and 36 → 16 × 9 = 144.

Check if 144 is a perfect square: √144 = 12.

Since 144 is already a perfect square, it is the smallest such number.

∴ The correct answer is 144.

Alternate Method

Given: Numbers are 16 and 36.

Formula Used: Prime factorization and LCM.

⇒ Prime factorization of 16 = 2 × 2 × 2 × 2 = 2⁴

⇒ Prime factorization of 36 = 2 × 2 × 3 × 3 = 2² × 3²

⇒ LCM (16, 36) = 2⁴ × 3² = 16 × 9 = 144

⇒ For a number to be a perfect square, all exponents in its prime factorization must be even.

⇒ In 144 = 2⁴ × 3², the exponents 4 and 2 are both even.

⇒ Thus, 144 is a perfect square (12²).

∴ The correct answer is 144.

Additional Information

Perfect Square Property

A number is a perfect square if and only if every prime factor in its prime factorization occurs an even number of times (e.g., n = p^2a × q^2b).

Least Common Multiple (LCM)

The LCM of two numbers is the smallest positive integer that is divisible by both. It is found by taking the highest power of every prime factor present in the numbers.

Smallest Square Multiple Rule

To find the smallest perfect square divisible by certain numbers, first find their LCM. If any prime factor in the LCM has an odd exponent, multiply the LCM by that factor to make the exponent even.

Given:

Total mixture = 80 liters

Ratio (acid : water) = 7 : 9

Acid added = 8 liters

Formula used:

Quantity = (Ratio part ÷ Total ratio) × Total

Calculation:

Total ratio = 7 + 9 = 16

Initial acid ⇒ 7 ÷ 16 × 80 = 35 liters

Initial water ⇒ 9 ÷ 16 × 80 = 45 liters

After adding acid = 35 + 8 = 43 liters

Water = 45 liters

New ratio ⇒ 43 : 45

∴ New ratio = 43 : 45.

Given:

Side of square = 14 cm

Circle is inscribed in the square

Formula used:

Area of circle = π × r²

Calculation:

Diameter of circle = Side of square = 14 cm

⇒ Radius r = 14 ÷ 2 = 7 cm

Area of circle

⇒ (22 ÷ 7) × 7 × 7

⇒ 22 × 7

⇒ 154 cm² ≈ 153. 94 $cm^2$

∴ The correct answer is option 4.

Given:

Radius of sphere = $r$

Radius of cylinder = $2r$

Height of cylinder = $h$

Formula used:

Volume of sphere = $\frac{4}{3}\pi r^3$

Volume of cylinder = $\pi R^2 h$

As the sphere is melted and recast into a cylinder:

Volume of sphere = Volume of cylinder

Calculations:

$\frac{4}{3}\pi r^3 = \pi (2r)^2 h$

⇒ $\frac{4}{3}r^3 = 4r^2 h$

⇒ $\frac{4r^3}{3} = 4r^2 h$

⇒ $\frac{r}{3} = h$

⇒ $h:r = 1:3$

∴ The correct answer is option (2).

Given:

Let the radius of the solid hemisphere and sphere be r.

Total Surface Area of Hemisphere (TSA) = Volume of Sphere (V)

Formula used:

TSA of Hemisphere = 3πr²

Volume of Sphere = (4/3)πr³

Calculation:

3πr² = (4/3)πr³

⇒ 3r² = (4/3)r³

⇒ 9r² = 4r³ (Multiplying both sides by 3)

⇒ r = 9/4

⇒ r = 2.25

∴ The correct answer is option (1).

Shortcut Trick

Check options based on the given conditions:

Condition 1: Denominator − Numerator = 5. In option (3), 12 − 7 = 5.

Condition 2: Add 3 to both: (7 + 3) ÷ (12 + 3) = 10 ÷ 15 = 2/3.

The fraction 7/12 satisfies both the conditions perfectly.

∴ The correct answer is 7/12.

Alternate Method

Given: Difference between denominator and numerator = 5. Resultant fraction after adding 3 to both = 2/3.

Formula: Original Fraction = Numerator / Denominator

Let the numerator be x.

Then the denominator = x + 5.

Original fraction = x / (x + 5)

According to the question:

⇒ (x + 3) / (x + 5 + 3) = 2/3

⇒ (x + 3) / (x + 8) = 2/3

⇒ 3 × (x + 3) = 2 × (x + 8)

⇒ 3x + 9 = 2x + 16

⇒ 3x − 2x = 16 − 9

⇒ x = 7

Numerator = 7

Denominator = 7 + 5 = 12

∴ The correct answer is 7/12.

Additional Information

Proper Fraction

A fraction where the numerator is less than the denominator (e.g., 7/12).

Improper Fraction

A fraction where the numerator is greater than or equal to the denominator (e.g., 12/7).

Equivalent Fractions

Fractions that represent the same value even though they look different, found by multiplying/dividing numerator and denominator by the same number.

Reciprocal

The reciprocal of a fraction a/b is b/a. The product of a fraction and its reciprocal is always 1.

Given:

b − 1/b = 3

Formula used:

(b − 1/b)² = b² + 1/b² − 2

(b² + 1/b²)² = b⁴ + 1/b⁴ + 2

(b² + 1/b²)(b⁴ + 1/b⁴) = b⁶ + 1/b⁶ + b² + 1/b²

Calculation:

(b − 1/b)² = 3²

⇒ b² + 1/b² − 2 = 9

⇒ b² + 1/b² = 11

Now, (b² + 1/b²)² = 11²

⇒ b⁴ + 1/b⁴ + 2 = 121

⇒ b⁴ + 1/b⁴ = 119

Now

(b² + 1/b²)(b⁴ + 1/b⁴)

⇒ 11 × 119 = 1309

⇒ b⁶ + 1/b⁶ + 11 = 1309

⇒ b⁶ + 1/b⁶ = 1309 − 11

⇒ 1298

∴ Required value = 1298.

Given:

 $\frac{\sqrt{45} + \sqrt{20}}{\sqrt{5}}$

Formula used:  a√b+c√b=a+c√b 

Calculations: 

Simplify the square roots in the numerator:

√45 = √9 x 5 = 3√5

√20 = √ 4 x 5 = 2√ 5

Substitute back into the expression:

3√5 + 2√5 / √5

Combine like terms and devide:

5√5 / √5 = 5

∴ The correct answer is “Option 3.”

Given:

(cos²x − sin²x) ÷ (1 − sin²x)

Formula used:

cos²x − sin²x = cos2x

1 − sin²x = cos²x

Calculation:

⇒ (cos²x − sin²x) ÷ (1 − sin²x)

⇒ (cos²x − sin²x) ÷ cos²x

⇒ (cos²x ÷ cos²x) − (sin²x ÷ cos²x)

⇒ 1 − tan²x

∴ Simplified value = 1 − tan²x.

Given:

sin2A = 3/5

Formula used:

sin²θ + cos²θ = 1

Calculation:

cos²2A = 1 − sin²2A

⇒ 1 − (3/5)²

⇒ 1 − 9/25

⇒ 16/25

⇒ cos2A = 4/5

∴ cos2A = 4/5.

Given:

$\sin^2A+\cos^2A=1$

tanA = 2

Formula used:

tanA = $\frac{\sin A}{\cos A}$

$\sin^2A+\cos^2A=1$

Calculation:

tanA = 2 = $\frac{\sin A}{\cos A}$

⇒ sinA = 2 × cosA

$\sin^2A + \cos^2A = 1$

⇒ $(2 \cos A)^2 + \cos^2A = 1$

⇒ $(4\cos^2A) + \cos^2A = 1$

⇒ $(5\cos^2A) = 1$

⇒ $\cos^2A = \frac{1}{5}$

⇒ cosA = $\frac{1}{\sqrt{5}}$

sinA = 2 × cosA

⇒ sinA = 2 × $\frac{1}{\sqrt{5}}$

⇒ sinA = $\frac{2}{\sqrt{5}}$

∴ The correct answer is option (1): sinA = $\frac{2}{\sqrt{5}}$, cosA = $\frac{1}{\sqrt{5}}$.