SSC CHSL 2025 Tier-1 (Held On: 30 Nov, 2025 Shift 3) (Previous Year Paper)

The correct answer is '1' i.e. These pieces of jewelleries are designed by a highly acclaimed expert .

Key Points

• The word 'jewelleries' is incorrect because the noun "jewellery" is uncountable and does not take a plural form.
• The correct term should be 'pieces of jewellery' to indicate the plural form of jewellery in the context.
• The sentence should read: 'These pieces of jewellery are designed by a highly acclaimed expert.'

Correct sentence: These pieces of jewellery are designed by a highly acclaimed expert.

Additional Information

• Common errors with uncountable nouns:
• Uncountable nouns like "furniture," "equipment," and "jewellery" do not take plural forms.
• To indicate plurality, use phrases like "pieces of," "items of," or "types of."
• Example: "The furniture is stylish" (correct), not "The furnitures are stylish" (incorrect).
• Examples of proper usage:
• Incorrect: These furnitures are expensive.
• Correct: These pieces of furniture are expensive.
• Incorrect: She bought many jewelleries.
• Correct: She bought many pieces of jewellery.

The correct answer is '4' i.e. The academic committee was undivided in their decision to hire the new staff. .

Key Points

• The incorrect sentence is: "The academic committee was undivided in their decision to hire the new staff."
• This sentence contains an error in subject-verb agreement and pronoun usage.
• The subject "academic committee" is singular, and therefore, the pronoun referring to it should also be singular. The correct pronoun is "its", not "their."
• The word "undivided" indicates a collective action, reinforcing the singular nature of the subject.

Correct sentence: The academic committee was undivided in its decision to hire the new staff.

Additional Information

• Subject-Verb Agreement:
• Rule: Singular subjects require singular verbs and pronouns, while plural subjects require plural verbs and pronouns.
• Example: The team is practicing its strategy. (Singular)
• Example: The students are preparing their presentations. (Plural)
• Pronoun Usage:
• Rule: Pronouns must agree with their antecedents in terms of number and gender.
• Example: The committee made its decision. (Singular)
• Example: The employees voiced their opinions. (Plural)

The correct answer is '2' i.e. in .

Key Points

• The sentence requires a preposition to indicate the action of investing in renewable energy startups.
• The correct preposition to use in this context is "in."
• Using "in" signifies that the investment is directed towards renewable energy startups.
• Other options such as "into," "to," or "for" do not appropriately convey the intended meaning of the sentence.

Correct sentence: He invested heavily in renewable energy startups last year.

Additional Information

• Common Uses of Prepositions:
• Into: Indicates movement or transformation, e.g., "He went into the room."
• To: Indicates direction or purpose, e.g., "She gave the book to her friend."
• For: Indicates benefit or purpose, e.g., "This gift is for you."
• In: Indicates location, state, or involvement, e.g., "He works in finance."

The correct answer is '3' i.e. yet .

Key Points

• The conjunction "yet" is used to show contrast between two clauses.
• In the given sentence, there is a positive clause ("The patient responded well to the treatment") followed by a contrasting negative clause ("the prognosis remains guarded").
• This contrast is best conveyed by using the conjunction "yet."

Correct sentence: The patient responded well to the treatment, yet the prognosis remains guarded.

Additional Information

• Usage of the other options:
• "Hence": Indicates cause and effect, which is not suitable for this sentence.
• "Therefore": Also indicates cause and effect, which doesn’t align with the contrasting ideas in the sentence.
• "Because": Indicates reason or explanation, which is not appropriate in this context.

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

Key Points

• The word “Mirage” refers to an optical illusion or something that appears to be real but is not.
• A synonym for “Mirage” would be a word that conveys a similar meaning, such as “Fantasy”, which describes an imagined or unreal scenario.
• The other options do not align with the meaning of “Mirage”:
• Reality: This is the opposite of what “Mirage” conveys.
• Evidence: This refers to proof or facts, which is unrelated to the idea of illusion.
• Proof: Similar to “Evidence,” it does not align with the concept of an illusion or fantasy.

Correct sentence: The most appropriate synonym for “Mirage” is Fantasy.

Additional Information

• Synonym: A word or phrase that has the same or nearly the same meaning as another word.
• Example: The synonym for “beautiful” is “gorgeous.”
• Antonym: A word with the opposite meaning. For example, the antonym of “Fantasy” is “Reality.”

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

Key Points

• The word "Committee" is the correct spelling and refers to a group of people appointed for a specific function.
• Option 2 ("Committy") is incorrect because it does not exist in the English language.
• Option 3 ("Commitee") and Option 4 ("Comitee") are misspelled versions of the word and therefore incorrect.

Correct word: Committee.

Additional Information

• Definition: Committee refers to a group of people appointed for a particular task or responsibility.
• Example: The planning committee met to discuss the upcoming event.
• Usage: Commonly used in organizational, governmental, or formal contexts.

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

Key Points

• The word obsolete means something that is no longer in use or outdated.
• To find the most appropriate antonym, we need a word that signifies the opposite—something that is modern, recent, or currently in use.
• Among the given options:
• Option 1: Outdated - This is synonymous with "obsolete" and thus incorrect.
• Option 2: Ancient - Refers to something very old and is not the opposite of "obsolete." Hence, incorrect.
• Option 3: Current - Refers to something modern or presently in use, which is the correct antonym.
• Option 4: Disused - Similar in meaning to "obsolete," and thus incorrect.

Correct sentence: The most antonym of the word "obsolete" is Current.

Additional Information

• Synonyms of Obsolete:
• Outdated
• Disused
• Old-fashioned
• Antonyms of Obsolete:
• Current
• Modern
• Up-to-date

The correct answer is '1' i.e. most surely .

Key Points

• The phrase "most sure" in the sentence is grammatically incorrect and does not convey the proper meaning.
• The word "sure" in this context needs to be modified in a way that aligns with standard English usage.
• The correct form is "most surely," which is grammatically appropriate and conveys the intended emphasis on certainty.

Correct sentence: The trend of wearing boots is something that has most surely come around this season.

Additional Information

• Usage of "most surely":
• "Most surely" is used to emphasize certainty or inevitability in a statement.
• Example: She most surely deserves the award for her hard work.
• Incorrect Options:
• Option 2 ("very certainly"): Although it conveys certainty, it is less commonly used and does not fit the natural flow of the sentence.
• Option 3 ("very sure"): Grammatically awkward in this context; "sure" is not typically modified with "very" in this manner.
• Option 4 ("maybe"): Directly contradicts the intended meaning of certainty in the sentence.

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

Key Points

• A Fatalist is a person who believes that all events are predetermined and inevitable, emphasizing the role of fate.
• The other options are incorrect because:
• Realist: A realist is someone who sees things as they are and deals with situations practically.
• Idealist: An idealist is someone who envisions or pursues perfection or high ideals, often unrealistic.
• Optimist: An optimist is a person who always expects a positive outcome or looks at the bright side of things.

Correct sentence: A person who believes in fate is called a Fatalist.

Additional Information

• Definitions of other options:
• Realist: Focuses on practical and real-world concerns, avoiding idealism or speculation.
• Idealist: Driven by high principles or ideals, often disregarding practical considerations.
• Optimist: Believes in positive outcomes and looks forward to favorable possibilities.

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

Key Points

• The word cajole means to persuade someone to do something using flattery, coaxing, or gentle urging.
• Antonyms are words that have opposite meanings. To find the antonym of cajole, we need to identify a word that conveys forceful or aggressive persuasion.
• Bully is the most appropriate antonym because it signifies using intimidation or aggression to compel someone to act.

Correct sentence: The antonym of cajole is Bully.

Additional Information

• Other options:
• Entice: Means to attract or tempt someone, often using clever or indirect methods. It is similar to cajole rather than being an antonym.
• Persuade: Means to convince someone to do something, which is closely related to cajole.
• Flatter: Means to praise excessively or insincerely, often to gain favor, which aligns with cajole rather than contrasting it.
• Usage Tip: Always evaluate the context and meaning of the word before selecting its antonym.

The correct answer is '1' i.e. "Have you been preparing regularly and will you be ready by Monday?"

Key Points

• The given sentence is in indirect speech and needs to be converted into direct speech.
• Indirect speech statements often use verbs such as "asked," "said," or "told" to report speech, while direct speech reproduces the exact words spoken.
• In the original sentence, "had been preparing regularly" and "would be ready by Monday" are reported in indirect speech. To convert these to direct speech:
• "Had been preparing" changes to "Have you been preparing," as it directly asks about a continuous action.
• "Would be ready" changes to "Will you be ready," as it directly asks about future readiness.

Correct sentence: The mentor asked, "Have you been preparing regularly and will you be ready by Monday?"

Additional Information

• Rules for Direct Speech Conversion:
• When converting indirect speech to direct speech, ensure the tense aligns with the context of the original sentence.
• Maintain proper punctuation: quotation marks ("") surround the spoken words.
• Examples:
• Indirect: She asked whether he had been eating well. → Direct: She asked, "Have you been eating well?"
• Indirect: He wondered if they would arrive on time. → Direct: He wondered, "Will they arrive on time?"

The correct answer is '1' i.e. They will have debated the new policy for months before it is implemented .

Key Points

• The sentence is originally written in the passive voice, where the subject (the new policy) is acted upon.
• To convert the sentence into the active voice, the subject performing the action must be explicitly stated (they).
• The structure of the active voice is Subject + verb + object. In this case, the subject is "they," the verb is "will have debated," and the object is "the new policy."

Correct sentence: They will have debated the new policy for months before it is implemented.

Additional Information

• Active vs Passive Voice:
• Active Voice: The subject performs the action. Example: She wrote the book.
• Passive Voice: The subject is acted upon. Example: The book was written by her.
• Usage: Active voice is preferred for clarity and directness, while passive voice is used when the focus is on the action or when the performer of the action is unknown or unimportant.

The correct answer is '1' i.e. She told them that they would be surprised. .

Key Points

• The given sentence is expressed in direct speech and needs to be converted into indirect speech.
• In indirect speech, the pronouns and tenses are changed according to the rules of reported speech.
• In this case, the reporting verb "said to" is changed to "told," and the tense of the verb "will be" is changed to "would be" because the reporting verb is in the past tense.
• The pronoun "you" changes to "they" to maintain consistency with the subject "them."

Correct sentence: She told them that they would be surprised.

Additional Information

• Rules for Changing Direct Speech to Indirect Speech:
• Change of pronouns: Pronouns in the direct speech are changed to match the subject and context of the reporting clause.
• Change of tense: If the reporting verb is in the past tense, the tense of the verb in the direct speech is shifted to the past tense (e.g., "will" changes to "would").
• Reporting verb change: "Said to" is often replaced with "told" when the indirect speech includes an object (e.g., "them").
• Example:
• Direct: She said, "I am happy."
• Indirect: She said that she was happy.

The correct answer is '3' i.e. The patient is being examined by the doctor .

Key Points

• The sentence provided is in the active voice, where the subject (doctor) performs the action of examining the patient.
• To transform the sentence into the passive voice, the focus shifts to the object of the action (patient).
• The structure for transforming present continuous tense sentences into passive voice is: Object + is/are + being + past participle + by + subject.

Correct sentence: The patient is being examined by the doctor.

Additional Information

• Active voice: The subject performs the action. Example: The teacher is teaching the students.
• Passive voice: The object of the action becomes the subject. Example: The students are being taught by the teacher.
• Key Transformation Rules:
• Identify the tense of the sentence.
• Use the correct form of the verb "to be" (is/are/was/were) based on the tense.
• Add "being" for present/past continuous tense.
• Use the past participle of the verb.

The correct answer is Option 1.

Key Points

• To transform a sentence from Active to Passive Voice, the object of the active sentence becomes the subject of the passive sentence.
• Active Structure: Gourmet enthusiasts (Subject) + often extol (Verb) + its coarse granules (Object) + for the nuanced crunch... (Prepositional Phrase).
• Passive Structure: Its coarse granules (New Subject) + are often extolled (Auxiliary 'be' + Past Participle) + by gourmet enthusiasts (Agent) + for the nuanced crunch... (Remaining Phrase).
• Option 1 correctly follows the Present Indefinite Passive rule: Subject + is/am/are + V3 + by + Agent.
• Why other options are incorrect:
• Option 2: It changes the meaning of the sentence. It suggests the granules are the ones performing the action of "conferring the extolled crunch" rather than being the thing that is extolled.
• Option 3: It incorrectly identifies "The nuanced crunch" as the primary object being extolled. In the original sentence, the enthusiasts extol the granules.
• Option 4: This remains in the active voice and changes the verb from "extol" to "praised," which is an unnecessary alteration.

Therefore, the correct answer is 1.

Analytical Insight: In competitive exams, voice transformation questions often include a long prepositional phrase (like "for the nuanced crunch...") to distract you. Always focus on the core Subject-Verb-Object relationship first.

Additional Information

• Extol: To praise enthusiastically or highly.
• Provenance: The place of origin or earliest known history of something.
• Nuanced: Characterized by subtle differences or shades of meaning, expression, or sound.
• Passive Voice: Used when the focus is on the action or the recipient of the action rather than the performer.

The correct answer is Option 3.

Key Points

• To transform a sentence from Present Simple to Past Perfect, we must change the finite verbs in both the main clause and the subordinate clause to follow the $had + V3$ (past participle) structure.
• Original (Present Simple): Advocates claim (V1) it offers (V1) health benefits...
• Transformation (Past Perfect):
• "claim" becomes "had claimed".
• "offers" becomes "had offered".
• Option 3 correctly applies the Past Perfect tense to both actions, indicating they were completed before a certain point in the past.
• Why other options are incorrect:
• Option 1: "Claimed" is Past Simple, not Past Perfect.
• Option 2: While the first verb is correct, "offered" is Past Simple. This creates a mix of tenses rather than a full transformation to Past Perfect.
• Option 4: "Had been offering" is Past Perfect Continuous, which changes the aspect of the verb to show an ongoing action in the past.

Therefore, the correct answer is 3.

Analytical Insight: In competitive exams, tense transformation often involves "Reported Speech" logic. When moving a sentence into the "past of the past," both the reporting verb and the reported action typically shift to the Past Perfect to maintain chronological consistency.

Additional Information

• Past Perfect Tense: Used to describe an action that was finished before another action in the past.
• Empirical Substantiation: Evidence based on observation or experience rather than theory or pure logic.
• Zenith: The time at which something is most powerful or successful; the peak.
• Myriad: A countless or extremely great number.

The correct answer is Option 1.

Key Points

• To determine the meaning of "provenance," we look at the first sentence: "...each possessing distinctive characteristics shaped by geological provenance and processing methods."
• The passage discusses how different salts (Himalayan, Sea, Volcanic) get their traits based on where they come from (e.g., "ancient seabeds in the Punjab region" or "evaporation of seawater").
• In English, provenance refers to the place of origin or the earliest known history of something. It is frequently used in art, archaeology, and geology to describe where an object was created or found.
• Why other options are incorrect:
• Option 2: While the passage mentions "hue" and "blush," these are results of the salt's provenance (like iron oxide in the soil), not the meaning of the word itself.
• Option 3: "Texture" (coarse granules, delicate crust) is a physical characteristic, but "provenance" explains why or where those characteristics formed.
• Option 4: "Purity" refers to the level of refinement (mentioned regarding table salt), but the sentence distinguishes between provenance (origin) and processing methods (refinement).

Therefore, the correct answer is 1.

Analytical Insight: In competitive exams, vocabulary words related to "Origin" (like provenance, genesis, or etymology) are common. A helpful tip is to look at the surrounding context; since the passage immediately begins naming specific locations (Punjab, seawater, salt pans), "Origin" is the only logical fit.

Additional Information

• Ubiquitous: Present, appearing, or found everywhere.
• Myriad: A countless or extremely great number.
• Artisanal: Relating to or characteristic of an artisan; made in a traditional or non-automated way.
• Connoisseurship: Expert knowledge or training, especially in the fine arts or matters of taste.

The correct answer is Option 2.

Key Points

• To understand "connoisseurship," we look at the final sentence: "...rendering them as much a subject of connoisseurship as of necessity."
• The author is contrasting "necessity" (salt as a basic biological need) with "connoisseurship" (the ability to taste, compare, and judge the subtle differences between gourmet salts like Fleur de sel or Himalayan pink salt).
• A connoisseur is a person who has expert knowledge and a refined taste in a particular field, such as fine arts, wine, or food. Therefore, connoisseurship is the quality of expert appreciation and judgment.
• Why other options are incorrect:
• Option 1: Mass production is associated with "table salt" and "industrial contexts," which the passage contrasts with the artisanal salts that require connoisseurship.
• Option 3: Connoisseurship is about the quality and subtlety of consumption, not the volume or "large amounts."
• Option 4: There is no legal or regulatory context provided for this word in the passage.

Therefore, the correct answer is 2.

Analytical Insight: In competitive exams, words ending in -ship often denote a status or an art (like craftsmanship or statesmanship). When you see "connoisseurship" paired with "necessity," the author is moving from a basic functional level to a high-level expertise level.

Additional Information

• Artisanal: Relating to or characteristic of an artisan; made in a traditional or non-automated way.
• Zenith: The point of culmination; peak or highest point.
• Embellishment: A decorative detail or feature added to something to make it more attractive.
• Provenance: The place of origin or earliest known history of something.

The correct answer is Option 3.

Key Points

• To find the specific description, we look at the paragraph discussing "Fleur de sel."
• The passage states: "“Fleur de sel”... Prized for its rarity and textural delicacy, it is more an embellishment than a staple seasoning."
• An embellishment is something added to make another thing more beautiful or interesting (like a garnish), while a staple is a basic, everyday necessity (like common table salt).
• The text highlights that because of its artisanal production and delicate crust, it is used as a finishing touch rather than a primary cooking ingredient.
• Why other options are incorrect:
• Option 1: Black salt is described as lending "complexity to traditional savouries," but not as an embellishment.
• Option 2: Himalayan pink salt is mentioned for its "blush" and contested health benefits, but not specifically as an embellishment over a staple.
• Option 4: Sea salt is noted for its "nuanced crunch" and trace minerals, but it is still widely used as a seasoning rather than a rare garnish.

Therefore, the correct answer is 3.

Analytical Insight: In competitive exams, questions often target specific vocabulary pairings. Linking the word "embellishment" to "Fleur de sel" requires scanning the text for that exact phrase. Understanding that Fleur de sel is a "finishing salt" helps reinforce this logical connection.

Additional Information

• Embellishment: A decorative detail or feature added to something to make it more attractive.
• Staple: A main or important element of something, especially of a diet.
• Artisanal: Produced in a traditional way by hand.
• Zenith: The highest point or the peak of something.

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

Key Points

• The paragraph must have logical flow and coherence.
• Option 2 (R, Q, P, S) forms a meaningful and grammatically correct paragraph.
• Explanation of the arrangement:
• R introduces the motivation behind the sculpture by describing the photo of the grandmother.
• Q follows logically, describing how the sculptor worked for months inspired by the grandmother's photo.
• P then describes the result of the effort—the sculpture with an expression of sorrow.
• S concludes the paragraph, tying it back to the purpose of the sculpture—to honor the grandmother’s resilience.

Correct arrangement: R, Q, P, S.

Additional Information

• Guidelines for Rearranging Sentences:
• Identify the introductory sentence (usually gives context or introduces the main idea).
• Look for logical connectors or chronological clues for sequencing.
• Ensure the paragraph ends with a conclusion or summary tying back to the main idea.

The correct answer is '3' i.e. S, Q, R, P .

Key Points

• To form a meaningful and grammatically correct paragraph, the sentence parts need to be arranged in a logical sequence based on the progression of ideas.
• The sequence should follow the natural flow of events or actions described.
• Each part contributes to the narrative, starting with the introduction of the situation and progressing to the resolution or conclusion.

Correct arrangement:

• S: As the patient explained their symptoms, the doctor paid close attention.
• Q: In order to search for particular markers, he ordered a number of imaging scans and blood tests.
• R: He went over all the information, comparing it to what he knew about medicine.
• P: He presented his diagnosis and suggested a course of treatment with assurance.

Additional Information

• The sequence starts with the doctor listening to the patient’s explanation (S).
• It then progresses to the doctor’s actions to investigate the issue further by ordering tests (Q).
• After gathering the necessary information, the doctor analyzes and compares it to his knowledge (R).
• Finally, the doctor provides a diagnosis and suggests a treatment plan (P).

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

Key Points

• The word bluffing refers to the act of deceiving or pretending something that is not true.
• In the given sentence, the person is described as using confidence and theatrical gestures to create an impression that may not be genuine.
• Among the options provided:
• Option 1: Explaining - This does not fit the context as bluffing is not about providing explanations.
• Option 2: Pretending - This is the correct replacement as bluffing involves pretending to be something one is not.
• Option 3: Proving - Bluffing does not involve proving anything; it is more about deception.
• Option 4: Admitting - Bluffing is contrary to admitting, as admitting involves revealing the truth.

Correct sentence: He knew the art of Pretending with confidence and theatrical gestures.

Additional Information

• Synonyms for Bluffing: Pretending, deceiving, feigning.
• Related Context: Bluffing is often used in situations like games, negotiations, or storytelling where deception plays a role.

The correct answer is '4' i.e. oracle, auricle .

Key Points

• The word oracle refers to a person or entity that provides wise or prophetic predictions, often associated with divine or supernatural knowledge. In the context of the sentence, the villagers brought the boy to an oracle.
• The word auricle refers to the external part of the ear (or pinna). It fits the sentence, as the boy is being examined closely, and the mole is spotted on his left auricle.
• The other options are incorrect because they either repeat the same word twice (e.g., "oracle, oracle" or "auricle, auricle") or mix them incorrectly.

Correct sentence: The villagers brought the little boy to the oracle, who examined him closely, spotted a mole on his left auricle, and solemnly declared him the chosen one.

Additional Information

• Oracle:
• Definition: A person or medium through whom advice or prophecy is sought.
• Usage: Refers to someone who provides wisdom or divine predictions.
• Example: The oracle foretold the coming of a great leader.
• Auricle:
• Definition: The external part of the ear.
• Usage: Often used in medical or anatomical contexts.
• Example: The doctor examined the auricle for signs of infection.

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

Key Points

• The word "archiac" in the sentence is spelled incorrectly.
• The correct spelling is "archaic," which means "old-fashioned" or "belonging to an earlier period."
• Spelling errors can change the meaning of the sentence or make the text difficult to understand.

Correct sentence: The author’s penchant for archaic diction often obfuscated the text’s underlying message.

Additional Information

• Common spelling mistakes to watch out for:
• "Definately" → Correct: "Definitely"
• "Seperate" → Correct: "Separate"
• "Occured" → Correct: "Occurred"
• Importance of correct spelling:
• Ensures clarity and professional communication.
• Helps avoid misunderstandings in written texts.

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

Key Points

• An antitoxin is a substance produced in the blood to neutralize harmful toxins that are introduced into the body, such as those produced by bacteria or other pathogens.
• It is specifically designed to counteract poisons or toxins and prevent their harmful effects.
• Antitoxins are crucial for combating diseases caused by toxins, such as tetanus or diphtheria.

Correct explanation: Antitoxins refer to substances in the blood that neutralize harmful matter, such as toxins, making them harmless.

Additional Information

• Antibody:
• Antibodies are proteins produced by the immune system to identify and neutralize foreign invaders like bacteria and viruses.
• They are part of the body’s immune response, but they do not neutralize toxins directly.
• Antioxidant:
• Antioxidants are substances that protect cells from damage caused by free radicals.
• They are not specifically designed to neutralize toxins in the blood.
• Antigen:
• Antigens are substances that trigger an immune response in the body, such as bacteria or viruses.
• They are not neutralizers but are the targets of antibodies.

The logic is based on professionalism and integrity.

Option 1: Give incorrect information – Unethical and misleading.

Option 2: Cancel the presentation – Avoids responsibility.

Option 3: Explain the inaccuracy and present correct information – Honest and professional approach.

Option 4: Blame others – Unprofessional behavior.

Among these, Option 3 ensures accuracy, accountability, and professionalism.

Hence, the correct answer is Option 3.

Given:

A person walks 5 km north,

then 4 km east, and

finally 5 km south.

Thus, the person isto the east of his starting point.

Hence, "Option 3" is the correct answer.

Given: 

The government has announced a ban on the use of single-use plastic bags in all stores across the country.

⇒ The given statement mentions that the government has announced a ban on the use of single-use plastic bags in all stores across the country.

This implies that stores cannot provide single-use plastic bags and people will need alternatives when shopping.

Now, let's evaluate the given inferences:

I. People will have to start carrying their own reusable bags when they go shopping – True 

Since stores cannot provide single-use plastic bags, shoppers will need to carry reusable bags or alternatives.

II. All stores will have to shut down as they will not be able to use plastic bags anymore – False 

The statement does not suggest that stores will close. Stores can still operate using alternatives like cloth or paper bags.

III. The ban on single-use plastic bags will not have any impact on the environment – False 

The purpose of the ban is to reduce plastic pollution, so it is intended to have a positive impact on the environment.

Hence, only inference I follows from the given statement.

Hence, the correct answer is "Option 1".

The logic is based on emotional intelligence and supportive behavior.

Option 1: Avoid talking – Shows lack of support.

Option 2: Force advice – May increase pressure.

Option 3: Dismiss feelings – Not empathetic.

Option 4: Offer to listen without pushing – Shows understanding and support.

Among these, Option 4 reflects empathy and emotional intelligence.

Hence, the correct answer is Option 4.

Given Statements:

W $ N → W is either smaller than or equal to N → W ≤ N

N % B → N is neither greater than nor smaller than B → N = B

B * F → B is greater than F → B > F

Conclusions:

I. B % W – True (B is neither greater than nor smaller than W → B = W?)

Let’s check: From statements: W ≤ N and N = B → W ≤ B → So B ≥ W, but W ≤ B. Equality is possible if W = B. But definitely true? Not guaranteed. So conclusion I cannot be definitely true.

II. B * W – True (B > W?)

From statements: W ≤ N and N = B → W ≤ B → So B ≥ W. B > W is not definite; equality is possible. Hence conclusion II is not definitely true.

Hence, neither conclusion I nor conclusion II is definitely true.

The correct answer is Option 4.$

The logic followed here is:

thus, "2185" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

The logic followed here is:

Logic: A number divisible by both 13 and 17 must be divisible by their LCM (Least Common Multiple).

Calculation:

LCM of 13 and 17 = 13 × 17 = 221

Now check options:

663 ÷ 221 = 3 

425 ÷ 221 ≠ integer 

455 ÷ 221 ≠ integer 

729 ÷ 221 ≠ integer 

Hence, the correct answer is Option 1.

The logic is based on types of devices.

Option 1: Air fryer – A kitchen appliance used for cooking.

Option 2: Shredder – An office device used to destroy documents.

Option 3: Scanner – An office device used to scan documents.

Option 4: Fax machine – An office device used to send documents.

Among these, Shredder, Scanner, and Fax machine are office-related devices, while Air fryer is a kitchen appliance.

Hence, the odd one out is Option 1.

The logic followed here is:

thus, "67" will replace the question mark in the given series.

Hence, the correct option is "Option 1".

The logic followed here is:

thus, "52.5" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

Given Statements:

All Super are Big.

All Big are Bold.

Some Super are Tall.

The least possible Venn diagram for the given statements is:

Conclusions:

I. Some Tall is Big –  True (As some super are tall and all super are big. so, some tall are definitely big).

II. Some Bold is Tall – True (Since some Super are Tall and all Super are Bold through Big, those Super who are Tall are also Bold.)

III. All Super is Bold – True (All Super are Big and all Big are Bold, hence all Super are Bold.)

All the conclusions follow.

The correct answer is Option 4.

The logic followed here is:

So, 'G2197' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

The logic followed here is:

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

Hence, the correct answer is "Option 1".

The logic is based on ethical and professional response.

Option 1: Punish them for breaching rules – Ignores the seriousness of corruption.

Option 2: Praise them as a hero – May overlook procedural violations.

Option 3: Protect their identity and investigate the claim – Balanced and ethical approach.

Option 4: Fire them quietly – Avoids addressing the issue.

Among these, Option 3 ensures fairness, accountability, and proper investigation.

Hence, the correct answer is Option 3.

BODMAS Table: 

Given expression: 4 @ 3 # 2 = ?

Now, if the operations are applied as: @ → first × second + first, # → first + second × second, then:

⇒ 4 × 3 + 4 # 2 = ?

⇒ 16 # 2 = ?

⇒ 16 + 2 × 2 = ?

⇒ 16 + 4 = 20

Hence, the correct answer is "Option 4".

BODMAS Table: 

Given equation: 30 × 2 + 12 ÷ 6 − 3 = ?

Now, if the operations are interchanged as: + → ×, − → +, × → ÷, ÷ → −, then:

⇒ 30 ÷ 2 × 12 − 6 + 3 = ?

⇒ 15 × 12 − 6 + 3 = ?

⇒ 180 − 6 + 3 = ?

⇒ 174 + 3 = 177

Hence, the correct answer is "Option 3".

The logic is based on identifying the underlying assumption behind the decision.

Option 1: Employees dislike working in the office environment – Not necessarily implied.

Option 2: Flexibility in work location contributes positively to employee morale – Directly supports the goal of improving well-being.

Option 3: The company wants to reduce electricity bills – Not related to employee well-being.

Option 4: Employees are more productive at night – Not relevant to work-from-home policy.

Among these, Option 2 logically explains the reason behind the policy.

Hence, the correct answer is Option 2.

The logic is based on disease and the organ affected.

Glaucoma is a disease of the Eye.

Similarly, Nephritis is a disease of the Kidney.

Among the options, Kidney correctly matches Nephritis.

Hence, the correct answer is Option 1.

The logic is based on tool and its function.

Rake is used to Gather.

Similarly, Drill is used to Bore.

Among the options, Drill correctly matches the function Bore.

Hence, the correct answer is Option 4.

Given codes:

'find observe new arena' → fgk, rst, mop, tmu

'situation new find matters' → stk, rst, pnv, fgk

'observe clear new matters' → rtd, pnv, mop, rst

So, final mapping:

• arena = tmu
• observe = mop
• matters = pnv
• clear = rtd

Therefore, 'arena observe matters clear' → mop, pnv, rtd, tmu

Hence, the correct answer is Option 3.

The logic followed here is:

Pattern: nth term = n² × (n − 1)

thus, "180" will replace the question mark in the given series.

Hence, the correct option is "Option 1".

The logic followed here is:

Logic: The pattern involves multiplying the first number by 6 and then subtraction of 5 to get the second number.

Let’s analyze the given pairs:

763 : 4573

763 × 6 - 5 = 4578- 5 = 4573 

272 : 1627

272 × 6 - 5 = 1632 - 5 = 1627 

Now, for the unknown:

421 : ?

421 × 6 - 5  = 2526 - 5 = 2521 

Hence, the correct answer is Option 2.

The logic followed here is:

Logic: (1^st number - 18) ÷ 6 = 2^nd number

Let’s analyze the given pairs:

1962 : 324

(1962 - 18) ÷ 6 =  324 

1944 ÷ 6 =  324 

3378 : 560

(3378 - 18) ÷  6 = 560

For the unknown:

? : 238

(? - 18) ÷ 6 = 238

(? - 18) = 238 × 6 

(? - 18) = 1428

? = 1428 + 18 = 1446

thus, 1446 : 238

Hence, the correct answer is Option 1.

The logic followed here is:

Logic: The pattern involves using near-perfect squares for numbers and shifting letters forward in the alphabet. Specifically:

Number Pattern: The number on the left is adjusted from a perfect square  −1 to get the number on the right.

Letter Pattern: The first letter shifts +3, and the second letter shifts +6 in the alphabet.

Let’s analyze each option: 

Option 1) 120LD - 11OJ

Option 2) 170MR - 13PX

Option 3) 288CG - 17FM

Option 4) 224KB - 15NH

Hence, the odd one out is Option 2.

The logic followed here is:

Logic:"Check each option to see whether the given word (CRAFT) can be formed using its letters."

Hence, the correct answer is "Option 1".

Given:

Income = 60000

Essentials = 3/5

Rent = 1/4

Formula Used:

Savings = Income × (1 - total expenses fraction)

Calculation:

⇒ Total expenses = 3/5 + 1/4

⇒ Total expenses = 12/20 + 5/20 = 17/20

⇒ Savings fraction = 1 - 17/20 = 3/20

⇒ Savings = 60000 × 3 ÷ 20

⇒ Savings = 9000

∴ The correct answer is 9000.

Shortcut Trick

Apply the Rule of Alligation directly to find the mixing ratio:

Ratio = (Dearer Price − Mean Price) : (Mean Price − Cheaper Price)

Ratio = (50 − 40) : (40 − 30)

Ratio = 10 : 10 = 1 : 1

∴ The correct answer is 1 : 1.

Alternate Method

Given:

Cost Price of 1^st type of sugar (Cheaper) = ₹30/kg

Cost Price of 2^nd type of sugar (Dearer) = ₹50/kg

Selling Price of mixture = ₹40/kg (at no gain or loss, CP = SP)

Mean Cost Price (M) = ₹40/kg

Calculations:

⇒ Quantity of Cheaper (Q₁) : Quantity of Dearer (Q₂) = (D − M) : (M − C)

⇒ Q₁ : Q₂ = (50 − 40) : (40 − 30)

⇒ Q₁ : Q₂ = 10 : 10

⇒ Q₁ : Q₂ = 1 : 1

∴ The correct answer is 1 : 1.

Additional Information

Rule of Alligation

It is used to find the ratio in which two ingredients at different prices must be mixed to produce a mixture of a desired mean price. Ratio = (Price of Dearer − Mean Price) / (Mean Price − Price of Cheaper).

Mean Price

The cost price of a unit quantity of the mixture is called the Mean Price. If the mixture is sold at no profit/loss, the Selling Price equals the Mean Price.

Mixture with Profit %

If a profit % is given on Selling Price, first calculate Mean CP using the formula: CP = [100 / (100 + Profit%)] × SP before applying alligation.

Shortcut Trick

For 1 year, Compound Interest = Simple Interest

CI = P × R × T ÷ 100

= 2000 × 10 × 1 ÷ 100

= ₹200

∴ The correct answer is ₹200.

Alternate Method

Given:

Principal = ₹2000

Rate = 10% p.a.

Time = 1 year

Formula Used:

Amount = P(1 + R ÷ 100)^T

CI = Amount − Principal

Start 1 Year  P = ₹2000  Rate = 10% CI after 1 year

⇒ Amount = 2000(1 + 10 ÷ 100)¹

⇒ = 2000 × 110 ÷ 100

⇒ = ₹2200

⇒ CI = 2200 − 2000

⇒ CI = ₹200

∴ The correct answer is ₹200.

Additional Information

Simple Interest Formula

SI = P × R × T ÷ 100 where P = Principal, R = Rate, T = Time.

Compound Interest Formula

Amount = P(1 + R ÷ 100)^T and CI = Amount − Principal.

SI and CI Relation

For 1 year, Simple Interest and Compound Interest are always equal.

Rule of 72

Approximate doubling time = 72 ÷ Rate%.

Given:

Length = 6

Breadth = 8

Height = 10

Formula Used:

Space diagonal = √(length² + breadth² + height²)

Calculation:

⇒ Distance = √(6² + 8² + 10²)

⇒ Distance = √(36 + 64 + 100)

⇒ Distance = √200

⇒ Distance = 10√2 = 14.1

∴ The correct answer is 14.1.

Shortcut Trick

A Rational number can be expressed as a fraction p/q, meaning its decimal is terminating or repeating.

An Irrational number cannot be expressed as a fraction and has a non-terminating, non-repeating decimal expansion.

When you add a terminating/repeating decimal to a non-terminating, non-repeating decimal, the result will always be non-terminating and non-repeating.

Thus, the sum of a Rational and an Irrational number is always an Irrational number.

∴ The correct answer is Irrational number.

Alternate Method

Given: A Rational number and an Irrational number are to be added.

Concept: Proof by contradiction or decimal property of Real numbers.

⇒ Let a be a rational number and b be an irrational number.

⇒ Suppose a + b = c, where c is a rational number.

⇒ Then, b = c − a.

⇒ Since c and a are both rational, their difference (c − a) must also be rational.

⇒ This implies b is rational, which contradicts the fact that b is irrational.

⇒ Therefore, the assumption was wrong; the sum must be an Irrational number.

∴ The correct answer is Irrational number.

Additional Information

Rational Number Definition

Any number that can be expressed as p/q, where p and q are integers and q ≠ 0.

Irrational Number Properties

A number whose decimal expansion is non-terminating and non-recurring. Common examples include √2, √3, π, and e.

Product Property

The product of a non-zero rational number and an irrational number is always an irrational number.

Closure of Rationals

The set of Rational numbers is closed under addition, subtraction, multiplication, and division (except by zero).

Given:

Profit₁ = 20%

Loss₂ = 10%

Gain = 90

Formula Used:

Profit = SP - CP

Net gain = sum of individual gains

Calculation:

⇒ Let total CP = x

⇒ CP of 3/4 part = 3x/4

⇒ CP of 1/4 part = x/4

⇒ Profit on 3/4 part = 20% of 3x/4 = (20/100) × 3x/4 = 3x/20

⇒ Loss on 1/4 part = 10% of x/4 = (10/100) × x/4 = x/40

⇒ Net gain = 3x/20 - x/40

⇒ Net gain = (6x - x)/40 = 5x/40 = x/8

⇒ x/8 = 90

⇒ x = 90 × 8

⇒ x = 720

∴ The correct answer is 720.

Given:

A(0,0)

B(6,0)

C(2,6)

Formula Used:

Centroid = ( (x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3 )

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Calculation:

⇒ Centroid = ( (0 + 6 + 2)/3 , (0 + 0 + 6)/3 )

⇒ Centroid = ( 8/3 , 2 )

⇒ Distance = √[(2 - 8/3)² + (6 - 2)²]

⇒ Distance = √[(−2/3)² + 4²]

⇒ Distance = √[4/9 + 16]

⇒ Distance = √[(4 + 144)/9]

⇒ Distance = √(148/9)

⇒ Distance = √148 ÷ 3

⇒ Distance = 2√37 ÷ 3

∴ The correct answer is 2√37/3.

Given:

Total students = 12

Average (top 6) = 84.5

Average (bottom 6) = 72.75

Wrong score = 58.2

Correct score = 85.2

Formula Used:

Total = Average × number

Corrected total = old total + difference

Calculation:

⇒ Total (top 6) = 84.5 × 6 = 507

⇒ Total (bottom 6) = 72.75 × 6 = 436.5

⇒ Total = 507 + 436.5 = 943.5

⇒ Correction = 85.2 - 58.2 = 27

⇒ Corrected total = 943.5 + 27 = 970.5

⇒ Corrected average = 970.5 ÷ 12

⇒ Corrected average = 80.875

∴ The correct answer is 80.875.

Given:

Base sides = 0.6, 0.8

Length = 4.5

Density = 0.75 g/cm³

Formula Used:

Area of triangle = 1/2 × base × height

Volume = area × length

Mass = density × volume

Calculation:

⇒ Area = 1/2 × 0.6 × 0.8 = 0.24 m²

⇒ Volume = 0.24 × 4.5 = 1.08 m³

⇒ Convert volume = 1.08 × 1000000 = 1080000 cm³

⇒ Mass = 0.75 × 1080000 = 810000 g

⇒ Mass = 810000 ÷ 1000 = 810 kg

∴ The correct answer is 810.

Given:

cot θ = 5/12

Formula Used:

cot θ = adjacent/opposite

cosec θ = hypotenuse/opposite

Pythagoras theorem: hypotenuse² = adjacent² + opposite²

Calculation:

⇒ adjacent = 5

⇒ opposite = 12

⇒ hypotenuse² = 5² + 12²

⇒ hypotenuse² = 25 + 144

⇒ hypotenuse² = 169

⇒ hypotenuse = √169

⇒ hypotenuse = 13

⇒ cosec θ = hypotenuse/opposite

⇒ cosec θ = 13/12

∴ The correct answer is 13/12.

Given:

$\cos A = \frac{4}{5}$

Formula Used:

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

$1 + \tan^2 A = \sec^2 A$

$1 + \cot^2 A = \csc^2 A$

Calculation:

⇒ $\sin A = \sqrt{1 - (4/5)^2} = \sqrt{1 - 16/25} = 3/5$

⇒ $\frac{1 + \tan^2 A}{1 + \cot^2 A} = \frac{\sec^2 A}{\csc^2 A}$

⇒ $= \frac{1/\cos^2 A}{1/\sin^2 A}$

⇒ $= \frac{\sin^2 A}{\cos^2 A}$

⇒ $= \tan^2 A$

⇒ $= \left(\frac{3}{4}\right)^2 = \frac{9}{16}$

∴ The correct answer is 9/16.

Given:

⇒ Two triangles are congruent.

⇒ All corresponding medians

inradii

and altitudes of the triangles are equal.

Formula Used:

⇒ Congruent triangles have equal corresponding sides and angles.

⇒ Properties of congruent triangles: Equal medians

equal inradii

and equal altitudes.

Calculation:

⇒ Since the triangles are congruent

their corresponding sides and angles are equal.

⇒ Equal sides and angles imply equal medians.

⇒ Equal sides and angles imply equal inradii.

⇒ Equal sides and angles imply equal altitudes.

∴ The correct answer is option 4.

Given:

Chord = radius

Formula Used:

Chord = 2 × radius × sin(θ/2)

Calculation:

⇒ radius = 2 × radius × sin(θ/2)

⇒ 1 = 2 × sin(θ/2)

⇒ sin(θ/2) = 1/2

⇒ θ/2 = 30°

⇒ θ = 60°

∴ The correct answer is 60°.

Shortcut Trick

Speed of Train = 240 ÷ 4 = 60 kmph.

Speed of Car = 60 × 125% = 75 kmph | Speed of Bike = 75 × 60% = 45 kmph.

Time Difference = 150 × (1/45 − 1/75) hours = 150 × (2/225) × 60 minutes.

Time Difference = 80 min.

∴ The correct answer is 80 min.

Alternate Method

Given:

Distance covered by Train = 240 km, Time taken = 4 hr.

Car speed = 25% more than Train.

Bike speed = 40% less than Car.

New distance to cover = 150 km.

Formula Used:

Speed = Distance ÷ Time

Time = Distance ÷ Speed

⇒ Speed of Train = 240 ÷ 4 = 60 kmph.

⇒ Speed of Car = 60 + (25/100) × 60 = 60 + 15 = 75 kmph.

⇒ Speed of Bike = 75 − (40/100) × 75 = 75 − 30 = 45 kmph.

⇒ Time taken by Car = 150 ÷ 75 = 2 hours.

⇒ Time taken by Car (in min) = 2 × 60 = 120 min.

⇒ Time taken by Bike = 150 ÷ 45 = 10/3 hours.

⇒ Time taken by Bike (in min) = (10/3) × 60 = 200 min.

⇒ Difference = 200 − 120 = 80 min.

∴ The correct answer is 80 min.

Additional Information

Speed-Time Relationship

For a constant distance, speed is inversely proportional to time (Speed ∝ 1/Time). If speed increases, time decreases in the same ratio.

Unit Conversion

To convert hours to minutes, multiply by 60. To convert kmph to m/s, multiply by 5/18.

Percentage Change in Speed

If speed increases by x%, the new speed is S × (1 + x/100). If it decreases, the new speed is S × (1 − x/100).

Given:

$\angle ACB = 108^\circ$

Formula Used:

$\text{Angle in major arc} = 180^\circ - \text{angle in minor arc}$

$\angle APB = 180^\circ - \angle AOB$

$\angle AOB = 2 × \text{angle in major arc}$

Calculation:

⇒ $\text{Angle in major arc} = 180^\circ - 108^\circ = 72^\circ$

⇒ $\angle AOB = 2 × 72^\circ = 144^\circ$

⇒ $\angle APB = 180^\circ - 144^\circ$

⇒ $\angle APB = 36^\circ$

∴ The correct answer is 36°.

Given:

Two hemispheres form a sphere

Formula Used:

Surface area of sphere = 4πr²

Area of two flat faces = 2 × πr²

Calculation:

⇒ Total sphere surface area = 4πr²

⇒ Area of flat faces = 2 × πr²

⇒ Ratio = (2πr²) ÷ (4πr²)

⇒ Ratio = 1/2

⇒ Percentage = 1/2 × 100 = 50%

∴ The correct answer is 50%.

Shortcut Trick

For a square pyramid, Slant height (l) = √[Height² + (Side/2)²].

Here, l = √[9² + 7²] = √[81 + 49] = √130 ≈ 11.40 cm.

Lateral Surface Area (LSA) = 2 × Side × Slant height.

LSA = 2 × 14 × 11.40 ≈ 319.2 cm².

∴ The correct answer is 319.2 cm².

Alternate Method

Given:

Base side of the square pyramid (a) = 14 cm

Perpendicular height of the pyramid (h) = 9 cm

Formula Used:

1. Slant height (l) = √[h² + (a/2)²]
2. Lateral Surface Area (LSA) = 1/2 × Perimeter of base × Slant height

Calculations:

⇒ Half of base side = 14 ÷ 2 = 7 cm

⇒ Slant height (l) = √[9² + 7²]

⇒ l = √[81 + 49] = √130

⇒ l ≈ 11.40175 cm

⇒ Perimeter of square base = 4 × 14 = 56 cm

⇒ Lateral Surface Area = 1/2 × 56 × 11.40175

⇒ Lateral Surface Area = 28 × 11.40175 ≈ 319.249 cm²

⇒ Rounding to one decimal place, we get 319.2 cm².

Therefore, Option 3 is the correct value for the lateral surface area.

∴ The correct answer is 319.2 cm².

Additional Information

Total Surface Area (TSA) of a Pyramid

TSA = Lateral Surface Area + Area of the Base. For a square pyramid, TSA = 2al + a².

Volume of a Pyramid

Volume = (1/3) × Base Area × Perpendicular Height (h). For a square pyramid, V = (1/3) × a² × h.

Slant Edge of a Pyramid

The slant edge (e) connects the apex to a base corner: e = √[h² + (a√2/2)²] or e = √[l² + (a/2)²].

Shortcut Trick

Test with counter-examples to verify the statements quickly.

Statement I: 1$1\over2$ + 2$1\over2$ = 4. Result is an integer, not a mixed fraction. So, it is false.

Statement II: 5$1\over2$ − 1$1\over4$ = 4$1\over4$. Result is a mixed fraction (> 1), not a proper fraction. So, it is false.

A proper fraction must have a numerator less than the denominator and value less than 1.

Since both specific cases fail the general "always" condition, both statements are incorrect.

∴ The correct answer is Both statements are false.

Alternate Method

Given:

Statement I: Sum of two mixed fractions is always a mixed fraction.

Statement II: Difference of two mixed fractions (Larger − Smaller) is always a proper fraction.

Evaluation of Statement I:

⇒ Let the two mixed fractions be 2$3\over4$ and 1$1\over4$.

⇒ Sum = (2 + 1) + (3/4 + 1/4)

⇒ Sum = 3 + (4/4) = 3 + 1 = 4.

⇒ 4 is an integer (whole number), not a mixed fraction. Hence, Statement I is false.

Evaluation of Statement II:

⇒ Let the larger mixed fraction be 5$3\over4$ and the smaller be 2$1\over4$.

⇒ Difference = (5 − 2) + (3/4 − 1/4)

⇒ Difference = 3 + 2/4 = 3$1\over2$.

⇒ A proper fraction is always less than 1. Since 3 1/2 > 1, it is not a proper fraction. Hence, Statement II is false.

∴ The correct answer is Both statements are false.

Additional Information

Proper vs Improper Fractions

A proper fraction has Numerator < Denominator (e.g., 3/4), while an improper fraction has Numerator ≥ Denominator (e.g., 7/4).

Mixed Fractions

A mixed fraction is the sum of a non-zero whole number and a proper fraction (e.g., 2 1/3). It can always be converted to an improper fraction: a b/c = (a × c + b) / c.

Operations on Fractions

To add or subtract mixed fractions, handle the whole numbers and fractional parts separately or convert them into improper fractions first.

Given:

tan(x + 10°) = cot(3x - 20°)

Formula Used:

cot(θ) = tan(90° - θ)

Calculation:

⇒ tan(x + 10°) = cot(3x - 20°)

⇒ tan(x + 10°) = tan(90° - (3x - 20°))

⇒ tan(x + 10°) = tan(90° - 3x + 20°)

⇒ tan(x + 10°) = tan(110° - 3x)

⇒ x + 10° = 110° - 3x 

⇒ 4x = 100°

⇒ x = 100° ÷ 4

⇒ x = 25°

∴ The correct answer is x = 25°.

Given:

Initial = 5000

Increase = 20% for 3 hours

Decrease = 10% for 4^th hour

Increase = 25% for 5^th hour

Formula Used:

New value = Initial × (1 + rate/100)

New value = Initial × (1 - rate/100)

Calculation:

⇒ After 3 hours = 5000 × (1.2)³

⇒ After 3 hours = 5000 × 1.728 = 8640

⇒ After 4^th hour = 8640 × 0.9 = 7776

⇒ After 5^th hour = 7776 × 1.25 = 9720

∴ The correct answer is 9720.

Given:

Radius = 9

Slant height = 15

Formula Used:

Slant height² = radius² + height²

Calculation:

⇒ 15² = 9² + height²

⇒ 225 = 81 + height²

⇒ height² = 144

⇒ height = 12

⇒ New height = 12 × 3 ÷ 2 = 18

⇒ New slant height = √(9² + 18²) = √405

⇒ √405 ≈ 20.12

∴ The correct answer is 20.12.

Given:

Two consecutive even numbers = 2n, 2n + 2

Formula Used:

Product = (2n)(2n + 2)

Perfect square form = (2n + 1)²

Calculation:

⇒ Product = 2n × (2n + 2)

⇒ Product = 4n² + 4n

⇒ Required square = (2n + 1)²

⇒ (2n + 1)² = 4n² + 4n + 1

⇒ Difference = (4n² + 4n + 1) - (4n² + 4n)

⇒ Difference = 1

∴ The correct answer is 1.

Given:

Radius = 5

OP = 13

Formula Used:

Tangent length = √(OP² - radius²)

Area = 2 × (1/2 × base × height)

Calculation:

⇒ PA = √(13² - 5²)

⇒ PA = √(169 - 25) = √144 = 12

⇒ Area of ΔPAO = 1/2 × 5 × 12 = 30

⇒ Area of ΔPBO = 30

⇒ Area of quadrilateral PAOB = 30 + 30

⇒ Area = 60

∴ The correct answer is 60.

Given:

A(0, 0)

B(4, 0)

C(2, 6)

Formula Used:

Centroid = ( (x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3 )

Calculation:

⇒ x-coordinate = (0 + 4 + 2) ÷ 3 = 6 ÷ 3 = 2

⇒ y-coordinate = (0 + 0 + 6) ÷ 3 = 6 ÷ 3 = 2

⇒ Centroid = (2, 2)

∴ The correct answer is (2, 2).

Given:

AC = 5

BC = 3

Formula Used:

sin(A) = opposite ÷ hypotenuse

Pythagoras theorem: AC² = AB² + BC²

Calculation:

⇒ AB² = 5² - 3² = 25 - 9 = 16

⇒ AB = 4

⇒ sin(A) = BC ÷ AC = 3 ÷ 5

⇒ sin(A) = 3/5

∴ The correct answer is 3/5.

The correct answer is Kadamai.

Key Points

• Kadamai was the term used for land revenue in the Chola kingdom. It referred to the tax or dues collected from the landowners.
• The Chola dynasty, which ruled southern India from approximately the 9^th century to the 13^th century CE, had a well-organized revenue system for the administration of its vast territories.
• Land revenue under the Cholas was typically collected from agricultural land and was a major source of income for the kingdom. The term Kadamai denoted the obligation of farmers or landowners to pay taxes to the state or local authorities.
• Revenue officers called Vettiyan were appointed to collect Kadamai. These officials ensured compliance with tax obligations and maintained records of the land and its productivity.
• The revenue system under the Cholas also included taxes on irrigation facilities, which were extensively developed during their reign to support agriculture.
• Kadamai was an essential part of the Chola administrative structure, reflecting their efficient governance and resource management practices.

Additional Information

• Chola Dynasty:
• The Chola dynasty was one of the longest-ruling dynasties in Indian history, with its rule extending from the 9^th century to the 13^th century CE.
• The Cholas were known for their remarkable contributions to art, architecture, literature, and administration.
• Their capital was located at Thanjavur, and they expanded their kingdom to include parts of South India, Sri Lanka, and Southeast Asia.
• Land Revenue System:
• Under the Chola administration, land was classified based on its fertility and productivity, and taxes were levied accordingly.
• The tax rate varied but typically ranged from one-sixth to one-fourth of the produce.
• Irrigation facilities, including tanks and canals, played a crucial role in enhancing agricultural productivity and were often taxed separately.
• Other Revenue Terms:
• Vetti: A form of forced labor or tribute, often paid in goods or services instead of money.
• Cess Tax: While not specific to the Chola kingdom, the term is generally used for taxes levied for specific purposes, such as education or health.
• Ladder Tax: This term is unrelated to the Chola kingdom and typically refers to taxes levied in other historical contexts, such as those imposed on the use of ladders in medieval Europe.
• Significance of Kadamai:
• The term Kadamai highlights the structured approach the Cholas took to governance, ensuring a steady revenue stream to support their administrative and military needs.
• It also reflects the interdependence between the state and the agricultural sector, which was the backbone of the economy.

Important Points

• The Chola dynasty's efficient administrative system included local governance through village assemblies called sabhas. These assemblies played a role in managing revenue collection and agricultural activities.
• The Cholas constructed numerous irrigation facilities, such as the Kallanai Dam, which ensured a reliable water supply for agriculture and contributed to their economic prosperity.
• The Chola rulers were patrons of art and architecture, and the revenue collected through Kadamai funded the construction of grand temples like the Brihadeeswara Temple.
• The Chola dynasty's governance model, including its revenue system, influenced subsequent South Indian kingdoms and contributed to the region's historical legacy.

The correct answer is Sur Dynasty.

Key Points

• The Sur Dynasty ruled India for a brief period of only 15 years, from 1540 to 1555. It was established by Sher Shah Suri, a prominent ruler known for his administrative reforms and military strategies.
• Sher Shah Suri defeated the Mughal emperor Humayun at the Battle of Kannauj (1540) and effectively ended Mughal rule temporarily during his reign.
• The Sur Dynasty is celebrated for initiating notable reforms, such as the introduction of the Rupiya (currency) and significant improvements in road infrastructure, including the construction of the Grand Trunk Road.
• The Sur Empire declined after the death of Sher Shah in 1545, with a series of weak successors unable to hold the empire together. Humayun regained the throne in 1555, marking the end of the Sur Dynasty.
• The Sur Dynasty ruled primarily over northern India, extending its influence to parts of present-day Pakistan and Afghanistan during its brief reign.

Additional Information

• Khilji Dynasty:
• The Khilji Dynasty ruled India from 1290 to 1320. It was known for its military prowess, territorial expansion, and administrative efficiency under rulers like Alauddin Khilji.
• Alauddin Khilji introduced significant reforms, including market regulation and a centralized revenue system.
• The dynasty was prominent during the Delhi Sultanate period but ruled for a longer duration compared to the Sur Dynasty.
• Tughlaq Dynasty:
• The Tughlaq Dynasty ruled India from 1320 to 1414, making it one of the longest-reigning dynasties of the Delhi Sultanate.
• Notable rulers like Mohammad bin Tughlaq and Firoz Shah Tughlaq introduced significant reforms, although some, like the shifting of the capital to Daulatabad, were unsuccessful.
• The dynasty is remembered for its architectural contributions and expansion of territories.
• Lodi Dynasty:
• The Lodi Dynasty ruled from 1451 to 1526 and was the last dynasty of the Delhi Sultanate before the Mughals took over.
• Rulers like Sikandar Lodi and Ibrahim Lodi contributed to the administration and urban development of cities like Agra.
• The dynasty ended with the defeat of Ibrahim Lodi by Babur at the First Battle of Panipat (1526), leading to the establishment of the Mughal Empire.
• Sher Shah Suri’s Contributions:
• He introduced the Rupiya, the precursor to the modern Indian Rupee, standardizing the currency system.
• He constructed the Grand Trunk Road, connecting key trade routes from Bengal to Peshawar.
• His administrative policies, such as land revenue reforms, had a lasting impact on subsequent empires.
• He built the Rohtas Fort in Bihar and significantly improved the postal system.

Important Points

• The Battle of Kannauj: Sher Shah Suri’s victory over Humayun at Kannauj was a significant turning point in Indian history, leading to the temporary displacement of the Mughal Empire.
• Infrastructure Development: Sher Shah’s focus on road construction and trade routes facilitated economic growth and administrative efficiency in the region.
• Decline of the Sur Dynasty: After Sher Shah’s death in 1545, his successors were unable to maintain the empire, leading to its downfall and the restoration of Mughal rule.

The correct answer is Article 2.

Key Points

• Article 2 of the Indian Constitution empowers Parliament to admit new states into the Union of India or establish new states.
• This provision grants the Parliament the authority to create or incorporate new states into the Indian territory, ensuring flexibility in territorial expansion.
• The admission or establishment of new states under Article 2 is subject to the terms and conditions specified by Parliament.
• It is distinct from Article 3, which deals with changes in the boundaries or names of existing states. Article 2 strictly pertains to the inclusion of new states in the Union.
• Examples of states admitted under Article 2 include the inclusion of Sikkim as a full-fledged state in the Indian Union in 1975.

Additional Information

• Article 2 vs Article 3:
• Article 2: Deals with the admission or establishment of new states in the Union of India. It is applicable for territories that were not previously part of India.
• Article 3: Pertains to the reorganization of existing states, such as altering state boundaries, merging states, or changing state names.
• Sikkim's Inclusion:
• Sikkim was initially a protectorate under India and became a state under Article 2 in 1975 after a referendum.
• This marked a significant event in India's territorial expansion post-independence.
• Historical Context:
• After India's independence in 1947, various princely states and territories joined India through legal and constitutional provisions like Article 2.
• Examples include the inclusion of French territories like Pondicherry and Portuguese territories like Goa into the Indian Union.
• Role of Parliament:
• Parliament holds the supreme authority in deciding the terms and conditions for admitting new states under Article 2.
• Any such admission requires the passage of a law in Parliament, ensuring democratic oversight.

Important Points

• Constitutional Flexibility: Article 2 allows India to incorporate new territories or states, demonstrating the Constitution's adaptability to geopolitical changes.
• Global Examples: Similar provisions exist in other federal systems worldwide, such as the United States, which can admit new states into its union.
• Legal Framework: The inclusion of new states requires careful deliberation in Parliament, ensuring adherence to constitutional principles and democratic processes.
• Statehood Process: Territories aspiring for statehood typically undergo extensive negotiations and legal frameworks before being admitted under Article 2.

The correct answer is Neither I nor II.

Key Points

• Statement I: Article 30 of the Indian Constitution is not related to the abolition of titles. Instead, it provides rights to minorities to establish and administer educational institutions of their choice. Hence, this statement is incorrect.
• Article 18 of the Indian Constitution is the one that deals with the abolition of titles except for military and academic distinctions. It prohibits the state from conferring titles that create artificial distinctions in society.
• Statement II: Article 22 of the Indian Constitution is not related to the prohibition of employment of children in factories. Instead, it provides protection in cases of arrest and detention. Hence, this statement is incorrect.
• Article 24 is the constitutional provision that prohibits the employment of children below the age of 14 years in factories, mines, or any other hazardous employment.
• Since neither Statement I nor Statement II is correct, the correct answer is "Neither I nor II."

Additional Information

• Fundamental Rights in the Indian Constitution:
• Part III of the Indian Constitution (Articles 12-35) deals with Fundamental Rights, which are basic human rights guaranteed to all citizens.
• These rights are enforceable by the courts and are considered essential for the overall development of individuals.
• Examples include the Right to Equality (Articles 14-18), Right to Freedom (Articles 19-22), and Right against Exploitation (Articles 23-24).
• Article 30:
• Grants minorities the right to establish and administer educational institutions of their choice.
• This right aims to preserve the cultural and educational rights of minorities in India.
• Article 18 (Abolition of Titles):
• Prohibits the state from conferring titles except for military and academic distinctions.
• Prevents the practice of granting hereditary titles like "Raja" or "Maharaja."
• Ensures equality among citizens by eliminating societal distinctions based on titles.
• Article 22 (Protection in Cases of Arrest):
• Deals with protection against arbitrary arrest and detention.
• Provides rights such as being informed of the reasons for arrest, the right to consult a legal practitioner, and being produced before a magistrate within 24 hours.
• Article 24 (Prohibition of Child Labour):
• Prohibits the employment of children below 14 years in factories, mines, or hazardous work environments.
• Aims to protect children from exploitation and ensure their right to education under Article 21A.

Important Points

• Child Labour Prohibition: The Child Labour (Prohibition and Regulation) Act, 1986, prohibits the employment of children in hazardous occupations and regulates the working conditions of children in non-hazardous jobs.
• Right to Education: Article 21A ensures free and compulsory education for children aged 6 to 14 years, which complements the prohibition of child labour under Article 24.
• Judicial Enforcement: Fundamental Rights can be enforced through the courts under Article 32 (Supreme Court) and Article 226 (High Courts).
• Constitutional Amendments: Various amendments, such as the 86^th Amendment (2002), have strengthened the provisions related to child rights and education.

The correct answer is Manushi Chhillar.

Key Points

• Manushi Chhillar, an Indian model and beauty queen, was crowned Miss World on 18^th November 2017 at the event held in Sanya, China.
• She is the sixth Indian to win the prestigious title of Miss World, following notable winners like Aishwarya Rai (1994) and Priyanka Chopra (2000).
• Manushi Chhillar represented the state of Haryana in the competition, showcasing her talent, intelligence, and social initiatives.
• Her winning answer in the Q&A round focused on the significance of mothers’ contributions to society, resonating deeply with the judges and audience.
• She actively promoted her project titled "Project Shakti," aimed at spreading awareness about menstrual hygiene among women in India.

Additional Information

• Miss World Pageant:
• The Miss World competition is one of the oldest and most prestigious international beauty pageants, established in 1951.
• The pageant evaluates contestants based on their beauty, intelligence, and commitment to social causes through initiatives like the Beauty with a Purpose program.
• India has won the title six times, with winners including Reita Faria (1966), Aishwarya Rai (1994), Diana Hayden (1997), Yukta Mookhey (1999), Priyanka Chopra (2000), and Manushi Chhillar (2017).
• Manushi Chhillar’s Background:
• Born on 14^th May 1997, Manushi Chhillar hails from Sonipat, Haryana.
• She pursued her studies in medicine at the Bhagat Phool Singh Government Medical College for Women in Haryana.
• Her achievements highlight her dedication to promoting health-related issues and women’s empowerment.
• Project Shakti:
• Manushi Chhillar’s "Project Shakti" focuses on menstrual hygiene awareness among women in rural areas of India.
• The initiative emphasizes the importance of breaking taboos surrounding menstruation and ensuring access to hygienic products.
• It aligns with global efforts to improve women’s health and well-being.
• Other Indian Miss World Winners:
• Reita Faria (1966): First Indian to win Miss World.
• Aishwarya Rai (1994): Became an international film star post her win.
• Diana Hayden (1997): Known for her intelligence and grace.
• Yukta Mookhey (1999): Advocated for social causes post her victory.
• Priyanka Chopra (2000): Gained global fame as an actress and philanthropist.

Important Points

• Significance of Beauty Pageants:
• Beauty pageants like Miss World provide a platform for women to showcase their talents, intelligence, and commitment to social causes.
• They promote cultural exchange and inspire women to play active roles in community-building initiatives.
• Global Impact of Miss World:
• The Beauty with a Purpose initiative associated with Miss World encourages contestants to engage in projects addressing health, education, and environmental issues.
• Manushi Chhillar’s win has inspired many young women in India to contribute to social causes and pursue their dreams.

The correct answer is 50,000.

Key Points

• The Union Finance Minister in the Budget 2025-26 announced the establishment of 50,000 Atal Tinkering Labs (ATLs) in government schools across India over the next five years.
• Atal Tinkering Labs are part of the flagship initiative under the Atal Innovation Mission (AIM), launched by the NITI Aayog.
• The main aim of establishing these labs is to foster a culture of innovation and entrepreneurship among students by equipping schools with state-of-the-art infrastructure to allow hands-on learning.
• The initiative targets promoting STEM (Science, Technology, Engineering, and Mathematics) education in schools and emphasizes critical thinking, creativity, and problem-solving skills among young learners.
• These labs are expected to encourage students to work on real-world problems and develop prototype solutions using innovative technologies like 3D printing, IoT (Internet of Things), Robotics, and Artificial Intelligence.

Additional Information

• Atal Innovation Mission (AIM):
• Launched by the Government of India, AIM is a flagship initiative to promote a culture of innovation and entrepreneurship across the country.
• The mission includes multiple components such as Atal Tinkering Labs, Atal Incubation Centers, and ARISE (Applied Research and Innovation for Small Enterprises).
• AIM supports the creation of an ecosystem conducive to scientific exploration and promotes collaboration between academia, industry, and startups.
• Features of Atal Tinkering Labs (ATLs):
• Each ATL is equipped with cutting-edge tools like 3D printers, robotics kits, microcontrollers, IoT devices, and sensors.
• Students are encouraged to ideate and implement projects that address real-world challenges like water conservation, renewable energy, and health solutions.
• The labs provide a platform for students from Class 6 to Class 12 to explore and develop their innovative potential.
• Impact of ATLs:
• Encourages the development of entrepreneurial skills among students at a young age.
• Promotes interdisciplinary learning by integrating science, technology, and practical application.
• Helps in building a future-ready workforce equipped with 21^st-century skills.
• Fosters grassroots innovation and builds a culture of problem-solving and critical thinking in schools.
• Key Statistics:
• As of 2023, over 10,000 Atal Tinkering Labs have already been established in schools across India, benefiting thousands of students.
• The target of 50,000 labs aims to significantly expand the reach of this initiative, especially in rural and underprivileged areas.
• Each ATL receives a grant of up to INR 20 lakhs to set up the infrastructure and manage operational costs.

Important Points

• Eligibility: ATLs are set up in schools managed by government, local bodies, or private trusts, provided they meet the eligibility criteria set by the AIM.
• Training and Mentorship: The initiative includes training programs for teachers and students and connects schools with industry mentors for guidance.
• Global Competitiveness: ATLs aim to prepare Indian students to compete at international innovation challenges and hackathons.
• Alignment with NEP 2020: The initiative aligns with the National Education Policy 2020, which emphasizes experiential learning and skill development.