SSC CHSL 2025 Tier-1 (Held On: 13 Nov, 2025 Shift 3) (Previous Year Paper)

The correct answer is '1' i.e. The main affect .

Key Points

• The error in the sentence lies in the word 'affect'. It is incorrectly used as a noun.
• The correct word should be 'effect', which is the appropriate noun form.
• In English, 'affect' is primarily used as a verb meaning "to influence," while 'effect' is a noun meaning "a result or outcome."

Correct sentence: The main effect of the new policy will be an increase in productivity.

Additional Information

• 'Affect' vs 'Effect':
• Affect (verb): To influence something. Example: The weather affects my mood.
• Effect (noun): A result or outcome. Example: The medication had a positive effect on her health.
• Usage Tip: If you're looking for a noun, use "effect." If you're describing an action, use "affect."

The correct answer is '3' i.e. on .

Key Points

• The word contingent is often followed by the preposition "on" to indicate dependency or condition.
• The meaning of the sentence is that his promotion depends on the result of the annual review.
• Using the correct preposition ensures that the sentence conveys the intended meaning properly.

Correct sentence: His promotion was contingent on the outcome of the annual review.

Additional Information

• Common usage of "contingent on":
• Example: Success is contingent on hard work.
• Meaning: Success depends on hard work.
• Incorrect options:
• upto: Indicates a limit or extent, not suitable here.
• to: Indicates direction or relationship, not dependency.
• into: Indicates movement or change, not conditional dependence.

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

Key Points

• The word 'Transhistorical' refers to something that transcends or goes beyond historical boundaries or specific time periods.
• The most appropriate synonym for this is 'Timeless', as it conveys the idea of being independent of time or not limited by historical periods.
• The other options do not match the meaning accurately:
• Ancient: Refers to something very old or from a distant past, not beyond time.
• Recent: Refers to something that has occurred in the near past, which is not relevant here.
• Futuristic: Refers to something related to the future, not transcending time.

Correct synonym: Timeless.

Additional Information

• Timeless: Something that is eternal or beyond the constraints of time.
• Usage Example: The beauty of the mountains is timeless, captivating people from all eras.

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

Key Points

• The word Extroversion refers to the quality of being outgoing and socially confident.
• Among the given options, only option 1, Extroversion, is correctly spelt.
• Other options contain spelling errors:
• Option 2: Extroversoin - Incorrect due to misplaced letters.
• Option 3: Extroverssion - Incorrect due to an extra 's'.
• Option 4: Extroversin - Incorrect due to missing 'o'.

Correct Usage: The term Extroversion is often used in psychology to describe a personality trait where individuals gain energy from social interactions.

Additional Information

• Extroversion is the opposite of introversion, which refers to a preference for solitary activities and gaining energy from being alone.
• The term is widely used in personality studies and is one of the five traits in the Big Five Personality Traits model (OCEAN: Openness, Conscientiousness, Extroversion, Agreeableness, Neuroticism).

The correct answer is '3' i.e. The camera captured every minute detail of the insect’s wing .

Key Points

• The word "minute" in the given sentence refers to something extremely small or tiny.
• Option 3 uses the word "minute" with the same meaning, emphasizing the tiny details captured by the camera.
• Other options, such as 1, 2, and 4, refer to "minute" as a unit of time, which is not the intended meaning in the given sentence.

Correct sentence: The camera captured every minute detail of the insect’s wing.

Additional Information

• The word "minute" has two distinct meanings:
• Time-related: Refers to a unit of time equivalent to 60 seconds (e.g., "The meeting will start in a few minutes").
• Size-related: Refers to something extremely small or detailed (e.g., "A minute speck of dust").
• Understanding the context of the sentence is crucial to determining the correct meaning of the word.

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

Key Points

• Option 1, "Business," is the correctly spelt word referring to an occupation, profession, or trade.
• Option 2, "Busyness," refers to the state of being busy, which is unrelated to the intended context of the question.
• Option 3, "Bussiness," is incorrectly spelt and does not exist in standard English.
• Option 4, "Buseness," is also incorrectly spelt and does not exist in standard English.

Correct sentence: The correct spelling for the word is Business.

Additional Information

• Common spelling errors for "Business":
• "Bussiness" - Includes an extra "s" that is incorrect.
• "Buseness" - Misses the "i," making it a wrong spelling.
• Usage of "Business":
• Example: "She has started her own business."
• It is used to refer to professional work or a commercial enterprise.

The correct answer is Option 3.

 

Key Points

• The passage explicitly defines a "growing paradox" in the first paragraph: "while these technologies offer unparalleled convenience and power, they also undermine tried-and-true social forms and erode the very notion of what it means to be human."
• The author describes this as the "double-edged nature" of progress—balancing solutions to big problems with the creation of new social and existential issues.
• The text highlights specific contradictions, such as medical breakthroughs versus job displacement through automation and global connectivity versus feelings of disconnection.
• Option 3 directly captures both sides of this paradox (convenience vs. social/human erosion), whereas the other options focus only on one side or make exaggerated claims not supported by the text.

Therefore, the correct answer is Option 3.

 

Correct Sentence from Text: "But with our arrival in an age of artificial intelligence... comes a growing paradox: while these technologies offer unparalleled convenience and power, they also undermine tried-and-true social forms and erode the very notion of what it means to be human."

 

Additional Information

• Option 1: Incorrect. While the text says technology provides "standards of living much better," it immediately follows this with the negative "profound implications" like job loss, meaning it doesn't always just improve life.
• Option 2: Incorrect. The text says automation is taking jobs where "human labor can be automated," not that it eliminates all forms of labor.
• Option 4: Incorrect. The passage concludes that technology "brings new issues that human beings must resolve," contradicting the idea that there are no consequences.

The correct answer is Option 2.

 

Key Points

• The passage highlights several positive impacts of progress, specifically noting that "Medical advances like gene editing and precision medicine hold the promise to cure diseases that were once thought incurable."
• It also mentions that technological advances have generally provided "standards of living much better" and improved global cooperation through communication technology.
• Option 2 directly mirrors the text's description of medical progress as a revolutionary change.
• Other options represent negative impacts or factually incorrect statements based on the text (e.g., automation is causing job loss, not reducing it).

Therefore, the correct answer is Option 2.

 

Correct Sentence from Text: "Medical advances like gene editing and precision medicine hold the promise to cure diseases that were once thought incurable."

 

Additional Information

• Option 1: Incorrect. The passage states that "Automation is taking away jobs for millions of people," which is a negative impact.
• Option 3: Incorrect. The text states communication technology has allowed people to "work together across borders," rather than causing isolation.
• Option 4: Incorrect. The author explicitly states that technological advances "have provided standards of living much better."

The correct answer is Option 2.

 

Key Points

• The passage notes that the "speed of innovation has left millions behind," which results in a "feeling of disconnection, fear for the future."
• This is presented as a negative consequence alongside automation taking away jobs and the erosion of "what it means to be human."
• The author also points out that our dependence on technology is raising critical concerns regarding "privacy, security, and freedom."
• Option 2 directly reflects the text's description of the psychological and social impact of rapid technological change.

Therefore, the correct answer is Option 2.

 

Correct Sentence from Text: "The speed of innovation has left millions behind, and with it there is a feeling of disconnection, fear for the future."

 

Additional Information

• Option 1: Incorrect. Making life more comfortable (better standards of living) is described by the author as a positive impact.
• Option 3: Incorrect. Helping people work together across borders is listed as a positive result of communication technology.
• Option 4: Incorrect. The passage states that technology creates "questions regarding privacy," not that it eliminates the need for it; rather, it makes privacy more vulnerable.

The correct answer is Option 3.

 

Key Points

• The passage explores the shifting dynamic between humans and their inventions, particularly as AI and automation become deeply integrated into daily life.
• The author explicitly poses a philosophical question regarding our agency: "are we Master of Technology, or is technology the master of us?"
• This question arises from the paradox of progress, where our growing dependence on technology creates concerns about privacy, security, and the erosion of human identity.
• The text suggests that while we use technology to solve problems, the power it holds over social structures makes our control over it a central theme.

Therefore, the correct answer is Option 3.

 

Correct Sentence from Text: "As we introduce Al into everyday life, do we have to sit back and ask ourselves: are we Master of Technology, or is technology the master of us?"

 

Additional Information

• Option 1: Incorrect. The text focuses on the social and ethical implications of technology rather than its economic affordability.
• Option 2: Incorrect. While the text mentions working across "borders and cultures," it does not specifically discuss political conflicts.
• Option 4: Incorrect. The author does not suggest a complete rejection of technology; instead, they advocate for resolving new issues to ensure a "more just and sustainable tomorrow."

The correct answer is Option 2.

 

Key Points

• The passage identifies a "double-edged nature" of progress, where technology provides solutions to big problems but simultaneously introduces new, complex challenges.
• The author explicitly states that for progress to lead to a "more just and sustainable tomorrow," human beings must take the initiative to "resolve" these new issues.
• These issues include job displacement via automation, privacy and security concerns, and the social disconnection caused by the rapid pace of innovation.
• Option 2 directly captures the author's concluding argument that human intervention and problem-solving are required to navigate the paradox of technology.

Therefore, the correct answer is Option 2.

 

Correct Sentence from Text: "On one hand, technology comes bearing answers to some of humankind's biggest problems, yet it also brings new issues that human beings must resolve in order to make progress mean a more just and sustainable tomorrow."

 

Additional Information

• Option 1: Incorrect. The text lists "dependence on technology" as a cause of ethical questions regarding freedom and security, not as a requirement for sustainability.
• Option 3: Incorrect. The passage describes technological breakthroughs as part of "human evolution"; the focus is on resolving the side effects of innovation rather than halting innovation itself.
• Option 4: Incorrect. The text presents automation as a potential threat to millions of jobs, making it an issue to be managed rather than the primary solution for a just future.

The correct answer is '3' i.e. An integral and unavoidable component .

Key Points

• The idiom "Part and parcel" means an essential or integral part of something.
• It refers to something that is unavoidable or inherent in a particular situation or process.
• For example, "Stress is part and parcel of being a doctor," means stress is an unavoidable component of the profession.

Correct sentence: Hard work is part and parcel of success in life.

Additional Information

• Idioms are phrases or expressions that have a figurative meaning different from their literal meaning.
• Understanding idioms is essential for improving language fluency and comprehension, as they are commonly used in both spoken and written communication.

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

Key Points

• The word Credulous refers to someone who is too willing to believe things without questioning them, often described as gullible or naive.
• Among the given options:
• Trusting: Similar to credulous, as it implies belief without doubt.
• Skeptical: The opposite of credulous, as it refers to someone who is doubtful and questions things.
• Gullible: Synonymous with credulous, indicating someone easily deceived.
• Naive: Related to credulous, as it implies a lack of experience or sophistication.
• Thus, the most appropriate antonym is Skeptical.

Correct sentence: The most appropriate antonym of "Credulous" is Skeptical.

Additional Information

• Antonyms are words with opposite meanings. In this case:
• Credulous: Tends to believe things easily.
• Skeptical: Doubts or questions the truth of things.
• It is important to distinguish between synonyms (similar meanings) and antonyms (opposite meanings).

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

Key Points

• The term Matricide refers to the act of killing one’s own mother.
• Let us analyze the other options:
• Patricide: The act of killing one’s own father.
• Homicide: The act of killing another human being.
• Fratricide: The act of killing one’s own brother.

Correct answer: The killing of one’s own mother is referred to as Matricide.

Additional Information

• The word Matricide is derived from the Latin words mater (meaning mother) and -cidium (meaning act of killing).
• It is important to understand the distinctions between similar terms like Patricide, Fratricide, and Homicide to avoid confusion.

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

Key Points

• An Exodus refers to a large-scale departure or movement of people from one place to another, usually due to certain circumstances like war, famine, or other crises.
• The word Emigration (Option 2) refers to leaving one’s own country to settle in another, which is not necessarily on a large scale.
• The word Immigration (Option 3) refers to coming to live in a country permanently, which is the opposite of emigration.
• Migration (Option 4) refers to the movement of people or animals from one place to another, but it may not necessarily mean a large-scale departure.

Correct sentence: A large-scale departure of people from one place is called an Exodus.

Additional Information

• Exodus in History:
• The term is often associated with the biblical account of the Israelites leaving Egypt under the leadership of Moses, which is considered a significant historical exodus.
• Modern Examples:
• Mass departures due to wars, natural disasters, or political instability are often described as exoduses.

The correct answer is '1' i.e. The city council is constructing a new bridge .

Key Points

• The given sentence is in the passive voice. The structure is "A new bridge is being constructed by the city council."
• To convert a sentence from passive to active voice, the subject (doer of the action) becomes the focus of the sentence.
• In the active voice, the subject "the city council" is performing the action of constructing the bridge.
• The correct sentence in the active voice is: "The city council is constructing a new bridge."

Correct sentence: The city council is constructing a new bridge.

Additional Information

• Active vs. Passive Voice:
• Active Voice: The subject performs the action. Example: "The cat chased the mouse."
• Passive Voice: The subject is acted upon. Example: "The mouse was chased by the cat."
• When to Use Active Voice:
• Use active voice for clear and direct sentences.
• Example: "She is writing a book" (active) vs. "A book is being written by her" (passive).

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

Key Points

• The word "Ineffable" means something that is too great or extreme to be expressed or described in words.
• To find an antonym, we must look for a word that means the opposite – i.e., something that can be expressed or described.
• Among the given options:
• 1) Expressible: Means something that can be expressed, making it the correct antonym of "ineffable."
• 2) Inarticulate: Means unable to express oneself clearly, which is not the opposite of ineffable.
• 3) Unfathomable: Means difficult or impossible to understand, which is a synonym of ineffable, not an antonym.
• 4) Indescribable: Means something that cannot be described, which is again a synonym of ineffable.

Correct answer: The most appropriate antonym of "Ineffable" is "Expressible."

Additional Information

• Synonyms of "Ineffable": Indescribable, unutterable, inexpressible.
• Antonyms of "Ineffable": Expressible, describable, definable.

The correct answer is '1' i.e. The manager said that they would make a decision by Friday. .

Key Points

• The given sentence is in direct speech, and the task is to convert it into indirect speech.
• In indirect speech, changes are made to the pronouns and tense, and the quotation marks are removed.
• Here, the direct speech is in the future tense ("We will make"), which changes to the future in the past tense ("they would make").
• Additionally, the pronoun "we" changes to "they" to match the indirect speech.

Correct sentence: The manager said that they would make a decision by Friday.

Additional Information

• Changes in tense when converting to indirect speech:
• Simple present → Simple past
• Present continuous → Past continuous
• Future simple ("will") → Future in the past ("would")
• Pronoun changes:
• "We" → "They" (depending on the subject).

The correct answer is '2' i.e. Twenty minutes is the time .

Key Points

• The subject of the sentence, "Twenty minutes," is considered singular because it refers to a single period of time.
• When a singular subject is used, the correct verb form is "is", which agrees with the singular subject.
• The sentence correctly uses "Twenty minutes is the time" because it identifies the specific duration needed.

Correct sentence: Twenty minutes is the time I need to get ready for the party.

Additional Information

• Singular vs Plural Subject:
• Singular: Refers to one entity (e.g., "Twenty minutes is the time").
• Plural: Refers to multiple entities (e.g., "Minutes are passing quickly").
• Agreement Rules:
• Ensure the verb agrees with the subject in number and tense.
• For singular subjects, use singular verbs; for plural subjects, use plural verbs.

The correct answer is '2', i.e. 'it has originally been designed for short ones'.

Key Points

• The sentence mentions that the Rover was designed for short drives but was modified for long drives, which describes an action that was completed in the past (designing the Rover).
• The use of “has been” in the correct option highlights the past action of designing the Rover while maintaining relevance to the present context.
• The word “ones” is used to correctly replace the plural noun "short drives."

Correct sentence: Necessity being the mother of invention, he resourcefully modifies the Rover to go on long drives even though it has originally been designed for short ones.

Additional Information

• Option 1: "it has originally have been designed for short one" – Incorrect because of the unnecessary use of “have” and the singular form “one” instead of “ones.”
• Option 3: "it has originally was designed for short ones" – Incorrect because "has" and "was" cannot be used together; they create a grammatical error.
• Option 4: "it has originally has been designed to short one" – Incorrect because of redundancy in "has" and "has been" and the use of the singular form “one” instead of “ones.”

The correct answer is '3' i.e. The renowned author will have released his newest novel by the end of the year .

Key Points

• The given sentence is in the future perfect tense in the active voice.
• In future perfect tense sentences, the passive voice structure is: Subject + will have + past participle + Object .
• The correct transformation of the given sentence to active voice is: The renowned author will have released his newest novel by the end of the year.

Correct sentence: The renowned author will have released his newest novel by the end of the year.

Additional Information

• Active Voice: The renowned author will have released his newest novel by the end of the year.
• Structure: Subject + will have + past participle + object.
• Passive Voice: The renowned author’s newest novel will have been released by the end of the year.
• Structure: Object + will have been + past participle + by + subject.

The correct answer is '2' i.e. We should have been kept informed about the progress of the investigation by you.

Key Points

• The given sentence is in the active voice: "You should have kept us informed about the progress of the investigation."
• To convert the sentence into the passive voice, the subject ("you") becomes the agent, and the object ("us") becomes the subject of the sentence.
• The correct passive structure for the sentence is: "We should have been kept informed about the progress of the investigation by you."
• Option 2 correctly represents this transformation and maintains the tense and meaning of the original sentence.

Correct sentence: We should have been kept informed about the progress of the investigation by you.

Additional Information

• Active Voice: The subject performs the action (e.g., "You should have kept us informed").
• Passive Voice: The subject becomes the recipient of the action (e.g., "We should have been kept informed").
• The passive voice often includes the preposition "by" to indicate the agent performing the action.

The correct answer is '2' i.e. The manager said, "Your hard work and dedication have been noticed and appreciated."

Key Points

• To express the sentence in direct speech, we need to focus on the exact words spoken by the speaker.
• The direct speech should retain the original meaning and tense as conveyed in the indirect speech.
• The indirect sentence states that the manager told the team their hard work and dedication "had been noticed and appreciated," which implies past perfect tense. However, in direct speech, the context changes slightly to present perfect tense, as it reflects the immediate recognition.

Correct sentence: The manager said, "Your hard work and dedication have been noticed and appreciated.".

Additional Information

• Understanding Direct Speech:
• Direct speech involves quoting the exact words spoken by a person, enclosed in quotation marks.
• Example: He said, "I am going to the park."
• Understanding Indirect Speech:
• Indirect speech paraphrases what was said, often adjusting tense and pronouns.
• Example: He said that he was going to the park.

The correct answer is '1' i.e. "Would you have been able to finish the report today if I had not helped you with the research, which was a very tedious process?" he asked me. .

Key Points

• The given sentence is in indirect speech, where the speaker asks about a hypothetical situation in the past.
• To convert this into direct speech, we need to maintain the tense and structure of the original question.
• The structure in direct speech reflects the use of would in hypothetical situations, as it matches the reported question.

Correct sentence: "Would you have been able to finish the report today if I had not helped you with the research, which was a very tedious process?" he asked me.

Additional Information

• Direct Speech: Involves quoting the exact words of the speaker, often enclosed in quotation marks.
• Indirect Speech: Involves paraphrasing the speaker's words without quotation marks, often changing the tense accordingly.
• Key Rule: In hypothetical questions, "would" is used to express unreal conditions.

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

Key Points

• The paragraph should be logically arranged so that the sequence of events flows meaningfully and grammatically.
• Step 1: Sentence P introduces the preparation of the batter and baking of the cake layers.
• Step 2: Sentence S describes the preparation of the icing and the leveling of the cake layers.
• Step 3: Sentence R explains the stacking of the layers with icing and coating the cake.
• Step 4: Sentence Q concludes the paragraph by describing the finished product—ready for celebration.
• Thus, the correct sequence is P, S, R, Q.

Correct sentence sequence: P. She created a decadent batter and baked three layers of cake flawlessly. S. Before gently leveling each cake layer, she created a light and creamy icing. R. She coated the outside of the entire cake after stacking the layers with icing between them. Q. The finished cake was a stunning design, prepared for the celebration and the candles.

Additional Information

• Tips for paragraph arrangement:
• Identify the introduction, main body, and conclusion of the paragraph.
• Look for logical connectors or keywords that indicate sequence, such as "first," "then," "after," etc.
• Ensure the paragraph maintains a coherent flow of ideas.
• In this case, the sequence of events aligns perfectly with option 2: P, S, R, Q.

Checking the options

Option 1: Reject the offer and risk bankruptcy

This decision is driven by emotion and may lead to complete business failure.

Option 2: Accept the offer to save the company

This ensures survival but gives up majority ownership without attempting better terms.

Option 3: Negotiate to retain some strategic control

This approach balances survival with ownership interests by attempting a mutually beneficial agreement.

Option 4: Quit and look for a job

This abandons the entrepreneurial effort instead of exploring strategic solutions.

Hence, the correct answer is Option 3.

Checking the options:

Option 1: Publicly shame them

This reaction is emotionally driven and can damage the relationship. Public humiliation does not solve the issue and may create unnecessary conflict.

Option 2: Stop talking to them

This avoids the issue rather than addressing it directly. While it may protect you temporarily, it does not communicate boundaries or resolve the financial concern maturely.

Option 3: Set clear terms for future lending and politely ask for repayment of existing loan

This is a balanced and mature approach. It maintains respect in the relationship while clearly establishing boundaries. It also encourages accountability without aggression.

Option 4: Lend more to avoid conflict

This reinforces irresponsible behavior and increases personal discomfort. It avoids confrontation but worsens the situation.

Hence, the correct answer is Option 3.

According to the given information,

There are 32 cars parked in a straight line.

Car P is positioned 8th from the left end.

Car Q is positioned 14th from the right end.

The objective is to determine the number of cars between P and Q.

The most appropriate approach should:

Convert both positions from the same reference point

Identify their exact positions numerically

Calculate the difference accurately

Checking the steps:

Step 1: Determine Q’s position from the left side

Since Q is 14th from the right in a row of 32 cars:

Position from left = 32 − 14 + 1 = 19

So, Q is 19th from the left.

Step 2: Identify positions

P is 8th from the left.

Q is 19th from the left.

Step 3: Find the number of cars between them

Number of cars between P and Q = 19 − 8 − 1 = 10

Hence, the correct answer is 10 cars.

Checking the options:

Course of Action I: Ban all online banking services immediately

This step is extreme and impractical. Online banking is an essential service, and banning it would create widespread inconvenience without directly solving the issue of fraudulent apps. Therefore, this does not logically follow.

Course of Action II: Increase cybersecurity measures and run awareness campaigns for users

This step directly targets the problem by strengthening security systems and educating users about fraud prevention. It is practical, preventive, and logically connected to the issue stated. Therefore, this logically follows.

Hence, only Course of Action II follows.

The logic followed here is:

Thus, the missing letter in the series is Q.

 Hence, the correct answer is Q.

Checking the options:

Option 1: Organize a marathon

This does not reduce pollution levels. It is unrelated to solving the environmental issue.

Option 2: Introduce stricter emissions regulations

This directly targets one of the main causes of pollution (vehicle and industrial emissions). It is a practical and policy-based step that protects public health and addresses the root problem.

Option 3: Paint the buildings

Painting buildings does not reduce pollution. It is unrelated to the core issue.

Option 4: Open more markets

Opening more markets may increase traffic and pollution rather than reduce it.

Hence, the correct answer is Option 2

Given Word: ENDEAVORS

VOTE - Cannot be formed (because The letter T is not present)

ROSE - can be formed.

END - can be formed.

Road - can be formed.

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

Answer

Option 3 :

Checking the options:

Option 1: Give everything to his own constituency

This is biased and unfair. It ignores the needs of other sectors and does not serve the overall public interest.

Option 2: Delay the decision indefinitely

Avoiding the decision does not solve the problem. It may create dissatisfaction and hinder development.

Option 3: Allocate equally regardless of need

Although it seems fair, it is not practical. Some sectors may require more urgent funding than others. Equal distribution without analysis may reduce overall impact.

Option 4: Conduct a needs assessment and prioritize based on impact

This is a logical and structured approach. It ensures that funds are allocated where they are most needed and will create maximum benefit. It promotes fairness, transparency, and effective use of limited resources.

Hence, the correct answer is Option 4.

Checking the options:

Option 1: Close helpline

This is extreme and unreasonable. It removes public support instead of improving the system.

Option 2: Ignore duplicates

Ignoring queries can reduce service quality and create dissatisfaction among citizens.

Option 3: Punish callers

This is inappropriate and unfair. Citizens may not be aware that their queries are repetitive.

Option 4: Introduce FAQ and automated response system

This is the most efficient solution. An FAQ section and automated responses can quickly address common queries, reduce workload, and improve service speed while maintaining support access.

Hence, the correct answer is Option 4.

The logic followed here is

D → C (–1)

C → B (–1)

Each letter is shifted one step backward in the alphabet.

FG : ?

F → E (–1)

G → F (–1)

Hence, the correct answer is EF.

The logic followed here is:

The logic is based on the cubes of consecutive numbers starting from 9, subtracted by 9:

9³ - 9 = 729 - 9 = 720

10³ - 9 = 1000 - 9 = 991

11³ - 9 = 1331 - 9 = 1322

12³ - 9 = 1728 - 9 = 1719

13³ - 9 = 2197 - 9 = 2188

Thus, the missing term in the series is 2188.

Hence, the correct answer is "Option 4".

Logical followed here:

Consecutive perfect squares

Option 1: 36, 49

36 = 6²

49 = 7²

Option 2: 20, 9

20 is not a perfect square

9 = 3²

Option 3: 25, 16

25 = 5²

16 = 4²

Option 4: 81, 100

81 = 9²

100 = 10²

Hence, the correct answer is Option 2 .

Given Equation :  7 @ 14 ^ 4 ? 12 = ? 

Calculation:

7 @ 14 ^ 4 ? 12 = ?

After interchanging the symbol with signs,

7 ÷ 14 + 4 - 12 = ?

⇒ 1/2 + 4 - 12 = ?

⇒ (1 + 8 - 24)/2 = ?

⇒ -15/2 = ?

Hence, the correct answer is -15/2.

It will appear when opened:

Hence, the correct answer is "Option 1".

The question figure is hidden/embedded in the following option figure:

Hence, the correct answer is "Option 3".

The pattern followed here: 

Row 1

7 + 5 + 3 = 15

15 × 2 = 30 

Row 2

6 + 5 + 9 = 20

20 × 2 = 40 

Similarly, 

Row 3

? + 7 + 10 = ?

Let the missing number be x.

x + 7 + 10 = x + 17

(x + 17) × 2 = 36

x + 17 = 18

x = 1

Hence, 1 is the correct answer

The number of triangles in given figure is as shown below :

∴ Here, there are '15' triangles in given figure.

Hence, the correct answer is "Option 2".

According to the given Venn diagram:

The shaded area represents the number of shoes which are pants → 9 + 8 = 17 

Hence, the correct answer is "Option 3"

The logic followed here is

Because none of these items belong to the same category as the others (i.e., there is no overlap in what they are), they must be represented by three separate, non-overlapping circles.

Option 4

 

Hence, the correct answer is "Option 4".

The option that represents the correct order of the given words as they would appear in an English dictionary is shown below:

Metabolism

Metamorphosis

Metaphysical

Methodology

Metropolitan

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

The option figure will complete the pattern in the question figure is: 

Option 3  

Hence, the correct answer is "Option 3".

The logic followed here is,

Logic: Number of Sides - 1 = Number of Lines

Option:1

 

Option 1 has 4 sides and 4 lines

Does not follow the logic.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: Zig zag line change to straight line and vice versa.

The change moves from the top line down to the bottom line in a specific order:

Box 1 to Box 2: The 1st (top) line changes. It was a zig-zag and becomes a straight line.

Box 2 to Box 3: The 2nd line changes. It was a zig-zag and becomes a straight line.

Box 3 to Box 4: The 3rd line changes. It was a zig-zag and becomes a straight line.

Box 4 to Box 5 (The Solution): The 4th line changes. It was a zig-zag and now becomes a straight line.

Hence, the correct answer is "Option 2".

The logic followed here is that each letter is shifted 3 positions backward (-3 pattern) in the alphabetical series.

For LAST : IXPQ

For PREZ : MOBW

Applying the same logic to INTO : ?

The resulting code is FKQL.

Hence, the correct answer is "Option 2".

Shortcut Trick

Loss of 10% implies that the Selling Price is 90% of the Cost Price.

Desired gain of 15% implies that the new Selling Price should be 115% of the Cost Price.

Given: 90% → ₹1800

Therefore: 115% → (1800 ÷ 90) × 115 = 20 × 115 = ₹2300.

∴ The correct answer is ₹2300.

Alternate Method

Given:

First Selling Price (SP₁) = ₹1800

Loss Percentage (L%) = 10%

Desired Profit Percentage (P%) = 15%

Formula Used:

Cost Price (CP) = [SP × 100] ÷ [100 − Loss%]

New Selling Price (SP₂) = [CP × (100 + Profit%)] ÷ 100

Calculations:

⇒ CP = (1800 × 100) ÷ (100 − 10)

⇒ CP = (1800 × 100) ÷ 90

⇒ CP = 20 × 100 = ₹2000

⇒ SP₂ = [2000 × (100 + 15)] ÷ 100

⇒ SP₂ = [2000 × 115] ÷ 100

⇒ SP₂ = 20 × 115 = ₹2300

∴ The correct answer is ₹2300.

Additional Information

Profit and Loss Percentage

Profit % = (Profit ÷ CP) × 100 and Loss % = (Loss ÷ CP) × 100. Both are always calculated on the Cost Price (CP) unless stated otherwise.

Relationship between SP and CP

SP = CP × (100 ± Change%) ÷ 100. Use (+) for Profit and (−) for Loss.

Marked Price and Discount

Selling Price (SP) = Marked Price (MP) − Discount. Discount is always calculated on the Marked Price.

Given:

A's contribution = Rs. 12,000

B's contribution = Rs. 15,000

C's contribution = Rs. 18,000

B withdraws Rs. 5,000 after 6 months

C adds Rs. 10,000 after 6 months

Total profit = Rs. 54,000

Formula Used:

Profit share = (Investment × Time)

Total profit share ratio = Sum of all individual profit shares

Individual's profit = (Individual share ratio ÷ Total share ratio) × Total profit

Calculation:

⇒ A's share = 12,000 × 12 = 144,000

⇒ B's share (first 6 months) = 15,000 × 6 = 90,000

⇒ B's share (next 6 months) = 10,000 × 6 = 60,000

⇒ Total B's share = 90,000 + 60,000 = 150,000

⇒ C's share (first 6 months) = 18,000 × 6 = 108,000

⇒ C's share (next 6 months) = 28,000 × 6 = 168,000

⇒ Total C's share = 108,000 + 168,000 = 276,000

⇒ Total share ratio = 144,000 + 150,000 + 276,000 = 570,000

⇒ C's profit = (276,000 ÷ 570,000) × 54,000

⇒ C's profit = 0.4842 × 54,000

⇒ C's profit = Rs. 26,147

∴ The correct answer is ₹26,147.

Given:

Expression: sinx × cotx + cosx × tanx

Formula Used:

cotx = cosx ÷ sinx

tanx = sinx ÷ cosx

Calculation:

⇒ sinx × cotx + cosx × tanx

⇒ sinx × (cosx ÷ sinx) + cosx × (sinx ÷ cosx)

⇒ cosx + sinx

∴ The correct answer is sinx + cosx.

Given:

Ratio of chairs to tables = 3:2

Number of chairs = 30

Formula Used:

Total parts in the ratio = Sum of the ratio terms

Number of tables = (Number of chairs ÷ Ratio of chairs) × Ratio of tables

Calculation:

⇒ Total parts in the ratio = 3 + 2 = 5

⇒ Number of tables = (30 ÷ 3) × 2

⇒ Number of tables = 10 × 2

⇒ Number of tables = 20

∴ The correct answer is 20.

Shortcut Trick

For half-yearly compounding, the Rate becomes 10% (20% ÷ 2) and Time becomes 3 periods (1.5 years × 2).

Using the Effective Rate for 3 periods at 10%: 10 + 10 + 1 = 21%; 21 + 10 + 2.1 = 33.1%.

Compound Interest = 33.1% of ₹8,000.

CI = 8,000 × 0.331 = ₹2,648.

∴ The correct answer is ₹2,648.

Alternate Method

Given:

Principal (P) = ₹8,000

Rate (R) = 20% p.a.

Time (T) = 1 year 6 months = 1.5 years

Since interest is compounded half-yearly:

⇒ New Rate (r) = 20% ÷ 2 = 10% per half-year

⇒ Number of periods (n) = 1.5 × 2 = 3 half-years

Formula Used: Amount (A) = P(1 + r/100)ⁿ

⇒ A = 8,000 × (1 + 10/100)³

⇒ A = 8,000 × (11/10) × (11/10) × (11/10)

⇒ A = 8 × 1,331

⇒ A = ₹10,648

Compound Interest (CI) = Amount − Principal

⇒ CI = 10,648 − 8,000

⇒ CI = ₹2,648

Therefore, Option (3) is the correct answer.

∴ The correct answer is ₹2,648.

Additional Information

Half-Yearly Compounding Rule

When interest is compounded half-yearly, the annual rate is divided by 2 (R' = R/2) and the time in years is multiplied by 2 (n = T × 2).

Quarterly Compounding Rule

For quarterly compounding, the rate is divided by 4 (R' = R/4) and the time in years is multiplied by 4 (n = T × 4).

Compound Interest vs Simple Interest

For the first compounding period, CI is equal to SI. From the second period onwards, CI > SI because interest is earned on previously accumulated interest.

Given:

Principal (P) = ₹1,50,000

Rate of Interest (R) = 10% p.a.

Time (T) = 2 years

50% of the first year’s interest is withdrawn.

Formula Used:

Compound Interest (CI) = P × (1 + R/100)^T - P

Amount (A) = Principal + Interest

Calculation:

For the first year:

⇒ Interest for 1st year = ₹1,50,000 × 10 / 100

⇒ Interest for 1st year = ₹15,000

⇒ Amount after 1st year = ₹1,50,000 + ₹15,000

⇒ Amount after 1st year = ₹1,65,000

⇒ Withdrawn = 50% of ₹15,000 = ₹7,500

⇒ Balance after withdrawal = ₹1,65,000 - ₹7,500

⇒ Balance after withdrawal = ₹1,57,500

For the second year:

⇒ Interest for 2nd year = ₹1,57,500 × 10 / 100

⇒ Interest for 2nd year = ₹15,750

⇒ Amount after 2nd year = ₹1,57,500 + ₹15,750

⇒ Amount after 2nd year = ₹1,73,250

∴ The correct answer is ₹1,73,250.

Given:

Ratio of two numbers = 3:4

LCM = 120

Formula Used:

Let the numbers be 3x and 4x.

LCM of two numbers = product of the numbers ÷ HCF

Calculation:

⇒ LCM = 120

⇒ Numbers are 3x and 4x.

⇒ Product of numbers = 3x × 4x = 12x²

⇒ HCF of 3x and 4x = x

⇒ LCM = (Product of numbers ÷ HCF) = (12x² ÷ x) = 12x

⇒ 12x = 120

⇒ x = 10

⇒ Numbers are 3x = 30 and 4x = 40

⇒ Sum of numbers = 30 + 40 = 70

∴ The correct answer is 70.

Given:

Average age of 20 students = 18 years

Total number of students after 5 new students join = 20 + 5 = 25

New average age = 20 years

Formula Used:

Total age = Average age × Number of students

Age of 5 new students = Total age of 25 students - Total age of 20 students

Average age of 5 new students = Total age of 5 new students ÷ 5

Calculation:

⇒ Total age of 20 students = 18 × 20 = 360

⇒ Total age of 25 students = 20 × 25 = 500

⇒ Total age of 5 new students = 500 - 360 = 140

⇒ Average age of 5 new students = 140 ÷ 5 = 28

∴ The correct answer is 28.

Shortcut Trick To find the least value, quickly calculate each percentage by shifting decimals or simplifying ratios:

1. 18% × 450 = 9% × 900 = 81
2. 20% × 380 = 1/5 × 380 = 76
3. 25% × 300 = 1/4 × 300 = 75
4. 30% × 240 = 3 × 24 = 72 Comparing 81, 76, 75, and 72, the value 72 is the smallest. ∴ The correct answer is 30% of 240. Alternate Method Given: Four expressions involving Percentage of different base numbers.

Formula Used: Value = (Percentage / 100) × Number Calculating the numerical value for each option: ⇒ Option 1: 18% of 450 = (18 / 100) × 450 = 18 × 4.5 = 81 ⇒ Option 2: 20% of 380 = (20 / 100) × 380 = 2 × 38 = 76 ⇒ Option 3: 25% of 300 = (25 / 100) × 300 = 25 × 3 = 75 ⇒ Option 4: 30% of 240 = (30 / 100) × 240 = 3 × 24 = 72 Comparing the final results: 72 < 75 < 76 < 81. The minimum value obtained is 72, which corresponds to the expression 30% of 240. ∴ The correct answer is 30% of 240. Additional Information Percentage Interchangeability x% of y is always equal to y% of x. For example, 18% of 450 is the same as 450% of 18. Fractional Conversions Using common fractions can speed up calculations: 20% = 1/5, 25% = 1/4, 50% = 1/2, and 75% = 3/4. Comparison Technique When comparing p% of q, if p increases while q decreases significantly, the result may decrease. Actual calculation is safer when the product p × q is close.

Given:

Speed while going to school = 5 km/h

Speed while returning home = 3 km/h

Total time taken = 2 hours

Formula Used:

Time = Distance / Speed

Total Time = Time while going + Time while returning

Calculation:

Let the distance between home and school be D km.

Time while going = D ÷ 5

Time while returning = D ÷ 3

Total Time = D ÷ 5 + D ÷ 3

⇒ 2 = D ÷ 5 + D ÷ 3

Take LCM of 5 and 3, which is 15:

⇒ 2 = (3D + 5D) ÷ 15

⇒ 2 = 8D ÷ 15

Multiply through by 15:

⇒ 30 = 8D

⇒ D = 30 ÷ 8

⇒ D = 3.75 km

∴ The correct answer is 3.75 km.

Given:

A, B, C together can finish the job in 8 days.

A and B together take 12 days.

B and C together take 16 days.

Formula Used:

Work done in 1 day = 1 ÷ Total days taken.

Individual work rate = Combined work rate - Other individual's work rates.

Calculation:

⇒ Work rate of A, B, C together = 1 ÷ 8 = 1/8.

⇒ Work rate of A and B together = 1 ÷ 12 = 1/12.

⇒ Work rate of B and C together = 1 ÷ 16 = 1/16.

⇒ Work rate of C alone = (Work rate of A, B, C) - (Work rate of A and B).

⇒ Work rate of C alone = 1/8 - 1/12.

⇒ Work rate of C alone = (3 - 2) ÷ 24 = 1/24.

⇒ Total days for C alone = 1 ÷ (Work rate of C alone) = 1 ÷ (1/24) = 24 days.

∴ The correct answer is 24 days.

Given:

Selling price after 15% discount for 4 shirts = ₹2040

Discount = 15%

Profit = 20%

Formula Used:

Selling Price = Marked Price × (100 − Discount)% ÷ 100

Selling Price = Cost Price × (100 + Profit)% ÷ 100

Profit = Selling Price − Cost Price

Calculation:

⇒ 2040 = Marked Price × 85 ÷ 100

⇒ Marked Price = 2040 × 100 ÷ 85

⇒ Marked Price = 2400

⇒ 2040 = Cost Price × 120 ÷ 100

⇒ Cost Price = 2040 × 100 ÷ 120

⇒ Cost Price = 1700

⇒ Profit at full price = 2400 − 1700

⇒ Profit = 700

∴ The correct answer is 700.

Given:

Principal doubles in 5 years.

Time (T) = 5 years

Amount (A) = 2 × Principal (P)

Formula Used:

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

Amount (A) = Principal (P) + Simple Interest (SI)

Calculation:

⇒ A = 2P

⇒ SI = A - P = 2P - P = P

⇒ P × R × T ÷ 100 = P

⇒ R × 5 ÷ 100 = 1

⇒ R ÷ 20 = 1

⇒ R = 20%

∴ The correct answer is 20%.

Given:

Solid right circular cylinder is melted and recast into a right circular cone.

Base radius of the cylinder and cone is the same.

Cylinder’s height = h.

Formula Used:

Volume of cylinder = πr²h.

Volume of cone = (1/3)πr²H, where H is the height of the cone.

Calculation:

⇒ Volume of cylinder = Volume of cone (since material is conserved).

⇒ πr²h = (1/3)πr²H.

⇒ h = (1/3)H.

⇒ H = 3h.

∴ The correct answer is 3h.

Given:

Expression = √((12345)² + 12345 + 12346)

Formula Used:

(a + 1)² = a² + 2a + 1

Calculation:

⇒ (12345)² + 12345 + 12346

⇒ (12345)² + 12345 + (12345 + 1)

⇒ (12345)² + 2 × 12345 + 1

⇒ (12345)² + 2 × 12345 + 1

⇒ (12345 + 1)²

⇒ (12346)²

⇒ √((12346)²)

⇒ 12346

∴ The correct answer is 12346.

Given:

Initial quantity of milk = 50 liters

Milk removed in each operation = 5 liters

Total operations = 2

Formula Used:

Remaining milk after one operation = Initial quantity × (1 - (milk removed ÷ total volume))

Remaining milk after two operations = Remaining milk after first operation × (1 - (milk removed ÷ total volume))

Calculation:

⇒ After first operation: Remaining milk = 50 × (1 - (5 ÷ 50))

⇒ Remaining milk = 50 × (1 - 0.1)

⇒ Remaining milk = 50 × 0.9

⇒ Remaining milk = 45 liters

⇒ After second operation: Remaining milk = 45 × (1 - (5 ÷ 50))

⇒ Remaining milk = 45 × (1 - 0.1)

⇒ Remaining milk = 45 × 0.9

⇒ Remaining milk = 40.5 liters

∴ The correct answer is 40.5 liters.

Given:

Volume of a hemisphere = Total surface area of the hemisphere

Formula Used:

Volume of a hemisphere = (2/3)πr³

Total surface area of a hemisphere = 3πr²

Calculation:

⇒ (2/3)πr³ = 3πr²

⇒ (2/3)r³ = 3r² (dividing both sides by π)

⇒ (2/3)r = 3 (dividing both sides by r²)

⇒ r = 3 × (3/2)

⇒ r = 4.5 units

∴ The correct answer is 4.5 units.

Given:

Fraction of journey covered = 2/5

Time taken to cover 2/5 of the journey = 2 hours

Formula Used:

Total time for the journey = Time taken for covered part ÷ Fraction of journey covered

Time for remaining journey = Total time - Time taken for covered part

Calculation:

⇒ Total time = 2 ÷ (2/5)

⇒ Total time = 2 × (5/2)

⇒ Total time = 5 hours

⇒ Time for remaining journey = 5 - 2

⇒ Time for remaining journey = 3 hours

∴ The correct answer is 3 hours.

Shortcut Trick

The Centroid of a triangle is simply the arithmetic mean of the coordinates of its vertices.

x-coordinate ⇒ (1 + 5 + 1) ÷ 3 = 7 ÷ 3 ≈ 2.33

y-coordinate ⇒ (1 + 5 + 9) ÷ 3 = 15 ÷ 3 = 5.00

The Centroid is (2.33, 5.00).

∴ The correct answer is (2.33, 5.00).

Alternate Method

Given:

Vertices of ▵ABC: A(1, 1), B(5, 5), and C(1, 9).

Formula Used:

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

Calculations:

⇒ x_centroid = (x₁ + x₂ + x₃) ÷ 3

⇒ x_centroid = (1 + 5 + 1) ÷ 3 = 7 ÷ 3 = 2.333...

⇒ y_centroid = (y₁ + y₂ + y₃) ÷ 3

⇒ y_centroid = (1 + 5 + 9) ÷ 3 = 15 ÷ 3 = 5.00

⇒ G(x, y) = (2.33, 5.00)

∴ The correct answer is (2.33, 5.00).

Additional Information

Centroid Property

The centroid G divides each median of the triangle in the ratio of 2 : 1 from the vertex to the midpoint of the opposite side.

Coordinates of Incenter

The Incenter I is given by ((ax₁+bx₂+cx₃)/(a+b+c), (ay₁+by₂+cy₃)/(a+b+c)) where a, b, c are side lengths.

Area of Triangle (Vertices)

Area = 1/2 |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)| in square units.

Given:

Ratio of areas of similar triangles = 49:81

Formula Used:

Ratio of areas of similar triangles = (Ratio of corresponding altitudes)²

Calculation:

⇒ (Ratio of corresponding altitudes)² = 49:81

⇒ Ratio of corresponding altitudes = √49:√81

⇒ Ratio of corresponding altitudes = 7:9

∴ The correct answer is 7:9.

Given:

Point 1 = (2, 4)

Point 2 = (6, 10)

Formula Used:

Slope (m) = (y₂ − y₁) ÷ (x₂ − x₁)

Calculation:

⇒ m = (10 − 4) ÷ (6 − 2)

⇒ m = 6 ÷ 4

⇒ m = 3 ÷ 2

∴ The correct answer is 3 ÷ 2.

Given:

x ÷ (x + 1) + 1 ÷ x = 3

Formula Used:

a ÷ b + c ÷ d = (ad + bc) ÷ bd

If two rational expressions are equal, then their numerators are equal when denominators are same

Calculation:

⇒ x ÷ (x + 1) + 1 ÷ x = 3

⇒ (x × x + 1 × (x + 1)) ÷ (x(x + 1)) = 3

⇒ (x² + x + 1) ÷ (x(x + 1)) = 3

⇒ x² + x + 1 = 3x(x + 1)

⇒ x² + x + 1 = 3x² + 3x

⇒ 0 = 3x² + 3x − x² − x − 1

⇒ 0 = 2x² + 2x − 1

⇒ 2x² + 2x − 1 = 0

⇒ x = (−2 ± √(2² − 4 × 2 × (−1))) ÷ (2 × 2)

⇒ x = (−2 ± √(4 + 8)) ÷ 4

⇒ x = (−2 ± √12) ÷ 4

⇒ x = (−2 ± 2√3) ÷ 4

⇒ x = (−1 ± √3) ÷ 2

∴ The correct answer is (−1 ± √3) ÷ 2.

Shortcut Trick

For similar triangles, the ratio of all corresponding linear dimensions (sides, altitudes, medians, etc.) is equal.

Ratio of sides = 3 : 5

∴ Ratio of altitudes = 3 : 5

Given: Altitude of smaller triangle = 6 cm (corresponds to 3 units)

⇒ 3 units → 6 cm

⇒ 1 unit → 2 cm

⇒ 5 units → 5 × 2 = 10 cm

∴ The correct answer is 10 cm.

Alternate Method

Given:

⇒ Ratio of sides of two similar triangles = 3 : 5

⇒ Altitude of the smaller triangle (h₁) = 6 cm

Formula Used:

If two triangles are similar, the ratio of their corresponding altitudes is equal to the ratio of their corresponding side lengths.

⇒ (Altitude₁ / Altitude₂) = (Side₁ / Side₂)

Calculations:

⇒ Let the altitude of the larger triangle be h₂.

⇒ 6 / h₂ = 3 / 5

⇒ 3 × h₂ = 6 × 5

⇒ 3 × h₂ = 30

⇒ h₂ = 30 ÷ 3

⇒ h₂ = 10 cm

Thus, the length of the corresponding altitude of the larger triangle is 10 cm, which corresponds to Option (3).

∴ The correct answer is 10 cm.

Additional Information

Properties of Similar Triangles

The ratio of corresponding medians, angle bisectors, and perimeters of two similar triangles is also equal to the ratio of their corresponding sides.

Area Ratio Theorem

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides: Area₁/Area₂ = (s₁/s₂)².

AAA Similarity Criterion

Two triangles are similar if their corresponding angles are equal, which automatically makes their corresponding sides proportional.

Given:

16^3/2

16^-3/2

Formula Used:

a^m = (a^1/2)^m

a^-n = 1 / aⁿ

Calculation:

⇒ 16^3/2 = (16^1/2)³ = 4³ = 64

⇒ 16^-3/2 = 1 / 16^3/2 = 1 / 64

⇒ 16^3/2 + 16^-3/2 = 64 + 1/64

⇒ 64 + 1/64 = (4096 + 1) / 64

⇒ 4097 / 64

∴ The correct answer is 4097/64.

Given:

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

Formula Used:

a ÷ b + c ÷ d = (ad + bc) ÷ bd

sin²(x) + cos²(x) = 1

Calculation:

⇒ cos(x) ÷ (1 + sin(x)) + sin(x) ÷ (1 + cos(x))

⇒ (cos(x)(1 + cos(x)) + sin(x)(1 + sin(x))) ÷ ((1 + sin(x))(1 + cos(x)))

⇒ (cos(x) + cos²(x) + sin(x) + sin²(x)) ÷ ((1 + sin(x))(1 + cos(x)))

⇒ (sin²(x) + cos²(x) + sin(x) + cos(x)) ÷ ((1 + sin(x))(1 + cos(x)))

⇒ (1 + sin(x) + cos(x)) ÷ ((1 + sin(x))(1 + cos(x)))

∴ The correct answer is $\frac{\cos(x) + \sin(x) + 1}{(1 + \sin(x))(1 + \cos(x))}$.

The correct answer is Promotion of international peace and security.

Key Points

• Article 51 of the Indian Constitution falls under the Directive Principles of State Policy (Part IV).
• Its primary objective is the promotion of international peace and security, ensuring harmony between nations.
• This article explicitly outlines the role of India in fostering respect for international law and treaty obligations in dealings with organized nations.
• It emphasizes maintaining a just and equitable global order and encourages peaceful coexistence among countries.
• Article 51 is not enforceable by the courts but serves as a guiding principle for the government in formulating policies and decisions at the international level.

Additional Information

• Directive Principles of State Policy (DPSP):
• DPSPs are enumerated in Part IV of the Indian Constitution and are considered fundamental in the governance of the country.
• They are non-justiciable, meaning they are not enforceable by the courts, but they act as guidelines for the government to create laws and policies.
• Examples include Article 44 (Uniform Civil Code), Article 48 (Organization of Agriculture and Animal Husbandry), etc.
• Key Features of Article 51:
• It directs the state to work for the promotion of international peace and security.
• Urges maintaining friendly relations with other countries.
• Encourages respect for international law and treaty obligations.
• Promotes the resolution of disputes by arbitration instead of conflict.
• Relation to India’s Foreign Policy:
• Article 51 aligns with India's vision of non-alignment and peaceful coexistence as propagated by leaders like Jawaharlal Nehru.
• It is reflected in various international initiatives, including India's role in the United Nations and its emphasis on disarmament and global cooperation.
• India’s commitment to treaties like the Paris Climate Agreement and active participation in peacekeeping missions showcase adherence to Article 51.
• Examples of Implementation:
• India has supported global peace initiatives and participated in United Nations peacekeeping missions.
• It has advocated for nuclear disarmament and signed treaties promoting global security.
• India’s foreign policy often reflects respect for international law and the resolution of disputes through peaceful means.

Important Points

• Article 44: Relates to the Uniform Civil Code, aiming to unify personal laws across all religions in India.
• Article 48: Deals with the organization of agriculture and animal husbandry, promoting scientific methods and the prohibition of slaughter of certain animals.
• Article 43: Encourages the promotion of cooperative societies for economic development.
• These articles reflect the broader goals of the Directive Principles in ensuring equitable development and social justice.

The correct answer is Anurag Garg.

Key Points

• Anurag Garg was appointed as the Director General of the Narcotics Control Bureau (NCB) in September 2024.
• The Narcotics Control Bureau is India's premier agency responsible for combating drug trafficking and ensuring compliance with the Narcotic Drugs and Psychotropic Substances Act, 1985.
• Anurag Garg is a senior officer with vast experience in administrative and enforcement roles, making him suitable for this crucial position.
• The appointment comes at a time when the NCB is focusing on dismantling drug networks and addressing rising drug abuse cases in India.

Additional Information

• About Narcotics Control Bureau (NCB):
• The NCB was established in 1986 under the Narcotic Drugs and Psychotropic Substances Act, 1985.
• Its primary function is to coordinate with various states and international agencies to curb drug trafficking.
• The agency works under the administrative control of the Ministry of Home Affairs, Government of India.
• The NCB also monitors India's compliance with international drug control treaties and conventions.
• Key Functions of NCB:
• Investigating and prosecuting offenses related to narcotics and psychotropic substances.
• Coordinating between central and state agencies to strengthen anti-drug efforts.
• Providing training and resources to law enforcement agencies for better drug crime management.
• Promoting public awareness campaigns to reduce drug abuse in society.
• Anurag Garg's Background:
• Anurag Garg is a highly experienced officer with expertise in enforcement and administrative processes.
• He has held several senior positions in government and law enforcement agencies, contributing to the development of effective policies.
• His leadership is expected to address the challenges in drug trafficking and misuse comprehensively.
• India's Drug Problem:
• India faces significant challenges with drug trafficking due to its geographical proximity to the "Golden Triangle" and "Golden Crescent" regions.
• Rising substance abuse cases have made it imperative for agencies like NCB to adopt proactive measures.
• NCB's role in coordinating efforts at the national and international level is crucial in curbing this menace.

Important Points

• International Collaboration:
• NCB partners with agencies like the United Nations Office on Drugs and Crime (UNODC), Interpol, and World Customs Organization to combat drug trafficking.
• India is a signatory to several international treaties, such as the Single Convention on Narcotic Drugs, 1961, and the United Nations Convention against Illicit Traffic in Narcotic Drugs and Psychotropic Substances, 1988.
• Drug Awareness and Prevention:
• NCB conducts awareness campaigns targeting schools, colleges, and communities to educate people about the dangers of drug abuse.
• Effective rehabilitation programs are promoted to help individuals recover from addiction.

The correct answer is Jharkhand.

Key Points

• The Dharti Aaba Janjatiya Gram Utkarsh Abhiyan was launched on October 2, 2024, in the state of Jharkhand.
• This initiative focuses on the development and empowerment of tribal communities residing in rural areas of the state.
• The name “Dharti Aaba” is a tribute to Birsa Munda, a prominent tribal freedom fighter and social reformer from Jharkhand.
• The program aims to enhance the livelihood, education, and health facilities of tribal communities, ensuring inclusive growth and sustainable development.
• Jharkhand, being rich in tribal heritage and culture, is a key region for such initiatives that target the socio-economic upliftment of marginalized communities.

Additional Information

• Jharkhand:
• It is located in eastern India and was formed on November 15, 2000, carved out of Bihar.
• The state is known for its tribal population, which constitutes a significant part of its demographic composition.
• Prominent tribes include Santals, Oraons, Mundas, and Hos.
• Jharkhand is rich in natural resources, including minerals like coal, iron ore, and mica, which contribute significantly to its economy.
• Birsa Munda:
• Birsa Munda is a revered tribal leader, often referred to as “Dharti Aaba,” meaning “Father of the Earth.”
• He led a tribal uprising against British colonial rule during the late 19th century in the Chotanagpur region.
• Birsa Munda fought for the rights and dignity of tribal communities, emphasizing the importance of land ownership and cultural preservation.
• His birth anniversary, November 15, is celebrated as Jharkhand Foundation Day and Tribal Pride Day in India.
• Tribal Development Programs:
• Numerous government initiatives are aimed at improving the socio-economic conditions of tribal communities, such as the Vanbandhu Kalyan Yojana and Tribal Sub-Plan.
• These programs focus on areas like education, healthcare, infrastructure, and livelihood opportunities for tribal populations.
• Special attention is given to preserving tribal culture and traditions while ensuring access to modern amenities.
• October 2 Significance:
• October 2 is celebrated as Gandhi Jayanti, marking the birth anniversary of Mahatma Gandhi, the Father of the Nation.
• It is also recognized as the International Day of Non-Violence by the United Nations.
• Launching a tribal development initiative on this date underscores the values of inclusivity, equality, and social justice that Mahatma Gandhi advocated.

The correct answer is 39th.

Key Points

• India ranks 39th in the World Competitiveness Index 2024, improving from its previous rankings due to advancements in key economic sectors.
• The World Competitiveness Index is published annually by the International Institute for Management Development (IMD), focusing on the competitiveness of nations based on economic performance, government efficiency, business efficiency, and infrastructure.
• India's performance is attributed to factors such as economic reforms, infrastructure development, and digital transformation, which have significantly enhanced its competitiveness on the global stage.
• The index evaluates 64 economies worldwide by analyzing over 330 criteria, including both statistical data and survey responses.
• India’s key strengths include its strong economic growth, large consumer market, and advancements in technology sectors, which contribute to its improved ranking.
• Key contributors to India's ranking include government initiatives like Make in India, Digital India, and Start-Up India, which have fostered innovation and business growth.

Additional Information

• World Competitiveness Index:
• The IMD World Competitiveness Index assesses the ability of countries to create an environment that sustains businesses and drives economic prosperity.
• It uses a mix of hard statistics (e.g., GDP, employment rates) and survey data from business executives to evaluate performance.
• The four primary criteria are economic performance, government efficiency, business efficiency, and infrastructure.
• India’s Economic Growth:
• India's GDP growth rate is among the highest globally, driven by strong domestic demand and government reforms.
• Significant investments in infrastructure, digital technologies, and manufacturing have contributed to its competitiveness.
• India is recognized for its large consumer base, which attracts foreign investments and strengthens market dynamics.
• Global Trends in Competitiveness:
• The top-ranked countries in the index often feature strong governance, innovation capacity, and robust infrastructure.
• In 2024, countries like Switzerland, Sweden, and Singapore continue to lead due to their advanced economies and innovation-driven strategies.
• India’s ranking reflects an improving position but highlights areas requiring policy focus, such as education, healthcare, and labor market reforms.
• Government Initiatives Enhancing Competitiveness:
• Make in India: Promotes manufacturing and aims to position India as a global manufacturing hub.
• Digital India: Focuses on improving digital infrastructure and increasing internet accessibility to transform India into a digitally empowered society.
• Start-Up India: Encourages entrepreneurship by providing financial support and reducing bureaucratic hurdles.
• Comparison with Other Economies:
• India’s improvement in ranking highlights its growing importance in the global economic landscape.
• Countries like China and South Korea are close competitors in terms of innovation and efficiency, necessitating continued reforms in India.
• The index serves as a benchmark for policymakers to identify areas for improvement and align strategies to global standards.

Important Points

• India’s Position: India ranks 39th, indicating significant improvements but highlighting the need for further reforms in areas such as education, labor markets, and healthcare.
• Recent Data: Slipped to 41st in 2025.

The correct answer is UNICEF.

Key Points

• UNICEF stands for the United Nations International Children's Emergency Fund. It is a global organization responsible for promoting the rights and welfare of children worldwide.
• The State of the World’s Children is an annual flagship report published by UNICEF. It highlights the challenges and progress in children’s health, education, and rights globally.
• The 2024 edition of this report focuses on critical issues faced by children, such as poverty, education gaps, healthcare access, and climate change impacts.
• UNICEF has been producing the State of the World’s Children report since 1980, making it a trusted source for global data and analysis related to child development.
• This report is integral for guiding policymakers, governments, and organizations in addressing child-specific challenges and achieving sustainable development goals (SDGs) related to children.

Additional Information

• About UNICEF:
• UNICEF was established in 1946 after World War II to provide emergency relief to children affected by the war.
• Its headquarters are located in New York City, USA, and it operates in over 190 countries and territories.
• UNICEF works in areas such as education, healthcare, nutrition, child protection, and emergency relief.
• It is funded entirely by voluntary contributions from governments, private donors, and foundations.
• State of the World’s Children Report:
• The report covers various themes annually, focusing on issues like child poverty, malnutrition, education, healthcare, and climate change.
• It provides insights into data trends, challenges, and solutions to ensure the well-being of children globally.
• The report serves as a basis for governments and organizations to develop child-centric policies.
• Other Organizations and Reports:
• World Bank: Focuses on global economic development and publishes reports like the World Development Report.
• IMF: Specializes in financial stability and economic growth, producing reports such as the World Economic Outlook.
• World Economic Forum: Known for its Global Competitiveness Report and organizing annual meetings in Davos.
• UNICEF’s Contributions:
• Promotes child rights through initiatives such as the UNICEF Innocenti Research Centre.
• Focuses on improving child survival rates by addressing issues like immunization, sanitation, and nutrition.
• Advocates for gender equality and the empowerment of girls in education and other areas.

Important Points

• Sustainable Development Goals (SDGs):
• UNICEF actively supports achieving SDG 3 (Good Health and Well-being) and SDG 4 (Quality Education).
• Its reports help monitor progress on SDGs related to children, providing data for global and regional assessments.

The correct answer is lichen.

Key Points

• Allographa effusosoredica is a newly discovered species that belongs to the group of lichens.
• Lichens are symbiotic associations between a fungus and an alga or cyanobacterium, which work together to survive in various environments.
• This species was recently discovered in the Western Ghats of India, a biodiversity hotspot known for its rich and unique flora and fauna.
• The study and discovery of new lichen species like Allographa effusosoredica contribute significantly to understanding ecosystem dynamics and biodiversity.
• Lichens are considered excellent bioindicators of environmental health as they are sensitive to pollution and changes in their habitat.

Additional Information

• About Lichens:
• Lichens are composed of two organisms: a fungus (mycobiont) and a photosynthetic partner, which could be an alga or cyanobacterium (photobiont).
• They are found in diverse habitats, from arctic tundras to tropical rainforests, and even in extreme environments like deserts.
• Lichens play a crucial role in the ecosystem by contributing to soil formation and serving as a food source for various animals.
• Western Ghats:
• The Western Ghats, a UNESCO World Heritage Site, is one of the eight "hottest hotspots" of biological diversity in the world.
• It spans the states of Kerala, Tamil Nadu, Karnataka, Goa, Maharashtra, and Gujarat.
• This region is home to a large number of endemic species, including plants, animals, and fungi, and is a vital area for new species discoveries.
• Importance of Lichens:
• Lichens are used as bioindicators to monitor air pollution, as they are highly sensitive to pollutants like sulfur dioxide.
• They are also used in traditional medicines and dyes. For instance, some species produce unique compounds with antibacterial and antiviral properties.
• In addition, lichens contribute to carbon cycling in ecosystems by fixing atmospheric carbon dioxide.
• Other Options Explained:
• Cat: A domesticated mammal belonging to the family Felidae, with no relation to lichens or the species in question.
• Bat: A mammal capable of sustained flight, belonging to the order Chiroptera. It is not related to the discovery of Allographa effusosoredica.
• Butterfly: An insect belonging to the order Lepidoptera, known for its colorful wings and unrelated to lichens.

Important Points

• Scientific Research: The discovery of Allographa effusosoredica highlights the importance of systematic research in unexplored or under-researched regions like the Western Ghats.
• Conservation: Understanding lichen diversity is critical for conservation strategies, as these organisms are sensitive to environmental changes and can indicate ecological health.
• Global Significance: India’s biodiversity, especially in hotspots like the Western Ghats, is significant for global ecological balance and sustainability efforts.