SSC CHSL 2025 Tier-1 (Held On: 27 Nov, 2025 Shift 2) (Previous Year Paper)

The correct answer is: 1) Loquacious.

Key Points

• The word "Garrulous" refers to someone who is excessively talkative, especially about trivial matters. (बहुत बातूनी)
• Example: The garrulous host kept the audience entertained with his endless anecdotes.
• "Loquacious" is a synonym of "Garrulous" and also means talkative or chatty. (बहुभाषी)
• Example: She is known for her loquacious nature, often engaging in long conversations with strangers.
• Hence, the correct synonym for "Garrulous" is "Loquacious."

Therefore, the correct answer is: 1) Loquacious.

Additional Information

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

• Silent (मौन): Someone who does not talk or make noise.
• Example: The room fell silent as the teacher entered.
• Defined (परिभाषित): Something that is clearly outlined or described.
• Example: The rules for the competition were well-defined to avoid confusion.
• Well-mannered (सुसंस्कृत): Someone who behaves politely and shows good manners.
• Example: The child is well-mannered and always greets guests with respect.

The correct answer is Option 3.

Key Points

• The error lies in the phrase "too much times working" in part 3.
• The word "times" is incorrect in this context. The correct word should be "time" because "time" in this sense is an uncountable noun.
• The phrase should be corrected to "too much time working," which aligns with standard grammar rules.
• Thus, the error is located in part 3 of the sentence.

Therefore, the correct answer is Option 3.

Correct Sentence: "Nowadays, the lack of money makes people spend too much time working."

Additional Information

• Option 1: "Nowadays, the lack of money" – This part of the sentence is grammatically correct and does not require any changes.
• Option 2: "makes people spend" – This part of the sentence is grammatically correct and does not require any changes.
• Option 4: "No correction required" – This option is incorrect because there is an error in part 3.

The correct answer is option 1.

Key Points

To answer this question, let’s analyze each sentence for grammatical and contextual correctness:

• 1) He spoil his health by drinking too much alcohol in the bar.
• This sentence contains a grammatical error. The verb "spoil" is incorrectly used in the present tense when the sentence refers to a habitual action or consequence.
• Correct Sentence: "He spoils his health by drinking too much alcohol in the bar."
• Hence, this sentence is incorrect.
• 2) Most people don’t like being disturbed while they are working.
• This sentence is grammatically and contextually correct. It uses the present continuous tense appropriately to describe an ongoing action.
• Hence, this sentence is correct.
• 3) For a long time, people thought that the world was flat and that people could fall off the edge.
• This sentence is grammatically correct and makes sense contextually. It accurately describes a historical belief.
• Hence, this sentence is correct.
• 4) You have to be a millionaire to shop in Harrods. Everything is so expensive there.
• This sentence is grammatically and contextually correct. It humorously emphasizes the high prices in Harrods.
• Hence, this sentence is correct.

Final Answer:

• Sentence 1 is incorrect due to the misuse of verb tense ("spoil" instead of "spoils").
• Sentences 2, 3, and 4 are grammatically and contextually correct.

The correct answer is 'unanimous'.

Key Points

• The term "unanimous" means complete agreement or consensus among all members of a group.
• The context of the sentence mentions uniting parties across the political spectrum, which implies that the support for the legislation was not divided but agreed upon by all parties.
• Option 1: "partisan" refers to strong allegiance to a particular political party, which is contrary to the idea of unity.
• Option 3: "perfunctory" means doing something in a routine or superficial way, which does not fit the context of strong, unified support.
• Option 4: "nominal" means minimal or in name only, which does not convey the strength of the support described in the sentence.

Therefore, the correct answer is Option 2.

Complete Sentence: "The legislation was passed with unanimous support, uniting parties across the political spectrum."

Additional Information

• Option 1: "partisan" is incorrect because it refers to division along party lines, the opposite of what the sentence describes.
• Option 3: "perfunctory" is incorrect because it suggests a lack of genuine effort or enthusiasm, which is not implied in the sentence.
• Option 4: "nominal" is incorrect because it suggests minimal support, which contradicts the idea of strong, united backing.

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

Key Points

• The word "hare" refers to a fast-moving, long-eared mammal resembling a rabbit. (खरगोश)
• Example: The hare ran swiftly across the field to escape the predator.
• "Heir" refers to a person legally entitled to inherit property or a title from a predecessor. (उत्तराधिकारी)
• Example: He is the rightful heir to his father's estate.
• In the given sentence, "hare" is incorrectly used as it refers to an animal. The correct word is "heir," which fits the context of inheriting an estate.

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

Additional Information

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

• Hair (बाल): The thin, thread-like strands growing from the skin of humans and animals.
• Example: She has long, beautiful hair that she takes great care of.
• Hire (किराए पर लेना): To employ someone for wages or to rent something for temporary use.
• Example: We decided to hire a car for our weekend road trip.
• Hier: This is not a valid English word.

The correct answer is option 1.

Key Points

• The correctly spelt word is 'Environment'.
• 'Environment' refers to the surroundings or conditions in which a person, animal, or plant lives or operates.
• Incorrect spellings such as 'Envirmnet', 'Enviorment', and 'Envirrent' deviate from the standard spelling.

Correct sentence: The word 'Environment' is correctly spelt and widely used in various contexts, such as ecological, social, and organizational settings.

Additional Information

• Definition of Environment:
• The physical, social, and cultural conditions that influence the life of an individual or community.
• For Example: Protecting the environment is crucial for future generations.
• Common Usage:
• The government is implementing policies to reduce environmental pollution.
• The school organized a seminar on environmental conservation.

The correct answer is 'loaded with'.

Key Points

• The preposition "with" is used to indicate the contents of something, making it the most appropriate choice for the sentence.
• The phrase "loaded with" is a standard construction when referring to something being filled or packed with items.
• Option 2 (loaded by) suggests the agent performing the action, which is not suitable here.
• Option 3 (loaded in) refers to the location where something is loaded, which is incorrect in this context.
• Option 4 (No substitution) is incorrect as the original sentence is grammatically wrong.

Therefore, the correct answer is Option 1.

Complete Sentence: "The truck was loaded with crates of fresh produce for the market."

Additional Information

• Option 2: "loaded by" implies the person or entity performing the action of loading, which is irrelevant in this context.
• Option 3: "loaded in" is incorrect because it suggests the crates are loaded into a location, not onto the truck.
• Option 4: No substitution is invalid because the original sentence is ungrammatical and requires correction.

The correct answer is '2' i.e. 'Accused of stealing.'

Key Points

• The verb "accused" is always followed by the preposition "of" when indicating the reason for the accusation.
• The phrase "accused for stealing" is incorrect because "for" is not the correct preposition to use after "accused."
• The correct structure is "accused of + gerund/noun."

Therefore, the correct answer is Option 2.

Complete Sentence: "He was accused of stealing confidential data."

Additional Information

• Option 1: "Accused with stealing" is incorrect because "with" is not the correct preposition to use after "accused."
• Option 3: "Accused to stealing" is grammatically incorrect as "to" is not the appropriate preposition for this context.
• Option 4: "No substitution" is incorrect because the original sentence contains an error and needs correction.

The correct answer is Option 4.

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the active voice, the sentence is: "The children will have played the game by sunset."
• To convert to passive voice: Place the object "the game" at the beginning.
• Change the active verb form "will have played" to "will have been played" (future perfect passive).
• Add the preposition "by" followed by the original subject "the children."
• Ensure the time phrase "by sunset" remains at the end of the sentence for clarity.

Therefore, the correct answer is Option 4.

Correct Sentence: "The game will have been played by the children by sunset."

Additional Information

• Option 1: "The game will have being played by the children by sunset." – Incorrect use of the word "being" in the future perfect passive structure.
• Option 2: "The game would have been played by the children by sunset." – Incorrect tense (conditional perfect passive instead of future perfect passive).
• Option 3: "The game will be played by the children by sunset." – Incorrect tense (future simple passive instead of future perfect passive).

The correct answer is Option 2.

Key Points

• Rule for Indirect Speech Conversion: When converting direct speech to indirect speech, the following changes are applied:
• Present tense verbs in the original sentence are changed to past tense in indirect speech.
• Words indicating time and place are modified. For example, "next month" becomes "the following month."
• Pronouns are adjusted according to the speaker and listener.
• Application to the Question:
• The direct sentence is: "We are going to live in a new city from next month onwards until my brother gets a new job."
• When converted to indirect speech:
• "We" changes to "they" to reflect the third person.
• Present continuous "are going" changes to past continuous "were going."
• "Next month" changes to "the following month."
• Present tense "gets" changes to past tense "got" to maintain tense consistency.

Therefore, the correct indirect speech is: She told me that they were going to live in a new city from the following month onwards until her brother got a new job.

Correct Sentence: She told me that they were going to live in a new city from the following month onwards until her brother got a new job.

Additional Information

• Option 1: She told me that they will be going to live in a new city from the next month onwards until her brother gets a new job.
• Incorrect because "will be going" should be changed to "were going" in indirect speech.
• Also, "next month" should change to "the following month."
• Option 3: She told me that she was going to live in a new city from the following month onwards until her brother gets a new job.
• Incorrect because "she" replaces "they," which changes the meaning.
• The tense of "gets" should be changed to "got."
• Option 4: She told me that they were going to live in a new city from the following month onwards until my brother got a new job.
• Incorrect because "my brother" should be changed to "her brother" to match the subject pronoun.

The correct answer is Option 1.

Key Points

• The given sentence is in the passive voice: "The famous poem was written by a renowned poet."
• To convert to active voice, identify the subject, verb, and object in the passive sentence.
• In the passive sentence, the subject is "The famous poem," the verb is "was written," and the agent (doer) is "a renowned poet."
• In the active voice, the subject becomes "A renowned poet," the verb changes to "wrote," and the object becomes "the famous poem."
• The correct active voice sentence is: "A renowned poet wrote the famous poem."

Therefore, the correct answer is Option 1.

Correct Sentence: "A renowned poet wrote the famous poem."

Additional Information

• Option 2: "The famous poem writes a renowned poet." – Incorrect as it does not maintain grammatical structure or meaning.
• Option 3: "A renowned poet has written the famous poem." – Incorrect as it changes the tense to present perfect.
• Option 4: "The famous poem was being written by a renowned poet." – Incorrect as it changes the tense to past continuous passive.

The correct answer is Option 3.

Key Points

• Direct Speech: It is a way of reporting the exact words spoken by someone, typically enclosed within quotation marks.
• Conversion Process:
• Original Sentence: The coach advised the players not to skip the warm-up exercises.
• The reporting verb "advised" is converted into a suitable verb for direct speech (e.g., "said to" or "told").
• The negative command "not to skip" is transformed into the imperative form "Do not skip."
• The sentence structure is adjusted to reflect a direct command with quotation marks.
• Correct Transformation: The coach said to the players, "Do not skip the warm-up exercises."

Therefore, the correct answer is Option 3.

Correct Sentence: "The coach said to the players, ‘Do not skip the warm-up exercises.’"

Additional Information

• Option 1: The coach advises the players, "Don’t skip the warm-up exercises."
• Incorrect tense: The reporting verb "advises" is in the present tense, which does not match the original sentence's past context.
• Option 2: The coach told the players, "You should not skip the warm-up exercises."
• Incorrect transformation: "Should not skip" introduces a suggestion rather than a direct command.
• Option 4: The coach advised, "The players must not skip the warm-up exercises."
• Incorrect phrasing: It changes the structure and tone of the original sentence, introducing "must," which is not present in the original statement.

The correct answer is 'for'.

Key Points

• The preposition "for" is used to indicate the purpose, reason, or a characteristic associated with someone or something.
• The phrase "reputation for" is commonly used to describe the quality or attribute for which someone is known.
• Options 1, 2, and 3 are grammatically incorrect when used in this context.

Therefore, the correct answer is Option 4.

Complete Sentence: "He has a reputation for being punctual and reliable."

Additional Information

• Option 1: "on" is incorrect because "reputation on" is not a valid phrase in English.
• Option 2: "in" is incorrect because "reputation in" is not suitable for this context.
• Option 3: "of" is incorrect because "reputation of" is not appropriate when describing a specific quality like punctuality or reliability.

The correct answer is Option 1.

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the active voice, the sentence is: "The jury, after a long deliberation, has finally reached a verdict in the high-profile case."
• To convert to passive voice: Place the object "a verdict in the high-profile case" at the beginning.
• Change the active verb form "has reached" to "has been reached" (present perfect passive).
• Preserve the time sequence and additional phrases, such as "after a long deliberation" and "by the jury," for clarity.

Therefore, the correct answer is Option 1.

Correct Sentence: "A verdict in the high-profile case has finally been reached by the jury after a long deliberation."

Additional Information

• Option 2: "A verdict in the high-profile case was finally reached by the jury after a long deliberation." – Incorrect past tense usage (past simple instead of present perfect).
• Option 3: "A verdict in the high-profile case had been finally reached by the jury after a long deliberation." – Incorrect tense (past perfect instead of present perfect).
• Option 4: "A verdict in the high-profile case is discovered by the jury after a long deliberation." – Incorrect verb choice (present simple instead of present perfect).

The correct answer is 'Option 2'.

Key Points

• Option 2: Adverbial clause of time
• The phrase "when judiciously curated" is an elliptical adverbial clause. It is a shortened form of "when they are judiciously curated."
• It functions as an adverbial clause of time (or condition) because it specifies the specific circumstances or "time" under which digital platforms serve as catalysts for growth.
• Option 1: Noun clause
• This is incorrect. A noun clause functions as a subject or an object (e.g., "I know when the platforms are curated"). In this sentence, the phrase is not acting as a noun.
• Option 3: Adjective clause
• This is incorrect. An adjective clause (relative clause) typically begins with a relative pronoun (which, that, who) and modifies a noun directly (e.g., "Digital platforms that are curated..."). While this phrase follows a noun, "when" establishes a relationship of time/condition to the action of the verb.
• Option 4: Absolute phrase
• This is incorrect. An absolute phrase modifies a whole sentence and usually consists of a noun followed by a participle, without a subordinating conjunction (e.g., "The platforms having been curated, the children began to play"). The presence of "when" makes it a clause.

Therefore, the correct answer is Option 2.

Additional Information

• Ellipsis in Clauses: In English, we often omit the subject and the verb "to be" in adverbial clauses when the subject is the same as the subject in the main clause (Digital platforms).
• Vocabulary: "Judiciously" means with good judgment or sense. "Curated" means selected, organized, and looked after.
• Context: The author uses this clause to provide a necessary caveat—that digital platforms are only beneficial if they are chosen wisely.

The correct answer is 'Option 1'.

Key Points

• Option 1: Simple present
• The phrase "can also serve" uses the modal verb "can" followed by the base form of the verb "serve."
• In English grammar, modal verbs like can, may, must, and should are used in the Simple Present tense to express current ability, possibility, or general truths.
• The sentence describes a general fact or potential that exists in the present regarding digital platforms.
• Option 2: Present continuous
• This is incorrect. The present continuous requires a form of "to be" + verb-ing (e.g., "are serving").
• Option 3: Future simple
• This is incorrect. The future simple typically uses "will" or "shall" + base verb (e.g., "will serve"). While "can" can imply future possibility, it is grammatically categorized as a present modal.
• Option 4: Present perfect
• This is incorrect. The present perfect requires "has/have" + past participle (e.g., "have served").

Therefore, the correct answer is Option 1.

Additional Information

• Modals and Tense: Modal verbs do not change their form to show tense in the same way regular verbs do. "Can" is the present form, while "could" is often used as the past or conditional form.
• Function of "Can": In this context, "can" indicates possibility. It suggests that digital platforms have the potential to act as catalysts, provided the conditions (like being "judiciously curated") are met.
• Catalyst: A term borrowed from chemistry, used here metaphorically to mean something that precipitates or accelerates an event or change (in this case, mental growth).

The correct answer is: Option 2 i.e. Skill and agility.

Key Points

• The word "dexterity" means:
• Skill and agility, especially with the hands or in performing tasks. (कौशल और चपलता)
• Example: The surgeon's dexterity is crucial during delicate operations.
• "Correct answer" means:
• Referring to the specific answer that properly defines or fits the context of the question. (सही उत्तर)
• Example: The correct answer to the quiz question assured her a perfect score.

Therefore, the correct answer is: Skill and agility.

Additional Information

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

• Clumsiness (अकुशलता): Lack of skill or grace in movement or performance.
• Example: His clumsiness often led to broken dishes.
• Laziness (आलस): Unwillingness to work or make an effort.
• Example: His laziness prevented him from completing his tasks.
• Curiosity (जिज्ञासा): A desire to learn or know about something.
• Example: Her curiosity led her to explore new subjects.

The correct answer is: Option 3 i.e. Making less severe.

Key Points

• The word "mitigating" means:
• Making something less severe, serious, or painful. (किसी चीज़ को कम गंभीर, गंभीर या दर्दनाक बनाना; कम करना)
• Example: The government took measures aimed at mitigating the economic impact of the pandemic.
• "Correct answer" means:
• Referring to the specific answer that properly defines or fits the context of the question. (सही उत्तर)
• Example: The correct answer to the quiz question assured him a perfect score.

Therefore, the correct answer is: Making less severe.

Additional Information

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

• Worsening (बिगाड़ना): Making something worse.
• Example: His actions ended up worsening the situation.
• Preventing completely (पूरी तरह से रोकना): Stopping something from happening entirely.
• Example: Vaccination is key to preventing the spread of the disease completely.
• Ignoring (अनदेखा करना): Refusing to take notice of or acknowledge.
• Example: She kept ignoring his calls.

The correct answer is 'Option 2'.

Key Points

• Option 2: Combining them with real-world interaction
• The passage explicitly states that for digital platforms and educational video games, "these benefits are maximised when gameplay is balanced with real-world interaction."
• This balance is necessary to mitigate risks such as "social isolation and sedentary behaviour," ensuring that the cognitive gains from digital play translate effectively into personal growth.
• Option 1: Playing them for long hours
• This is incorrect. The passage cautions against "sedentary behaviour," which is often a result of excessive screen time without physical or social activity.
• Option 3: Using only offline versions
• This is incorrect. The passage discusses "digital platforms" and "educational video games" generally; it does not specify that they must be offline to be beneficial.
• Option 4: Avoiding all puzzles and strategy games
• This is incorrect. The passage actually highlights strategy games (like chess) and puzzles as "potent instruments for cognitive enhancement."

Therefore, the correct answer is Option 2.

Additional Information

• Cognitive Flexibility: The passage notes that educational games encourage children to "experiment with multiple solutions," which builds the mental ability to adapt to new information.
• Academic Resilience: By promoting traits like "patience, perseverance, and a tolerance for delayed gratification," these games prepare students for the long-term challenges of academic life.
• Intrinsic Motivation: When learning is embedded in an enjoyable framework (like a game), children are more likely to pursue it for their own satisfaction rather than due to external pressure.

The correct answer is Option 1.

Key Points

• The sequence of the sentences forms a coherent and logical paragraph that describes the process of purifying water step by step.
• Sentence P comes first as it introduces the initial action of collecting water and placing it over a fire:
• "He collected water from a stream into a pot and placed it over a fire."
• Sentence Q comes next as it describes the boiling process to kill pathogens:
• "He brought the water to a rolling boil for several minutes, killing all the pathogens."
• Sentence S follows as it explains the cooling and filtering of the boiled water:
• "He allowed the water to cool, then poured it through a cloth to filter out any sediment."
• Sentence R comes last as it concludes the paragraph by describing the final action of drinking the purified water:
• "He took a drink of the clear, safe water, his thirst finally quenched."
• The correct sequence is P, Q, S, R.

Coherent paragraph after rearrangement:

"He collected water from a stream into a pot and placed it over a fire. He brought the water to a rolling boil for several minutes, killing all the pathogens. He allowed the water to cool, then poured it through a cloth to filter out any sediment. He took a drink of the clear, safe water, his thirst finally quenched."

The correct answer is Option 1.

Key Points

• The paragraph discusses the agricultural achievements of the Incas, particularly their skill in building terraces for farming on steep mountain slopes.
• Sentence Q is the first sentence as it introduces the Incas and their skill in building terraces:
• "The Incas were skilled builders who carved terraces onto the Andes mountains' precipitous slopes."
• Sentence R follows as it explains the purpose of these terraces and the benefits they provided:
• "Where there had previously been no level, fruitful soil, these terraces produced it."
• Sentence P is the third sentence as it elaborates on how this innovation helped sustain the growing population:
• "As a result, they were able to produce crops that would feed a population that was growing quickly."
• Sentence S is the fourth as it links the agricultural innovation to the stability and wealth of the Inca Empire:
• "Their empire's stability and wealth were mainly due to their agricultural inventiveness."
• The correct sequence is Q, R, P, S.

Coherent paragraph after rearrangement:

"The Incas were skilled builders who carved terraces onto the Andes mountains' precipitous slopes. Where there had previously been no level, fruitful soil, these terraces produced it. As a result, they were able to produce crops that would feed a population that was growing quickly. Their empire's stability and wealth were mainly due to their agricultural inventiveness."

The correct answer is: 3) Eternal.

Key Points

• The word "Ephemeral" means something that lasts for a very short time or is fleeting. (अल्पकालिक)
• Example: The beauty of a sunset is ephemeral, fading as soon as the sun dips below the horizon.
• "Eternal" refers to something that lasts forever, without any end, and is permanent. (शाश्वत)
• Example: The love of a mother for her child is often described as eternal.
• Hence, the antonym of "Ephemeral" is "Eternal".

Therefore, the correct answer is: Eternal.

Additional Information

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

• Temporary (अस्थायी): Refers to something that exists for a short time and is not permanent.
• Example: The company hired temporary staff to handle the holiday rush.
• Momentary (क्षणिक): Refers to something that lasts for a very brief period of time.
• Example: There was a momentary pause before the speaker resumed the presentation.
• Fleeting (क्षणभंगुर): Refers to something that passes quickly or is short-lived.
• Example: The fleeting glimpse of a shooting star left everyone amazed.

The correct answer is: 1) Bright.

Key Points

• The word "Tenebrous" means dark, shadowy, or obscure. It is often used to describe something that lacks light or is associated with gloominess. (अंधकारमय/अंधेरा)
• Example: The old, tenebrous forest seemed eerie and unwelcoming.
• The word "Bright" refers to something that emits or reflects a lot of light or is full of energy and positivity. (चमकदार)
• Example: The bright sunlight filled the room with warmth and cheer.
• As the meaning of "Tenebrous" is associated with darkness, its antonym would naturally be "Bright," which signifies light and clarity.

Therefore, the correct answer is: 1) Bright.

Additional Information

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

• Shadowy (छायादार): Something that is full of shadows or dark areas; partially dark.
• Example: The shadowy corners of the room made it feel mysterious.
• Murky (धुंधला/मैला): Something that is dark, gloomy, or cloudy.
• Example: The water in the pond was murky and full of algae.
• Obscure (अस्पष्ट/अनजाना): Something that is not clearly expressed or easily understood.
• Example: The professor's explanation was obscure and left the students confused.

The correct answer is option 4.

Key Points

• The word 'apocryphal' is correctly spelled and refers to something of doubtful authenticity, although widely circulated as being true.
• The other options are misspelled versions of the word:
• Option 1: 'apocriphyll' - Incorrect spelling.
• Option 2: 'apocryfull' - Incorrect spelling.
• Option 3: 'apocriphal' - Incorrect spelling.

Correct sentence: The historian's theory was considered apocryphal by mainstream scholars.

Additional Information

• Word Origin: 'Apocryphal' comes from the Greek word 'apokryphos', meaning 'hidden'.
• Usage Example: The story of the haunted house is most likely apocryphal.

The correct answer is: Option 1 i.e. Penitence.

Key Points

• The word "Penitence" means the feeling of regret or sorrow for one's wrongdoing or sin, often accompanied by the desire to atone or make amends. (पश्चाताप)
• Example: She expressed deep penitence for her harsh words and apologized to her friend.
• In the context of the question, "penitence" perfectly describes the idea of self-punishment or remorse for one's sins or wrongdoings.

Therefore, the correct answer is: Option 1 i.e. Penitence.

Additional Information

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

• Vindication (सत्यापन): The action of clearing someone of blame or suspicion.
• Example: The new evidence led to the vindication of the wrongly accused man.
• Exoneration (दोषमुक्ति): The act of officially absolving someone from blame or fault.
• Example: The DNA evidence resulted in the exoneration of the suspect.
• Redemption (मोचन): The act of saving or being saved from sin, error, or evil; it can also mean regaining possession of something in exchange for payment.
• Example: He sought redemption by helping those in need after years of selfish behavior.

Given:

A is 17th from the top among passed students.

A is 22th from the bottom among passed students.

Number of failed students = 7

Total = Rank from Top + Rank from Bottom − 1

Number of passed students = 17 + 22 − 1

= 39 − 1 = 38 passed students.

Total students = Passed students + Failed students

= 38 + 7 = 45 students.

Hence, the correct answer is "Option 1".

Given:

P is 17th from the left.

Q is 15th from the right.

R is 6th to the right of P and is exactly in the middle of P and Q.

R = 17 + 6 = 23rd from the left.

Since R is exactly in the middle of P and Q:

Distance between P and R = Distance between R and Q = 6

So, Q’s position from the left = 23 + 6 = 29th

Total children = (Position from left) + (Position from right) − 1

= 29 + 15 − 1

= 44 − 1

= 43 children.

Hence, the correct answer is "Option 4".

Given:

Rima is 12th from the left.

Sita is 18th from the right.

After interchanging positions, Rima becomes 25th from the left.

After interchange, Rima takes Sita’s original position.

So, Sita’s position from the left = 25

Total = Rank from Left + Rank from Right − 1

Total students = 25 + 18 − 1

= 43 − 1

= 42 students.

Hence, the correct answer is "Option 4".

Family tree,

P is Grandfather of U.

Hence, the correct answer is “Option 2”.

Statement:

No fruit is a vegetable.

All vegetables are green.

Conclusions:

I. No fruit is green → Does not follow (There is no direct relation given between fruit and green. so, it is possible not definite).

II. Some green are not fruits  → Follow (As all vegetables are green and no fruit is vegetable. so, green which are vegetable are never be fruit).

Only conclusion II follows.

Hence, the correct answer is “Option 2”.

Logic followed here is,

9 × 3 + 4 = 31

31 × 4 + 4 = 128

128 × 3 + 4 = 388

388 × 4 + 4 = 1556

1556 × 3 + 4 = 4672

4672 × 4 + 4 = 18692

18692 × 3 + 4 = 56080

Hence, the correct answer is “Option 2”.

Logic followed here is,

-419 - 11 = -430

-430 - 12 = -442

-442 - 13 = -455

-455 - 14 = -469 ≠ -468

-469 - 15 = -484

-484 - 16 = -500

-500 - 17 = -517

Hence, the correct answer is “Option 1”.

Logic followed here is,

5 × 3 + 3 = 18

18 × 4 + 3 = 75

75 × 3 + 3 = 228

228 × 4 + 3 = 915

915 × 3 + 3 = 2748

2748 × 4 + 3 = 10995

10995 × 3 + 3 = 32988

Hence, the correct answer is “Option 2”.

F + 4 = J

J + 3 = M

M + 2 = O

O + 1 = P

Hence, the correct answer is “Option 1”.

Logic: a # b = a × b × 4

35 # 10 = 1400 → 

35 × 10 × 4 = 1400

1 # 45 = 180 → 

1 × 45 × 4 = 180

Similarly,

44 # 55 → 

44 × 55 × 4 = 9680

Hence, the correct answer is “Option 1”.

Logic: a & b $ c = a - (b × c)

569 & 4 $ 14 = 513 → 

569 - 4 × 14 = 569 - 56 = 513

718 & 47 $ 38 = -1068 → 

718 - 47 × 38 = 718 - 1786 = -1068

Similarly,

890 & 5 $ 5 = ? → 

890 - 5 × 5 = 890 - 25 = 865

Hence, the correct answer is “Option 2”.

Statements:

Only a few Youth is Young

Some Young is Elder

All Elder is Older

Conclusions:

I. Some Youth is not Older → Does not follow (There is no direct relation given between youth and older. so, it is possible not definite).

II. Some Older is Young  → Follow (As all elder are older and some young is Elder. so, some older are definitely young).

Only conclusion II follows.

Hence, the correct answer is “Option 3”.

Six persons A, B, C, D, E and F lived in a building with 6 floors. Only one person lived on each floor.

1. B lived just above D.
2. 2 persons lived between D and F.
3. D lived on one of the floors above F.
4. A lived just above C who did not live on a floor second from the bottom. 

No one lived below E.

Hence, the correct answer is “Option 1”.

Price of K is more than L but less than H and J. 

J/H > K > L

Price of G is highest.

G > _ > _ > _ > _

If the price of H is less than J.

J > H

Combining all the information,

G > J > H > K > L

Price of two cups is more than H.

Hence, the correct answer is “Option 1”.

Given that there are 6 rectangles A, B, C, D, E and F with different lengths.

From the clues, we can deduce the following relationships:

1. Length of A is second longest.

→ Only one rectangle is longer than A.

2. Length of F is more than C and B but less than D and E.

→ D, E > F > C, B

3. Length of E is not the maximum.

→ E is not the longest.

4. Since A is second longest, the longest rectangle must be someone above A.
5. From condition (2), D and E are above F.

But E is not the maximum, so E cannot be the longest.

→ Therefore, D must be the longest rectangle.

Combining all these facts, we get:

→ D > A > E > F > C/B (order of C and B not fixed)

Thus, the rectangle with the longest length is D.

Hence, the correct answer is “Option 2”.

8 boys A, B, C, D, E, F, G and H are sitting around a circular table facing towards the centre (not necessarily in the same order).

1. H is to the immediate right of A.
2. H is not the immediate neighbour of E or D.
3. F is to the immediate left of B.
4. G is the immediate neighbour of E.
5. C is the immediate neighbour of E and F.

E is sitting second to the right of H.

Hence, the correct answer is “Option 2”.

• Qualities projected in this situation: (Logical Reasoning and Analytical Ability)

The correct answer is "option (1)".

Given Equation: 14 ∼ 10 ∼ 3 $ 2 = ?

BODMAS Rule:

Decoding the given information:

Now replacing the signs using BODMAS Rule, we get:

⇒ 14 × 10 × 3 + 2

⇒ 140 × 3 + 2

⇒ 420 + 2

⇒ 422

Hence, the correct option is "Option 2".

Given equation:

21 × 6 - 15 ÷ 3 + 18

Step 1: Interchange × and -

New equation: 21 - 6 × 15 ÷ 3 + 18

Step 2: Apply BODMAS rule

= 21 - 6 × 15 ÷ 3 + 18

= 21 - 6 × 5 + 18

= 21 - 30 + 18

= 39 - 30

= 9

Hence, the correct answer is "Option 3".

BODMAS Rule:

According to the question: Interchange numbers 3 and 5

I. Given equation: 2 × 5 + 3 - 8 ÷ 2 = 7

After interchanging 3 and 5:

⇒ 2 × 3 + 5 - 8 ÷ 2

Apply BODMAS:

⇒ 2 × 3 + 5 - 8 ÷ 2

⇒ 6 + 5 - 4

⇒ 11 - 4

⇒ 7

LHS = RHS ⇒ 7 = 7 (Correct)

II. Given equation: 7 × 5 + 3 - 9 ÷ 1 = 15

After interchanging 3 and 5:

⇒ 7 × 3 + 5 - 9 ÷ 1

Apply BODMAS:

⇒ 7 × 3 + 5 - 9 ÷ 1

⇒ 21 + 5 - 9

⇒ 26 - 9

⇒ 17

LHS ≠ RHS ⇒ 17 ≠ 15 (Incorrect)

Thus, only equation II is not correct.

Hence, the correct answer is "Option 2".

'BODS' is coded as 'HVJZ'

'SKIP' is coded as 'YROW'

Similarly,

'BOWL' be coded as,

Hence, the correct answer is “Option 2”.

'STOW' is coded as 'OOKR' 

'HEIR' is coded as 'DZEM'

Similarly,

'POSH' be coded as,

Hence, the correct answer is “Option 2”.

Given series: r_ss_jssrjs_rj_s

(1) j j r s 

rjss/ jjss/ rjsr/ rjss

(2) j r s s

rjss/ rjss/ rjss/ rjss (Repeat the pattern rjss)

(3) j r r r

rjss/ rjss/ rjsr/ rjrs

(4) j r r s

rjss/ rjss/ rjsr/ rjss

Hence, the correct answer is “Option 2”.

Pattern followed here is,

Hence, the correct answer is “Option 3”.

Pattern followed here is,

Hence, the correct answer is “Option 2”.

Given:

Value = 72

Total = 240

Formula used:

Percentage = (Value ÷ Total) × 100

Calculations:

⇒ Percentage = (72 ÷ 240) × 100

⇒ = (3 ÷ 10) × 100

⇒ = 30%

∴ Final Answer = 30%

Given:

Profit = 25% of selling price

Formula Used:

Profit % on cost price = (Profit ÷ Cost Price) × 100

Selling Price = Cost Price + Profit

Calculation:

⇒ Let Selling Price = 100

⇒ Profit = 25% of 100 = 25

⇒ Cost Price = Selling Price - Profit = 100 - 25 = 75

⇒ Profit % on Cost Price = (25 ÷ 75) × 100

⇒ Profit % on Cost Price = 33.33%

∴ The correct answer is 33.33%.

Given:

Principal = Rs. 1300

Rate = 6% per annum

Time = 4 years

Formula Used:

Simple Interest (SI) = (Principal × Rate × Time) ÷ 100

Calculation:

⇒ SI = (1300 × 6 × 4) ÷ 100

⇒ SI = (31200) ÷ 100

⇒ SI = 312

∴ The correct answer is Rs. 312.00.

Given:

Number of sides = 10

Side length = 12 cm

Formula Used:

Total border length = Number of sides × Side length

Calculation:

⇒ Total border length = 10 × 12

⇒ Total border length = 120 cm

∴ The correct answer is 120 cm.

Shortcut Trick

Ratio of Lateral Surface Area to Base Area = 2 π rh : π r²

Given: Lateral Surface Area = 2 × Base Area

⇒ 2 π rh = 2 × π r²

Cancelling 2 π r from both sides: h = r

∴ The correct answer is h = r.

Alternate Method

Given:

Let the radius of the cylinder be r and the height be h.

Formulas Used:

Lateral Surface Area (LSA) of a cylinder = 2πrh

Area of the circular base = πr²

Calculation:

According to the problem statement:

⇒ Lateral Surface Area = 2 × Base Area

⇒ 2 π r h = 2 × (π r²)

⇒ 2 π r h = 2 π r²

Dividing both sides by 2 π r:

⇒ h = r² ÷ r

⇒ h = r

∴ The correct answer is h = r.

Additional Information

Total Surface Area of Cylinder

The total surface area includes the lateral surface area and the area of both circular bases: TSA = 2πrh + 2πr² = 2πr(h + r).

Volume of Cylinder

The volume represents the space occupied by the cylinder: Volume = πr²h.

Curved Surface Area vs Lateral Surface Area

For a cylinder, the Curved Surface Area (CSA) is the same as the Lateral Surface Area (LSA), excluding the top and bottom bases.

Given:

Increase in surface area = 44%

Formula used:

Surface area of sphere ∝ r²

Calculations:

New surface area = 1.44 × original

⇒ r_new² = 1.44 r_old²

⇒ r_new = √1.44 × r_old

⇒ r_new = 1.2 r_old

⇒ Increase = (1.2 − 1) × 100 = 20%

∴ Radius increases by approximately 20%

Given:

Base is an isosceles triangle with equal sides = 25 cm

Base of the triangle = 30 cm

Slant height of the pyramid = 40 cm

Formula Used:

Area of base = 1/2 × base × height

Lateral surface area of pyramid = 1/2 × Perimeter of base × Slant height

Total surface area = Area of base + Lateral surface area

Calculation:

⇒ Height of triangle = √(25² − (30 ÷ 2)²)

⇒ Height of triangle = √(625 − 225)

⇒ Height of triangle = √400

⇒ Height of triangle = 20 cm

⇒ Area of base = 1/2 × 30 × 20

⇒ Area of base = 300 cm²

⇒ Perimeter of base = 25 + 25 + 30

⇒ Perimeter of base = 80 cm

⇒ Lateral surface area = 1/2 × 80 × 40

⇒ Lateral surface area = 1600 cm²

⇒ Total surface area = 300 + 1600

⇒ Total surface area = 1900 cm²

∴ The correct answer is 1900 cm².

Given:

Side of square base = 6 cm

Perpendicular height = 4 cm

Formula Used:

Slant height = √(base radius² + perpendicular height²)

Calculation:

Base radius = side of square base ÷ 2

⇒ Base radius = 6 ÷ 2

⇒ Base radius = 3 cm

Slant height = √(3² + 4²)

⇒ Slant height = √(9 + 16)

⇒ Slant height = √25

⇒ Slant height = 5 cm

∴ The correct answer is 5 cm.

Given:

$\tan θ = \frac{12}{5}$

Formula Used:

$\tan θ = \frac{\text{opposite}}{\text{adjacent}}$

$\sin θ = \frac{\text{opposite}}{\text{hypotenuse}}$

$\text{hypotenuse} = \sqrt{\text{opposite}^2 + \text{adjacent}^2}$

Calculation:

⇒ Opposite = 12, Adjacent = 5

⇒ $\text{Hypotenuse} = \sqrt{12^2 + 5^2}$

⇒ $\text{Hypotenuse} = \sqrt{144 + 25}$

⇒ $\text{Hypotenuse} = \sqrt{169}$

⇒ $\text{Hypotenuse} = 13$

⇒ $\sin θ = \frac{12}{13}$

∴ The correct answer is $\frac{12}{13}$.

Shortcut Trick

The ratio of investment is given as 7 : 3.

Total units of profit = 7 + 3 = 10 units.

Given, 10 units = Rs. 1,00,000 → 1 unit = Rs. 10,000.

B's profit share = 3 units = 3 × 10,000 = Rs. 30,000.

∴ The correct answer is Rs. 30,000.

Alternate Method

Given:

Ratio of investment (A : B) = 7 : 3

Total Profit earned = Rs. 1,00,000

Formula Used:

Individual Profit Share = (Individual Ratio Part / Sum of Ratios) × Total Profit

Calculations:

⇒ Sum of ratio parts = 7 + 3 = 10

⇒ B's share in profit = (3 / 10) × 1,00,000

⇒ B's share in profit = 3 × 10,000

⇒ B's share in profit = 30,000

∴ The correct answer is Rs. 30,000.

Additional Information

Profit Sharing Rule

In a partnership, if the time period of investment is the same for all partners, the profit is distributed in the direct ratio of their capital investments.

Variable Time Investment

If partners invest for different durations, the profit ratio is calculated as: Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂).

Working Partner

A partner who manages the business is a working partner and may receive an additional salary or percentage before the remaining profit is divided.

Given:

A's investment = Rs. 4,000

B's investment = Rs. 6,000 (after 4 months)

C's investment = Rs. 8,000 (after 8 months)

Total profit = Rs. 1,650

Formula Used:

Profit share = (investment × time) ÷ total ratio

Time calculation = months invested ÷ 12

Calculation:

⇒ A's ratio = 4,000 × 12 = 48,000

⇒ B's ratio = 6,000 × 8 = 48,000

⇒ C's ratio = 8,000 × 4 = 32,000

⇒ Total ratio = 48,000 + 48,000 + 32,000 = 128,000

⇒ C's profit share = (32,000 ÷ 128,000) × 1,650

⇒ C's profit share = 0.25 × 1,650 = Rs. 412.50

∴ The correct answer is Rs. 412.50.

Given:

Angle in radians: 7π47π4

Conversion factor: 180∘=π radians180∘=π radians

Formula Used:

Degrees = Radians × 180π180π

Calculation:

⇒ Degrees = 7π47π4

× 180π180π

⇒ Degrees = 7×18047×1804

⇒ Degrees = 1260412604

⇒ Degrees = 315

∴ The correct answer is 315°.

Shortcut Trick

Initial average of 25 students = 48.

Net surplus from 5 new students (avg 60) = 5 × (60 − 48) = +60.

Mark correction surplus = 70 − 40 = +30.

Total surplus spread over 30 students = (60 + 30) ÷ 30 = +3.

Final Average = 48 + 3 = 51.

∴ The correct answer is 51.

Alternate Method

Given:

Total original students = 25, Original average = 48.

New students joined = 5, Marks per new student = 60.

Data correction: Wrongly entered 40 instead of 70.

⇒ Total marks of 25 students = 25 × 48 = 1200

⇒ Total marks after 5 new students join = 1200 + (5 × 60) = 1200 + 300 = 1500

⇒ Final sum after correcting error = 1500 − 40 + 70 = 1530

⇒ Total students in the class = 25 + 5 = 30

⇒ Final average marks = 1530 ÷ 30 = 51

∴ The correct answer is 51.

Additional Information

Arithmetic Mean

Average = Sum of all observations ÷ Total number of observations.

Weighted Average Formula

Final Average = (n₁ × A₁ + n₂ × A₂) ÷ (n₁ + n₂), where n is count and A is average.

Correction in Average

New Average = Old Average + (Correct Value − Incorrect Value) ÷ Total Strength.

Shortcut Trick

Total Work = LCM(10, 12) = 60 units.

Efficiency: A = 6 units/day, B = 5 units/day.

Work done in 1 cycle (2 days) = 6 + 5 = 11 units.

For 5 cycles (10 days), work done = 11 × 5 = 55 units.

Remaining work (60 − 55 = 5 units) completed by A in 5/6 days.

∴ The correct answer is 10 5/6 days.

Alternate Method

Given: A can complete the work in 10 days and B in 12 days. They work on alternate days starting with A.

⇒ Total Work = LCM(10, 12) = 60 units.

⇒ Efficiency of A = 60 ÷ 10 = 6 units/day.

⇒ Efficiency of B = 60 ÷ 12 = 5 units/day.

⇒ Work done in the first 2 days (Day 1: A, Day 2: B) = 6 + 5 = 11 units.

⇒ Work done in 5 such cycles (10 days) = 11 × 5 = 55 units.

⇒ Remaining work = 60 − 55 = 5 units.

⇒ On the 11^th day, it is A's turn. Time taken by A to finish 5 units = 5 ÷ 6 days.

⇒ Total time = 10 days + 5/6 days = 10 5/6 days.

∴ The correct answer is 10 5/6 days.

Additional Information

Total Work and Efficiency

Total Work = Efficiency × Time. When work is constant, Efficiency is inversely proportional to Time.

Alternate Day Concept

Calculate work done in one complete cycle (usually 2 days) and find how many full cycles fit into the total work before calculating the remaining part.

Remaining Work Calculation

Time taken for remaining work = (Remaining Work) ÷ (Efficiency of the person whose turn it is).

Given:

Total surface area = 314 cm²

Radius = 7 cm

Formula Used:

Total surface area = πr(l + r)

π = 3.14

Calculation:

⇒ 314 = 3.14 × 7 × (l + 7)

⇒ 314 = 21.98 × (l + 7)

⇒ 314 ÷ 21.98 = l + 7

⇒ 14.28 = l + 7

⇒ l = 14.28 - 7

⇒ l = 7.28 cm

⇒ Rounded value of l = 7.2 cm

∴ The correct answer is 7.2 cm.

Given:

x - y = 7

xy = 60

Formula Used:

x² + y² = (x - y)² + 2xy

Calculation:

⇒ x² + y² = (7)² + 2 × 60

⇒ x² + y² = 49 + 120

⇒ x² + y² = 169

∴ The correct answer is 169.

Given:

Milk in original mixture = M liters

Water in original mixture = W liters

When 20 liters of water are added, milk = 40% of total

When 10 liters of milk are added, milk = 50% of total

Formula Used:

Total mixture = Milk + Water

Percentage of milk = (Milk ÷ Total mixture) × 100

Calculation:

⇒ M ÷ (M + W + 20) = 40 ÷ 100

⇒ 5M = 2(M + W + 20)

⇒ 5M = 2M + 2W + 40

⇒ 3M = 2W + 40

⇒ (M + 10) ÷ (M + W + 30) = 50 ÷ 100

⇒ 2(M + 10) = M + W + 30

⇒ 2M + 20 = M + W + 30

⇒ M = W + 10

Substitute M = W + 10 in 3M = 2W + 40:

⇒ 3(W + 10) = 2W + 40

⇒ 3W + 30 = 2W + 40

⇒ W = 10

⇒ M = W + 10

⇒ M = 10 + 10 = 20

Water : Milk = W : M

⇒ Water : Milk = 10 : 20

⇒ Water : Milk = 1 : 2

∴ The correct answer is 2.

Given:

Radius of inner embankment = 40 m

Width of outer embankment = 12 m

Formula Used:

Area of a circle = π × radius²

Area between two concentric circles = Area of outer circle - Area of inner circle

Calculation:

⇒ Radius of outer embankment = 40 + 12 = 52 m

⇒ Area of inner circle = π × 40² = 3.14 × 1600 = 5024 m²

⇒ Area of outer circle = π × 52² = 3.14 × 2704 = 8490.56 m²

⇒ Area between two embankments = 8490.56 - 5024 = 3466.56 m²

⇒ Approximate area = 3470 m²

∴ The correct answer is 3470 m².

Shortcut Trick

Identify values of a and b directly from the given sum and difference.

Sum (a + b) = 3, Difference (a − b) = 1

Value of a = (3 + 1) ÷ 2 = 2

Value of b = (3 − 1) ÷ 2 = 1

Value of a⁴ − b⁴ = 2⁴ − 1⁴ = 16 − 1 = 15

∴ The correct answer is 15.

Alternate Method

Given: a + b = 3 and a − b = 1

Formula Used: a⁴ − b⁴ = (a² − b²)(a² + b²)

⇒ a² − b² = (a + b)(a − b)

⇒ a² − b² = 3 × 1 = 3

⇒ (a + b)² + (a − b)² = 2(a² + b²)

⇒ 3² + 1² = 2(a² + b²)

⇒ 10 = 2(a² + b²) ⇒ a² + b² = 5

⇒ a⁴ − b⁴ = (a² − b²)(a² + b²) = 3 × 5 = 15

∴ The correct answer is 15.

Additional Information

Difference of Squares

The formula x² − y² = (x − y)(x + y) can be applied iteratively for higher powers like a⁴ − b⁴.

Algebraic Relationship

The relation between sum, difference, and squares is given by (a + b)² + (a − b)² = 2(a² + b²).

Product of Squares

The identity (a + b)² − (a − b)² = 4ab is useful for finding the product ab if required.

Shortcut Trick

Given sin A + cos A = 5/4.

Squaring both sides: 1 + sin 2A = 25/16 ⇒ sin 2A = 9/16.

We know that sin 2A = 2 tan A / (1 + tan² A).

Substituting values: 9/16 = 2t / (1 + t²) ⇒ 9t² − 32t + 9 = 0.

Solving for tan A: t = (16 − 5√7)/9, which is equivalent to (5 − √7)/(5 + √7).

∴ The correct answer is (5 − √7)/(5 + √7).

Alternate Method

Given: cos A + sin A = 5/4

Formula Used: (sin A + cos A)² = 1 + sin 2A; sin 2A = 2 tan A / (1 + tan² A)

⇒ (cos A + sin A)² = (5/4)²

⇒ cos² A + sin² A + 2 sin A cos A = 25/16

⇒ 1 + sin 2A = 25/16

⇒ sin 2A = 25/16 − 1 = 9/16

⇒ 2 tan A / (1 + tan² A) = 9/16

⇒ 32 tan A = 9 + 9 tan² A

⇒ 9 tan² A − 32 tan A + 9 = 0

⇒ Using Quadratic Formula: tan A = [32 ± √(32² − 4 × 9 × 9)] / (2 × 9)

⇒ tan A = [32 ± √(1024 − 324)] / 18 = [32 ± √700] / 18

⇒ tan A = [32 ± 10√7] / 18 = (16 ± 5√7) / 9

⇒ To match the options, Rationalize (5 − √7)/(5 + √7):

⇒ [(5 − √7) × (5 − √7)] / [(5 + √7) × (5 − √7)] = (25 + 7 − 10√7) / (25 − 7) = (32 − 10√7) / 18 = (16 − 5√7) / 9

∴ The correct answer is (5 − √7)/(5 + √7).

Additional Information

Trigonometric Pythagorean Identity

For any angle A, the sum of the squares of sine and cosine is always 1: sin² A + cos² A = 1.

Double Angle Formulas in terms of tan A

sin 2A = 2 tan A / (1 + tan² A) and cos 2A = (1 − tan² A) / (1 + tan² A).

Sum and Product of Roots

For the equation ax² + bx + c = 0, the roots are given by x = [−b ± √(b² − 4ac)] / 2a.

Given:

Speed 1 = S

Distance = D

Time taken at speed 1 = T

Speed 2 = S + 10 km/h

Time taken at speed 2 = T - 1 hour

Speed 3 = S + 20 km/h

Time taken at speed 3 = T - 1 hour - 45 minutes

Formula Used:

Time = Distance ÷ Speed

LCM method for time

Calculation:

⇒ T = D ÷ S

⇒ T - 1 = D ÷ (S + 10)

⇒ T - 1.75 = D ÷ (S + 20)

⇒ D ÷ S - D ÷ (S + 10) = 1

⇒ D ÷ (S + 10) - D ÷ (S + 20) = 0.75

Take LCM of (S), (S + 10), and (S + 20):

⇒ LCM = S × (S + 10) × (S + 20)

Use substitution and solve:

⇒ D = 420 km

∴ The correct answer is 420 km.

Given:

Check which option gives sum = 90

Formula used:

Convert mixed fractions into improper form and add

Calculations:

Option 1:

$42 \frac{4}{5}+6 \frac{1}{6}$

⇒ 42 + 4/5 + 6 + 1/6

⇒ 48 + (24/30 + 5/30)

⇒ 48 + 29/30 ≠ 90

Option 2:

$43 \frac{1}{2}+7 \frac{1}{4}$

⇒ 43 + 1/2 + 7 + 1/4

⇒ 50 + 3/4 = 50.75 ≠ 90

Option 3:

$45 \frac{1}{2}+\frac{89}{2}$

⇒ 45.5 + 44.5

⇒ = 90 ✔

Option 4:

$52 \frac{1}{7}+63$

⇒ 115 1/7 ≠ 90

∴ Correct answer = $45 \frac{1}{2}+\frac{89}{2}$

Given:

$\dfrac{\sqrt{72} - \sqrt{50}}{\sqrt{2}}$

Formula used:

√a / √b = √(a/b)

Calculations:

⇒ $\dfrac{\sqrt{72}}{\sqrt{2}} - \dfrac{\sqrt{50}}{\sqrt{2}}$

⇒ $\sqrt{\frac{72}{2}} - \sqrt{\frac{50}{2}}$

⇒ $\sqrt{36} - \sqrt{25}$

⇒ 6 − 5 = 1

∴ Final Answer = 1

Shortcut Trick

Identify the multiplier for the 2-year gap (from 3 to 5 years): Ratio = 12884.08 ÷ 10648 = 1.21.

Since it is Compound Interest, the 1-year multiplier (1 + r) = √1.21 = 1.1.

The Principal (Sum) is the amount at year 3 divided by the 3-year multiplier: P = 10648 ÷ (1.1)³.

Calculation: P = 10648 ÷ 1.331 = 8000.

∴ The correct answer is Rs. 8000.

Alternate Method

Given:

Amount after 3 years (A₃) = Rs. 10648

Amount after 5 years (A₅) = Rs. 12884.08

Formula Used:

A = P(1 + r/100)ⁿ

⇒ (A₅ / A₃) = [P(1 + r/100)⁵] / [P(1 + r/100)³]

⇒ 12884.08 / 10648 = (1 + r/100)²

⇒ 1.21 = (1 + r/100)²

⇒ 1 + r/100 = √1.21 = 1.1

⇒ Now, A₃ = P(1 + r/100)³

⇒ 10648 = P × (1.1)³

⇒ 10648 = P × 1.331

⇒ P = 10648 / 1.331 = 8000

∴ The correct answer is Rs. 8000.

Additional Information

Compound Interest Rate from Two Amounts

If amounts after t and (t+n) years are given, the rate r is found by (1 + r/100)ⁿ = A_t+n / A_t.

Successive Percentage Change

Compound interest is essentially a successive percentage increase on the principal and the interest accumulated.

Effective Annual Rate

For a rate of 10% compounded annually, the effective rate for 2 years is 21% and for 3 years is 33.1%.

Shortcut Trick

Ratio of Marked Price to Discount = 150 : 100 ⇒ 3 : 2.

Selling Price = Marked Price − Discount = 3 − 2 = 1 unit.

Required Percentage = (Marked Price / Selling Price) × 100 = (3 / 1) × 100 = 300%.

∴ The correct answer is 300 percent.

Alternate Method

Given:

Marked Price = 150% of Discount

Formula Used:

Selling Price = Marked Price − Discount

Required % = (Marked Price / Selling Price) × 100

Calculations:

⇒ Let the Discount = 100 units.

⇒ Marked Price = 150% of 100 = 150 units.

⇒ Selling Price = Marked Price − Discount

⇒ Selling Price = 150 − 100 = 50 units.

⇒ Required Percentage = (150 / 50) × 100

⇒ Required Percentage = 3 × 100 = 300%

∴ The correct answer is 300 percent.

Additional Information

Discount and Selling Price

The Selling Price is always calculated as Marked Price − Discount. If Discount is 0, then Selling Price equals Marked Price.

Mark-up Percentage

Mark-up % = [(Marked Price − Cost Price) / Cost Price] × 100. It shows how much the price is increased over the cost.

Percentage of Base Change

To find what percent A is of B, the formula is (A/B) × 100. In this question, the base is the Selling Price.

The correct answer is Razia Sultana.

Key Points

• Razia Sultana was the first and only woman to rule the Delhi Sultanate, reigning from 1236 to 1240 A.D.. She was the daughter of Sultan Iltutmish, a ruler of the Slave Dynasty.
• Her accession to the throne marked a significant event in Indian history, as she was chosen by her father over her brothers due to her administrative skills and leadership capabilities.
• Razia broke gender barriers by dressing in male attire, leading her troops into battle, and taking an active role in the governance of her empire. This was a bold move in a patriarchal society.
• Her administration was marked by efforts to strengthen the central government and promote trade and commerce. She also focused on maintaining law and order within her empire.
• Razia's rule was cut short due to internal conspiracies and opposition from nobles who were unwilling to accept a female ruler. She was eventually defeated and killed in 1240 A.D.

Additional Information

• Slave Dynasty:
• The Slave Dynasty, also known as the Mamluk Dynasty, was the first dynasty of the Delhi Sultanate, established by Qutb-ud-din Aibak in 1206 A.D.
• It is called the Slave Dynasty because its rulers were originally slaves who rose to power through military achievements and administrative skills.
• Notable rulers of this dynasty include Qutb-ud-din Aibak, Iltutmish, and Razia Sultana.
• Challenges faced by Razia Sultana:
• Razia faced strong resistance from the Turkish nobility (Chahalgani), who opposed the idea of a female ruler.
• Her close association with her Abyssinian slave and advisor, Jamal-ud-Din Yaqut, caused further dissent among the nobles.
• Her reign was marked by constant power struggles, which eventually led to her downfall and assassination.
• Other options:
• Noor Jahan: She was the wife of Mughal Emperor Jahangir and played a significant role in the Mughal court but was never a ruler.
• Rani Durgavati: A queen of Gondwana, she was a warrior known for her resistance against the Mughals but not a ruler of the Delhi Sultanate.
• Chand Bibi: She was a regent of Ahmednagar and Bijapur Sultanates and known for her resistance against the Mughal invasion, but she did not rule the Delhi Sultanate.
• Legacy of Razia Sultana:
• Razia Sultana is remembered as a symbol of women’s empowerment and as a ruler who challenged societal norms of her time.
• Her story has been celebrated in literature, films, and plays, making her an iconic figure in Indian history.

Important Points

• Razia's Reforms:
• She focused on strengthening the central administration and sought to reduce the power of the nobility.
• Razia appointed capable administrators and promoted merit over birth in her court and military.
• Historical Significance:
• Razia Sultana was the first Muslim woman to rule over Delhi and remains a pioneering figure in Indian history.
• Her reign is seen as a testament to her courage, intelligence, and determination to overcome societal barriers.

The correct answer is 12.

Key Points

• The Alvar saints were a group of 12 Tamil poet-saints who were devoted to the worship of the Hindu god Vishnu.
• Their devotional hymns, composed between the 6th and 9th centuries CE, are collectively known as the Nalayira Divya Prabandham, consisting of 4,000 verses.
• The Alvars played a crucial role in the Bhakti movement, promoting devotion (bhakti) to Vishnu as a personal and direct form of worship.
• Prominent Alvar saints include Andal (the only female Alvar), Nammalvar, and Thirumangai Alvar, among others.
• The Alvars' teachings emphasized equality and devotion, rejecting social hierarchies and fostering a sense of universal brotherhood in spirituality.

Additional Information

• Role of Alvars in Bhakti Movement:
• The Bhakti movement emerged as a significant reformist movement in medieval India, emphasizing individual devotion over ritualistic practices.
• The Alvars contributed to the spread of the Bhakti ideals in South India, especially in Tamil Nadu, through their accessible and emotive hymns.
• Their compositions were written in Tamil, making spiritual teachings accessible to the common people.
• Notable Alvars and Their Contributions:
• Nammalvar: Considered the greatest of the Alvars, he composed works like Tiruvaimozhi, expressing intense devotion and love for Vishnu.
• Andal: The only female Alvar, her hymns, particularly the Tiruppavai, are still recited in temples and during festivals.
• Periyalvar: Known for his hymns celebrating the childhood of Lord Krishna.
• Key Themes in Alvar Hymns:
• Devotion to Vishnu as the supreme deity.
• Rejection of caste-based discrimination and promotion of spiritual equality.
• Focus on surrender (Prapatti) as the path to salvation.
• Legacy of Alvars:
• The hymns of the Alvars were collected and compiled by Nathamuni in the 10th century into the Nalayira Divya Prabandham.
• The Alvars' contributions significantly shaped the Sri Vaishnavism tradition, which later influenced the teachings of philosophers like Ramanuja.
• Their works continue to inspire festivals, temple rituals, and cultural practices in South India.

Important Points

• Terminology:
• Alvar: Derived from the Tamil word "Azhwar," meaning "one who is immersed" in devotion.
• Bhakti: Refers to devotion and love for a personal god, central to the teachings of the Alvars.
• Temples Associated with Alvars:
• The Alvars are closely associated with the 108 Divya Desams (sacred Vishnu temples) mentioned in their hymns.
• These temples, spread across India, are significant pilgrimage sites for devotees of Vishnu.
• Modern Relevance:
• The Alvars' teachings continue to resonate with followers of Vaishnavism, emphasizing devotion, compassion, and equality.
• Their hymns are integral to religious practices and cultural traditions in South India.

The correct answer is Article 30.

Key Points

• Article 30 of the Indian Constitution grants minorities the right to establish and administer educational institutions of their choice.
• It ensures the protection of cultural, linguistic, and educational rights of minorities and is a significant provision under the Fundamental Rights.
• The term "minorities" under Article 30 refers to both religious and linguistic minorities as interpreted by the Supreme Court of India.
• The article allows minorities to preserve their unique culture and heritage by running educational institutions that cater to their specific needs.
• The State cannot discriminate against any minority educational institution in granting aid, ensuring equality and inclusivity in educational opportunities.

Additional Information

• Article 28:
• It prohibits religious instruction in educational institutions wholly maintained by state funds.
• However, it allows educational institutions established by trusts or endowments to provide religious instruction if required by the trust's objectives.
• Article 24:
• This article prohibits the employment of children below the age of 14 years in factories, mines, or any other hazardous employment.
• It is aimed at protecting children from exploitation and ensuring their right to education and safe childhood.
• Article 29:
• It provides the right to protection of language, script, and culture to any section of citizens residing in India.
• It ensures that no citizen shall be denied admission to educational institutions based on religion, race, caste, or language.
• Significance of Article 30:
• Ensures that minorities can establish institutions to preserve their cultural identity.
• Provides the right to receive government aid without discrimination.
• Strengthens the secular fabric of India by promoting diversity in education.

Important Points

• Definition of Minority:
• The Supreme Court of India, in the T.M.A. Pai Foundation case (2002), defined minorities as those based on religion or language, assessed at the state level.
• For example, Muslims, Christians, and Sikhs are considered minorities in India.
• Constitutional Safeguards:
• Articles 29 and 30 together ensure the protection and promotion of minority rights.
• These provisions are part of the Fundamental Rights enshrined in the Indian Constitution.
• Challenges:
• Despite constitutional safeguards, minority educational institutions face issues like bureaucratic hurdles and limited resources.
• Efforts are needed to ensure effective implementation of these rights to promote equality and inclusivity.

The correct answer is IORA (Indian Ocean Rim Association).

Key Points

• Sanjiv Ranjan, a seasoned diplomat, assumed the role of Secretary General of the Indian Ocean Rim Association (IORA) on January 1, 2025.
• The Indian Ocean Rim Association (IORA) is an intergovernmental organization that promotes regional cooperation and sustainable development within the Indian Ocean region.
• The IORA was established in 1997 and comprises 23 member states that share a coastline along the Indian Ocean, including countries such as India, Australia, South Africa, and Indonesia.
• The role of the Secretary General involves overseeing policy implementation, fostering cooperation among member states, and facilitating dialogue on issues such as maritime security, trade, and disaster risk management.
• The appointment of Sanjiv Ranjan to this position reflects India's growing commitment to enhancing its engagement within the Indian Ocean region.

Additional Information

• IORA (Indian Ocean Rim Association):
• The IORA was established on March 7, 1997, in Port Louis, Mauritius, following the vision of promoting sustainable growth and balanced development in the Indian Ocean region.
• The organization focuses on six priority areas: maritime safety and security, trade and investment facilitation, fisheries management, disaster risk management, academic and scientific cooperation, and tourism promotion.
• IORA's Secretariat is based in Ebene, Mauritius.
• The organization's members include countries from Asia, Africa, and Oceania, such as India, Australia, Indonesia, South Africa, and Kenya.
• Sanjiv Ranjan:
• He is a senior Indian diplomat with extensive experience in foreign policy and international relations.
• Prior to his appointment as the Secretary General of IORA, he served in various capacities within the Indian Foreign Service (IFS), including as Ambassador to Colombia and Mexico.
• Other Regional Organizations:
• SAARC (South Asian Association for Regional Cooperation): Established in 1985, SAARC focuses on regional cooperation in South Asia, comprising countries like India, Pakistan, Nepal, and Sri Lanka.
• ASEAN (Association of Southeast Asian Nations): Established in 1967, ASEAN promotes economic and political cooperation among Southeast Asian nations such as Indonesia, Malaysia, and Thailand.
• BRICS: An acronym for Brazil, Russia, India, China, and South Africa, BRICS focuses on economic collaboration among emerging economies.

Important Points

• IORA's Importance:
• The Indian Ocean is a vital trade route, handling approximately 70% of the world's oil shipments and 50% of global container traffic.
• IORA plays a crucial role in ensuring maritime security and addressing challenges such as piracy, illegal fishing, and climate change.
• India's Role in IORA:
• India has been an active member of IORA, advocating for regional cooperation and contributing to initiatives like the Blue Economy and disaster risk management.
• India's maritime strategy aligns with IORA's goals, emphasizing the importance of the Indian Ocean Region (IOR) in global geopolitics.

The correct answer is Milkha Singh.

Key Points

• Milkha Singh, popularly known as the "Flying Sikh," was one of India's most celebrated athletes and a national sports icon.
• He earned the nickname "Flying Sikh" after his outstanding performance in the 1960 Rome Olympics and his incredible speed and stamina in track events.
• Milkha Singh was a four-time Asian Games gold medalist and represented India in the 1956, 1960, and 1964 Olympics.
• His most notable performance came during the 1960 Rome Olympics, where he finished fourth in the 400 meters final, narrowly missing a medal.
• Milkha Singh's story of resilience and determination, particularly in overcoming the traumas of the Partition of India, has inspired millions of Indians and was immortalized in the Bollywood biopic "Bhaag Milkha Bhaag" released in 2013.

Additional Information

• Milkha Singh's Achievements:
• He won the gold medal in the 1958 Commonwealth Games, becoming the first Indian male athlete to achieve this feat.
• He clinched four gold medals in the Asian Games: two in the 1958 Games (200m and 400m) and two in the 1962 Games (400m and 4x400m relay).
• Nickname Origin:
• The title "Flying Sikh" was reportedly given to him by the then President of Pakistan, General Ayub Khan, after Milkha Singh's victory in a race against Pakistan's Abdul Khaliq in 1960.
• Early Life:
• Milkha Singh was born on 20 November 1929, in Govindpura, a village now in Pakistan.
• He witnessed the horrors of the Partition of India, during which he lost his parents and several family members.
• He joined the Indian Army in 1951, which marked the beginning of his career in athletics.
• Legacy:
• Milkha Singh passed away on 18 June 2021, but his legacy continues to inspire budding athletes in India and abroad.
• His autobiography, "The Race of My Life," co-written with his daughter, provides insights into his journey of struggle and success.

Important Points

• Avinash Sable:
• An Indian track and field athlete specializing in 3000m steeplechase.
• He holds the national record in steeplechase and represented India in multiple international events.
• Vikas Gowda:
• An Indian discus thrower and shot putter who has won medals at Commonwealth Games and Asian Games.
• He was the first Indian male athlete to win a gold medal in discus throw at the 2014 Commonwealth Games.
• Harbhajan Singh:
• A renowned Indian cricketer who played as an off-spinner in the Indian cricket team.
• He is one of the most successful bowlers in Indian cricket history and played a pivotal role in India's victory in the 2007 ICC T20 World Cup and 2011 ICC Cricket World Cup.