SSC CHSL 2025 Tier-1 (Held On: 28 Nov, 2025 Shift 2) (Previous Year Paper)

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

Key Points

• The word "convinced" in the sentence means being certain or assured about something.
• Option 1, "Assured," is the correct synonym as it conveys the same meaning of being confident or sure.
• Option 2, "Cynical," means being distrustful or skeptical of others' motives, which is the opposite of the intended meaning.
• Option 3, "Skeptical," means having doubts or reservations, which is contrary to the word "convinced."
• Option 4, "Doubtful," also refers to uncertainty, which is not similar to the meaning of "convinced."

Correct sentence: Columbus was convinced that the earth was round, meaning he was assured of this fact.

Additional Information

• Synonyms for "convinced": Assured, confident, certain.
• Antonyms for "convinced": Doubtful, skeptical, uncertain.
• Understanding the context of the sentence is crucial for identifying the correct synonym.

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

Key Points

• The term Garrulous refers to a person who talks a lot, often excessively or in a verbose manner.
• The other options provided do not match the meaning of the sentence:
• Precipitous: Refers to something steep or sudden, not related to speech.
• Circumvent: Means to avoid or bypass, not related to talking.
• Sparkling: Refers to something bright or shining, unrelated to speech.
• Hence, option 1 (Garrulous) is the correct one-word substitution for a person who talks non-stop or continuously.

Correct sentence: A person who can talk non-stop is Garrulous.

Additional Information

• One-word substitutions are used to express lengthy sentences or phrases in a concise manner.
• Examples of similar one-word substitutions:
• Loquacious: Another word for someone who talks a lot.
• Taciturn: The opposite of garrulous; refers to someone who speaks very little.

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

Key Points

• The sentence describes Neha as a beginner who is eager to learn the basics of her new hobby.
• The word Apprentice refers to a person who is learning a skill or trade under someone more experienced, making it the most suitable one-word substitute.
• Other options, such as Veteran (experienced person), Mentor (guide/teacher), and Expert (highly skilled person), do not match the description of a beginner.

Correct sentence: Neha approached her new hobby with enthusiasm, eager to grasp the basics as an Apprentice.

Additional Information

• Veteran: Refers to someone with extensive experience in a particular field.
• Mentor: Refers to someone who guides or teaches others.
• Expert: Refers to someone with advanced skills or knowledge in a specific area.
• Apprentice: Refers to someone learning as a beginner, often under the guidance of a mentor or teacher.

The correct answer is '2' i.e. tell you .

Key Points

• The given sentence is an example of a third conditional sentence, which is used to describe hypothetical situations in the past.
• The structure of the third conditional is "If + past perfect, would have + past participle".
• In the result clause of the conditional sentence, the verb should be in the form "would have + past participle".
• However, the verb "tell" in the result clause is incorrect and should be replaced with "would have told".

Correct sentence: If you had spoken to my mother, she would have told you where I was.

Additional Information

• 1^st Conditional Sentence:
• Structure: If + Present Simple, will + base verb.
• Example: If it rains, we will cancel the picnic.
• Usage: Describes real or possible situations in the future with likely outcomes.
• 2^nd Conditional Sentence:
• Structure: If + Past Simple, would + base verb.
• Example: If I were rich, I would travel the world.
• Usage: Describes hypothetical or unlikely situations in the present or future.
• 3^rd Conditional Sentence:
• Structure: If + Past Perfect, would have + past participle.
• Example: If she had studied harder, she would have passed the exam.
• Usage: Refers to unreal past situations and their imagined outcomes.

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

Key Points

• The word "Aggregate" is correctly spelt.
• It means to combine or sum up multiple elements into a whole.
• Options 1, 3, and 4 are incorrect spellings of the word.

Correct sentence: The correct spelling is "Aggregate", which refers to a total amount or sum of individual parts.

Additional Information

• Common usage:
• It is often used in mathematics, business, and daily life to describe a collection or sum.
• Example: The aggregate score of the team was 250.
• Synonyms: Total, sum, collection, entirety.
• Antonyms: Individual, single, separate.

The correct answer is '3' i.e. around that tree.

Key Points

• The phrase "running over" is incorrect in the context of the given sentence because it implies physically stepping on or passing over the tree, which is illogical.
• The correct preposition to use in this context is "around," as it conveys the idea of the puppy running in a circular or surrounding motion near the tree.
• Each option was evaluated:
• Option 1: "on that tree" suggests the puppy is physically on top of the tree, which does not fit the context.
• Option 2: "across that tree" implies moving from one side of the tree to another, which is incorrect here.
• Option 3: "around that tree" is the most appropriate as it matches the intended meaning of movement near or encircling the tree.
• Option 4: "No substitution" is incorrect as the original phrase needs correction.

Correct sentence: I don't understand why the puppy keeps running around that tree.

Additional Information

• Use of Prepositions:
• "On": Indicates physical contact with a surface. Example: The book is on the table.
• "Across": Refers to movement from one side to the other. Example: He swam across the river.
• "Around": Suggests movement in a circular or surrounding manner. Example: They walked around the park.
• Choosing the correct preposition depends on the context and the action being described.

The correct answer is '1' i.e. Good at painting .

Key Points

• The phrase “good at” is the correct collocation to describe someone's skill or proficiency in an activity.
• “Good in” is not appropriate in this context as it does not convey the right meaning in English.
• Other options like “good with” and “good for” do not fit the sentence grammatically.

Correct sentence: She is good at painting but weak in studies.

Additional Information

• Common Collocations:
• Good at: Refers to proficiency or skill in a particular activity. Example: She is good at swimming.
• Good with: Refers to being skilled in handling or working with objects or people. Example: He is good with kids.
• Good for: Refers to something beneficial or suitable for a purpose. Example: Exercise is good for health.

The correct answer is '3' i.e. Let the blue wire be cut all at once; otherwise, the entire thing has to be thrown out of the house by you with your maximum strength.

Key Points

• The sentence is in the imperative form, and the passive voice of an imperative sentence typically begins with "Let."
• In the passive voice, the object of the active voice sentence becomes the subject.
• The correct structure for the passive voice in this sentence is: Let + object + be + past participle.
• The second part of the sentence, "you have to throw the entire thing out of the house with your maximum strength," is converted to passive voice as "the entire thing has to be thrown out of the house by you with your maximum strength."

Correct sentence: Let the blue wire be cut all at once; otherwise, the entire thing has to be thrown out of the house by you with your maximum strength.

Additional Information

• Common Passive Voice Structures:
• Imperative Active Voice: Cut the wire. → Passive Voice: Let the wire be cut.
• Present Simple Active Voice: She throws the ball. → Passive Voice: The ball is thrown by her.
• Future Simple Active Voice: He will complete the project. → Passive Voice: The project will be completed by him.
• Note: Always ensure the correct placement of "by" and the subject when converting sentences to passive voice.

The correct answer is '1' i.e. Rajan told Rini that he had very often informed her that they had to attend the meeting every Saturday.

Key Points

• The sentence is in direct speech and needs to be converted to indirect speech.
• When converting direct speech into indirect speech:
• The verb tense changes based on the reporting verb (past tense here).
• Pronouns are adjusted according to the context of the sentence.
• Words indicating time or frequency, such as "very often" and "every Saturday," remain unchanged as they do not affect the tense.
• The direct speech, "I have very often informed you that we have to attend the meeting every Saturday," becomes "Rajan told Rini that he had very often informed her that they had to attend the meeting every Saturday." This is because:
• "Have informed" changes to "had informed" (past perfect tense).
• "You" changes to "her" (adjusted for the listener).
• "We" changes to "they" (adjusted for the speaker and listener).

Correct sentence: Rajan told Rini that he had very often informed her that they had to attend the meeting every Saturday.

Additional Information

• Rules for changing direct to indirect speech:
• If the reporting verb is in the past tense, the verb in the reported clause must be changed to a corresponding past form.
• Personal pronouns must be adjusted to reflect the speaker and listener.
• Time expressions such as "today," "tomorrow," "yesterday" may need to be changed based on the context.
• Examples of tense changes in indirect speech:
• Simple Present → Simple Past
• Present Perfect → Past Perfect
• Simple Past → Past Perfect

The correct answer is '2' i.e. on, next to.

Key Points

• The sentence describes a location where the cousin lives in relation to Carter Road and a bank.
• The correct preposition for describing a residence on a street is "on". For proximity to another landmark, "next to" is appropriate.
• Options such as "at" are incorrect because "at" is typically used for specific points or locations rather than streets.
• Similarly, "besides" and "beside" are less commonly used in this context compared to "next to" for indicating proximity.

Correct sentence: My cousin lives on Carter Road next to the bank.

Additional Information

• Usage of Prepositions:
• On: Used to indicate a position on a surface or street (e.g., "on Carter Road").
• Next to: Indicates a position immediately adjacent to something (e.g., "next to the bank").
• At: Refers to a specific point or location (e.g., "at the corner").
• Beside/Besides: Beside means "next to" but is less common in modern usage for locations, while besides means "in addition to" and is unrelated to physical positioning.

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

Key Points

• The word exacerbate means to make a problem, situation, or condition worse.
• Its antonym would describe the opposite action — to make a problem, situation, or condition better or less severe.
• The word alleviate fits perfectly as it means to reduce or ease the severity of something.

Correct Option: 1) Alleviate

Additional Information

• Option 2) Intensify: This means to make something stronger or more severe, which is similar in meaning to exacerbate, not an antonym.
• Option 3) Improve: While this could be seen as a positive change, it does not directly convey the idea of reducing or easing severity like alleviate does.
• Option 4) Aggravate: This is a synonym of exacerbate, meaning to worsen a situation, and is not an antonym.

The correct answer is '2' i.e. My sister is preparing dinner .

Key Points

• The given sentence is in the passive voice, as indicated by the use of "is being prepared."
• To change a sentence from passive to active voice, the subject performing the action must be placed at the beginning of the sentence.
• The subject in this case is "my sister," and the action being performed is "preparing dinner."
• The correct active voice structure is: Subject + is/am/are + verb + object.

Correct sentence: My sister is preparing dinner.

Additional Information

• Passive Voice Structure: Object + is/am/are + being + past participle + by + subject.
• Example: The book is being read by John.
• Active Voice Structure: Subject + is/am/are + verb + object.
• Example: John is reading the book.
• Option 1: "Dinner prepared my sister" is grammatically incorrect because "prepared" is in the past tense and the structure does not properly indicate the action.
• Option 3: "My sister prepares dinner" is in the present simple tense, which does not correspond to the continuous action implied by "is being prepared."
• Option 4: "My sister was preparing dinner" is in the past continuous tense, which also does not match the present continuous tense of the original sentence.

The correct answer is '4' i.e. "He said to me, 'Have you ever been to the Louvre?'".

Key Points

• The given sentence is an example of indirect speech, where a question is being reported.
• To convert indirect speech into direct speech for a question, the sentence must:
• Include quotation marks.
• Use the exact question format and wording.
• Retain the original tense of the question.
• In direct speech, the question is typically introduced with a reporting verb like "said to" or "asked."

Correct sentence: He said to me, "Have you ever been to the Louvre?".

Additional Information

• Rules for converting indirect speech to direct speech:
• Remove introductory words like "He asked me" or "He said."
• Use quotation marks to enclose the exact words spoken.
• Ensure proper punctuation, such as a question mark for questions.
• Preserve the tense from the original direct speech.
• Examples:
• Indirect: She asked if I was coming tomorrow. → Direct: She asked, "Are you coming tomorrow?"
• Indirect: He wondered whether it was raining. → Direct: He said, "Is it raining?"

The correct answer is '1' i.e. from, on .

Key Points

• The preposition "from" is commonly used with the verb "refrain" to indicate abstention or avoidance of an action. Hence, "refrained from" is grammatically correct.
• The preposition "on" is used with the verb "focused" to specify the target or area of concentration. Therefore, "focused on" is the correct usage.
• Options 2, 3, and 4 use incorrect prepositions, making the sentence grammatically and contextually incorrect.

Correct sentence: She refrained from commenting publicly and instead focused on internal communication.

Additional Information

• Usage of Prepositions:
• From: Indicates the source or point of abstention (e.g., refrained from eating).
• On: Specifies the focus or target area (e.g., focused on the task).
• Incorrect Options:
• Option 2 (of, in): "Refrained of" and "focused in" are grammatically incorrect.
• Option 3 (for, by): These prepositions do not align with the verbs "refrained" and "focused."
• Option 4 (with, to): "Refrained with" and "focused to" are incorrect usages.

The correct answer is '3' i.e. Concious is spelled incorrectly.

Key Points

• The word Concious is misspelled. The correct spelling is Conscious.
• The other words, Government, Embellish, and Perceive, are spelled correctly.
• This question tests your ability to identify misspelled words among a list of options.

Correct sentence: One of these words is spelled incorrectly. The correct word is Conscious.

Additional Information

• Tips for identifying spelling errors:
• Pay attention to commonly misspelled words, such as "Conscious," "Separate," and "Definite."
• Look for subtle differences in spelling, especially with vowels and consonant placement.
• Mnemonic for Conscious: "Be conscious of your spelling, as it has 'sci' in it."

The correct answer is '2' i.e. She told him that he had been sleeping .

Key Points

• The given sentence is in direct speech: She said to him, "You were sleeping."
• When converting a sentence from direct to indirect speech, the pronouns and tenses must be adjusted to match the context.
• Here, the past continuous tense in direct speech ("You were sleeping") changes to past perfect continuous tense ("he had been sleeping") in indirect speech.
• The pronoun "you" is changed to "he" to match the subject (him) in the indirect speech.

Correct sentence: She told him that he had been sleeping.

Additional Information

• Rules for changing direct to indirect speech:
• Change in pronouns: Adjust the pronoun to match the context of the sentence.
• Change in tense: The verb tense in the reported speech changes depending on the reporting verb (e.g., past continuous becomes past perfect continuous).
• Remove quotation marks: Replace them with conjunctions like "that".
• Example for practice:
• Direct: He said, "I am watching a movie."
• Indirect: He said that he was watching a movie.

The correct answer is '3' i.e. Perserverance is incorrectly spelled.

Key Points

• The word Perserverance in Option 3 is incorrectly spelled.
• The correct spelling of the word is Perseverance, which means persistence in doing something despite difficulty or delay in achieving success.
• The other words — Magnanimous, Vehement, and Recalcitrant — are correctly spelled and valid English words.

Correct Answer: The word Perseverance should replace the incorrect spelling Perserverance.

Additional Information

• Magnanimous: Generous or forgiving, especially toward a rival or less powerful person.
• Vehement: Showing strong feeling; forceful, passionate, or intense.
• Recalcitrant: Having an obstinately uncooperative attitude toward authority or discipline.

The correct answer is Option 4.

 

Key Points

• To identify the Present Perfect Tense, we look for the specific verb structure: Has/Have + Past Participle (V3).
• In Option 4, the sentence "Awareness... has grown" follows this exact formula (has + the third form of the verb grow). This tense is used to describe an action that happened at an unspecified time in the past or began in the past and continues to the present.
• Why other options are incorrect:
• Option 1: "Hospitals operate..." is in the Simple Present Tense (V1).
• Option 2: "...employee plays..." is in the Simple Present Tense (V1 + s).
• Option 3: "Many remain..." is in the Simple Present Tense (V1).

Therefore, the correct answer is 4.

 

Analytical Insight: In competitive exams, identifying tenses is a foundational skill. Always remember that the Present Perfect ("has grown") links the past to the present, whereas the Simple Past ("grew") would imply the action is finished and disconnected from now.

 

Additional Information

• Present Perfect: Subject + has/have + V3 (e.g., has worked, have seen).
• Simple Present: Subject + V1 (s/es) (e.g., works, see).
• Tireless: Having or showing great effort or energy.
• Psychological weight: The mental or emotional burden of a situation.

The correct answer is Option 1.

 

Key Points

• To identify the sentence with a Modal Verb, we look for auxiliary (helping) verbs that express necessity, possibility, permission, or ability. Common modal verbs include can, could, may, might, must, shall, should, will, and would.
• In Option 1, the word "may" is a modal verb used to express possibility or a likely scenario. The phrase "may have to" combines this possibility with an obligation.
• Why other options are incorrect:
• Option 2: "Emergency ward staff often faces..." uses a main verb in the simple present tense. "Often" is an adverb, not a modal verb.
• Option 3: "...employee is marked..." uses a helping verb "is" (part of the passive voice structure), but it is a primary auxiliary, not a modal.
• Option 4: "Hospital employees witness..." uses a simple action verb (V1) without any auxiliary.

Therefore, the correct answer is 1.

 

Analytical Insight: In high-level competitive exams, modal verbs are frequently tested because they change the "mood" or "tone" of a sentence. "Nurses attend" (a fact) is very different from "Nurses may have to attend" (a potential requirement).

 

Additional Information

• Modal Verb: A verb that is used with another verb to express ideas such as possibility, permission, or intention.
• Precision: The quality, condition, or fact of being exact and accurate.
• Compassion: Sympathetic pity and concern for the sufferings or misfortunes of others.
• Around the clock: Happening all day and all night.

The correct answer is Option 3.

 

Key Points

• To determine the meaning of "strain," we must look at the words surrounding it: "...long hours, high stress, and emotional strain."
• In this context, the author is discussing the psychological challenges faced by hospital workers. Strain here refers to the severe pressure or tension placed on one's mental state due to demanding circumstances.
• Option 3 is the most accurate because "emotional or mental pressure" aligns perfectly with the passage's discussion of "psychological weight" and witnessing "suffering, grief, and loss."
• Why other options are incorrect:
• Option 1: While "strain" can refer to a genetic variant of a virus (e.g., a "strain of COVID-19"), it does not fit the context of a worker's emotional state.
• Option 2: A "pulled muscle" is a physical strain, but the passage explicitly uses the adjective "emotional" to qualify the word.
• Option 4: Like option 2, a "physical injury" describes a different type of strain that is not supported by the context of emotional burden.

Therefore, the correct answer is 3.

 

Analytical Insight: In high-level competitive exams, vocabulary questions often use "Polysemous" words (words with multiple meanings). You must ignore the literal or scientific meanings (like a virus strain or muscle strain) and choose the one that fits the tone and topic of the passage.

 

Additional Information

• Strain: A state of worry and tension caused by a difficult situation.
• Tireless: Putting a lot of hard work and energy into something over a long period.
• Psychological weight: The mental burden or impact of experiencing difficult emotions or events.
• Fragile: Easily broken or damaged; in this context, it refers to the delicate mental well-being of workers.

The correct answer is Option 3.

 

Key Points

• To identify what "burden" implies, we look at the immediate context in the third paragraph: "...emotional burden. Hospital employees witness suffering, grief, and loss..."
• In this context, burden refers to something that is difficult to bear or carry. Since it is described as "emotional," it signifies the mental weight or the heavy emotional load that comes from dealing with human suffering.
• The author reinforces this later by using the phrase "psychological weight," which is a direct synonym for an emotional burden in this setting.
• Why other options are incorrect:
• Option 1: A legal responsibility refers to duties defined by law; the passage focuses on the feeling and impact of the work, not its legal status.
• Option 2: A financial cost involves money; there is no mention of the employees' personal expenses or debts.
• Option 4: A physical task refers to manual labor; while hospital work is physically demanding, the word "burden" is specifically paired with "emotional" in this sentence.

Therefore, the correct answer is 3.

 

Analytical Insight: In high-level competitive exams, "Contextual Implication" questions test your ability to link related terms across the passage. Notice how the author uses "burden," "strain," and "weight" to describe the same psychological concept.

 

Additional Information

• Burden: A load, typically a heavy one; or a duty/misfortune that causes hardship.
• Compassion: Sympathetic pity and concern for the sufferings or misfortunes of others.
• Precision: The quality of being exact and accurate.
• Unnoticed: Not seen or noticed; disregarded.

The correct answer is Option 3.

 

Key Points

• To identify the main message, we look for the core argument or conclusion the author reaches after presenting all the facts.
• The passage describes the hardships (long hours, stress, emotional burden) and the critical roles played by all hospital staff, not just doctors.
• The final paragraph provides the "call to action" or the ultimate point: "However, proper recognition, mental health support, and fair working conditions are still essential to ensure the well-being of those who care for others."
• Option 3 directly summarizes this need for acknowledgement and better support systems for these workers.
• Why other options are incorrect:
• Option 1: This contradicts the text, which emphasizes that "every hospital employee plays a critical role" and that others' contributions often go "unnoticed."
• Option 2: This is the opposite of the truth; the text states their lives are marked by "long hours" and "entire shifts without rest."
• Option 4: The passage uses words like "high stress," "emotional strain," and "suffering," which are the opposite of "fun and relaxing."

Therefore, the correct answer is 3.

 

Analytical Insight: In competitive exams, the "Main Message" is usually found in the concluding sentences of the passage. While the middle paragraphs provide evidence of the struggle, the end explains why that struggle matters and what needs to change.

 

Additional Information

• Around the clock: Day and night without stopping.
• Recognition: Appreciation or acclaim for an achievement or service.
• Well-being: The state of being comfortable, healthy, or happy.
• Unnoticed: Not seen or noticed; disregarded.

The correct answer is '4' i.e. P, Q, R, S .

Key Points

• The given sentence parts describe a sequential process of developing and deploying an app.
• The correct order must follow the logical and chronological progression of steps in app development.
• P: This is the first step where the interface is designed by creating mockups of each screen.
• Q: After the design, the app's core features and logic are programmed.
• R: Once the app is built, testing is done to ensure it runs well on various devices.
• S: Finally, the app is uploaded to the app store for users to download.

Correct sequence: P, Q, R, S.

Additional Information

• This type of question tests your ability to understand the logical flow and order of events in a process.
• Pay attention to keywords and phrases indicating sequence or steps, such as "created," "programmed," "tested," and "uploaded."
• Practicing such questions improves comprehension and sequencing skills.

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

Key Points

• The paragraph describes the process of designing and building a robot as part of a final assignment.
• Sentence P introduces the subject of the paragraph: a robot built as the students' final assignment.
• Sentence R follows logically, elaborating on the students' skills that contributed to building the robot.
• Sentence Q describes the detailed process of writing the code, which was a critical part of the assignment.
• Sentence S concludes the paragraph, highlighting the success of the robot's performance and the students' dedication.

Correct sequence: P, R, Q, S.

Additional Information

• When rearranging sentences, always identify the main subject or topic sentence, which is typically the first sentence of the paragraph.
• Look for sentences that elaborate on or provide details about the subject to follow logically.
• Conclude with a sentence that sums up the topic or provides an outcome.

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

Key Points

• Misanthropic refers to the dislike or distrust of humanity or people in general.
• The antonym of "Misanthropic" would be a word that reflects a positive attitude towards people or society.
• Sociable means enjoying the company of others, which is the opposite of being misanthropic.
• Other options:
• Reclusive: Refers to someone who prefers isolation, similar to misanthropic.
• Cynical: Suggests distrust or skepticism, which aligns with misanthropic attitudes.
• Pessimistic: Indicates a negative outlook, but is not directly related to disliking people.

Correct sentence: The antonym of "Misanthropic" is Sociable, which represents a positive attitude toward people and society.

Additional Information

• Synonyms of Misanthropic: Antisocial, distrustful, hermit-like.
• Sociable: Represents friendliness, openness, and willingness to interact with others.
• Context: Understanding antonyms often involves identifying the opposite traits or qualities described by the word.

The logic followed here is:

thus, "186" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

The logic followed here is:

Logic: Subtract the second number from the first and then divide by 3.

Given:

60 " 21 = (60 − 21) ÷ 3 = 39 ÷ 3 = 13

81 " 9 = (81 − 9) ÷ 3 = 72 ÷ 3 = 24

Now,

27 " 39 = (27 − 39) ÷ 3 = (−12) ÷ 3 = −4

Hence, the correct answer is Option 3.

The logic followed here is:

Logic: Last  Number = 6 × 1^st Number × 2^nd Number

Given:

47 @ 39 = 10998

Last Number = 6 × 47 × 39 = 10998

30 @ 51 = 9180

Last Number = 6 × 30 × 51 = 9180

Similarly, 30 @ 11 = ?

So, ? = 6 × 30 × 11 = 1980

Hence, the correct answer is Option 2.

The logic followed here is:

Logic: Cube of consecutive numbers starting from 4, then subtract 4

Checking the given series:

4³ − 4 = 64 − 4 = 60

5³ − 4 = 125 − 4 = 121

6³ − 4 = 216 − 4 = 212

7³ − 4 = 343 − 4 = 339

Now, for the next term:

8³ − 4 = 512 − 4 = 508

thus, "508" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

The logic followed here is:

Logic: The pattern is based on the square of the difference of digits.

61 → (6 − 1)² = 5² = 25

Similarly,

52 → (5 − 2)² = 3² = 9

Hence, the correct answer is Option 2.

The logic followed here is:

thus, "315" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

The logic followed here is:

The series combines letters in alphabetical order and numbers as squares:

A → 1, 1² = 1 → A4 (Number seems adjusted)

C → 3, 3² = 9 → C9

E → 5, 5² = 25 → E25

G → 7, 7² = 49 → G81 (Actually 9² = 81, so number follows square of odd numbers in sequence: 2², 3², 5², 9²)

H → 8, 8² = 64 → H90

Here, H90 does not fit the pattern of letter following odd positions and number being a perfect square.

Hence, the correct answer is Option 4.

The logic followed here is:

Given Sequence: x _ x _ x _ x x _ y x _ x _ _

Now, putting the letters in the blank spaces given in the options one by one:

Option 1) yxxxxxy → x y x x x x x x x y x x x x y

→ Pattern breaks, not consistent

Option 2) xyxxxyx → x x x y x x x x x y x x x y x

→ x and y appear in positions that maintain a consistent pattern

Option 3) yxxyxxx → x y x x x x x x y y x x x x x

→ Pattern inconsistent

Option 4) xyxyxyx → x x x y x x x x y y x x x y x

→ Pattern inconsistent

Here, “xyxxxyx” fills the blanks maintaining the correct sequence.

Hence, the correct answer is "Option 2".

The logic followed here is:

thus, "29" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

Given: Weights of 5 pens W, X, Y, Z, and A are all different.

Weight of A is less than Z but more than X → X < A < Z

Weight of Y is more than W

Weight of Y is second lowest

So, the second highest weight is A.

Hence, the correct answer is Option 2.

Given: Price of 5 cups G, H, J, K and L is compared.

Price of no two cups is the same.

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

Price of G is the highest.

Price of H is more than J.

Now, arranging the cups in descending order of price:

Cups with price less than J are K and L → total 2 cups.

Hence, the correct answer is Option 1.

Given: There are 6 flats on a floor in two rows (three in each row opposite to each other).

Flats of one row are facing north and the other row is facing south. Flats are allotted to A, B, C, D, E and F with the following conditions:

D and F get diagonally opposite flats.

F's flat is next to C's flat.

C gets a South-facing flat.

B and E face the same direction.

B is not next to D.

North-facing flats → B, E, D

From the options**, 'B' is the correct answer.**

Hence, the correct answer is Option 3.

The logic followed here is:

Logic: The pattern is based on adding 951 to the given number.

2943 + 951 = 3894

8615 + 951 = 9566

Similarly,

2617 + 951 = 3568

Hence, the correct answer is Option 2.

BODMAS Table: 

By interchanging the given two numbers (not digits) 3 and 2, we check each equation:

Equation I: 3 × 9 + 2 − 8 + 1 = 13

Interchange 3 and 2 → 2 × 9 + 3 − 8 + 1 = ?

⇒ 18 + 3 − 8 + 1 = 14 (≠ 13) → Not correct

Equation II: 2 × 8 + 3 − 9 + 1 = 17

Interchange 2 and 3 → 3 × 8 + 2 − 9 + 1 = ?

⇒ 24 + 2 − 9 + 1 = 18 (≠ 17) → Not correct

Hence, after interchanging, neither equation is correct.

The correct answer is Option 4.

BODMAS Table: 

Given equation: 19 * 11 * 2 * 48 * 6 = 33

Now, if * signs are replaced sequentially as +, ×, -, ÷, then:

⇒ 19 + 11 × 2 − 48 ÷ 6 = ?

⇒ 19 + 22 − 8 = ?

⇒ 41 − 8 = ?

⇒ 33

Hence, the correct answer is Option 3.

The logic followed here is:

Logic: The pattern is based on sum of positions of letters = given number.

Now, checking the options:

Option 1) KLMN → 11 + 12 + 13 + 14 = 50 

Option 2) QRST → 17 + 18 + 19 + 20 = 74 

Option 3) CDEF → 3 + 4 + 5 + 6 = 18 ≠ 28 

Option 4) VWXY → 22 + 23 + 24 + 25 = 94 

Hence, the correct answer is Option 3.

The logic followed here is:

Logic: Left number = (right number)³ − 1, and letters shift by −2 and −5

Checking the given pairs:

For, SN1330 − QI11

Number: 11³ − 1 = 1331 − 1 = 1330 

Letters: S → Q (−2), N → I (−5) 

For, MP999 − KK10

Number: 10³ − 1 = 1000 − 1 = 999 

Letters: M → K (−2), P → K (−5) 

For, TC728 − RX9

Number: 9³ − 1 = 729 − 1 = 728 

Letters: T → R (−2), C → X (−5) 

For, BW513 − ZR8

Number: 8³ − 1 = 512 − 1 = 511 (given 513)

Letters: B → Z (−2), W → R (−5) 

Since, the number pattern is not followed in the 4^th pair,

Hence, the correct answer is Option 4.

The logic followed here is:

Logic: The pattern is based on subtracting 590 from the number.

Now, checking the given options:

Option 1) 8032 − 590 = 7442 

Option 2) 7644 − 580 = 7064

Option 3) 6836 − 590 = 6246 

Option 4) 9888 − 590 = 9298 

Here, all pairs follow subtraction of 590 except the second pair.

Hence, the correct answer is Option 2.

The logic followed here is:

For, ‘KOOK’ is written as OSSO,

For, ‘FRIG’ is written as JVMK,

Similarly, for ‘ORBS’,

So, ‘ORBS’ will be written as ‘SVFW’.

Hence, the correct answer is Option 4.

Given word: VOLUNTEER

Original word: V O L U N T E E R

Available letters: V, O, L, U, N, T, E, E, R

Only VOLT can be formed using the letters of VOLUNTEER.

Hence, the correct answer is Option 1.

Given word: BOARD

 

Now, Checking options:

For, DEBARK

Contains B, A, R, D but no O 

For, ROADEN

Contains R, O, A, D but no B 

For, BROADEN

Contains B, O, A, R, D 

For, BARKED

Contains B, A, R, D but no O 

Hence, the correct answer is Option 3.

The logic followed here is:

Logic: The pattern is based on shifting letters backward (−2, −3) and multiplying the number by 3.

Now, checking the given pairs:

CX238 → AU714

NL94 → LI282

Similarly,

RA140 → ?

So,

RA140 → PX420

Hence, the correct answer is Option 4.

The logic followed here is:

Logic: The pattern is based on shifting both letters backward by 5 positions and taking the sum of positions of the new letters as the number.

Now, checking the given pairs:

XR42 → SM32

FL18 → AG8

Similarly,

WD27 → ?

So,

WD27 → RY43

Hence, the correct answer is Option 2.

The logic followed here is:

PN 112 : GI 392

FB 84 : UY 294

Similarly,

AR 56 : ?

Hence, the correct answer is Option (2).

The logic followed here is:

Hence, the correct term should be LV3840, but given is LU3840.

Hence, the correct answer is Option 4.

Shortcut Trick

Profit % = (Profit ÷ Cost Price) × 100

= (25 ÷ 125) × 100

= (1 ÷ 5) × 100

= 20%

∴ Answer = 20%

Alternate Method

Given:

Cost Price (CP) = 125

Profit = 25

Selling Price (SP) = 125 + 25 = 150

Formula used:

Profit % = (Profit ÷ CP) × 100

CP = 125 Profit = 25 SP = 150

Calculations:

⇒ Profit % = (25 ÷ 125) × 100

⇒ = (1 ÷ 5) × 100

⇒ = 20%

∴ The correct answer is 20%.

Shortcut Trick

Successive Discount Formula = x + y − (x × y / 100)

Here x = 15 and y = 10

Equivalent Discount = 15 + 10 − (15 × 10 / 100)

Equivalent Discount = 25 − 1.5 = 23.5%

∴ Answer = 23.5%

Alternate Method

Given:

First discount = 15%

Second discount = 10%

Formula used:

Net Discount % = [1 − (1 − d₁/100) × (1 − d₂/100)] × 100

 Marked Price (100%) Selling Price (76.5%)  23.5%  Total Discount Net Equivalent Discount = 23.5%

Calculations:

Assume the Marked Price (MP) = 100 units

⇒ Price after 15% discount = 100 − (15% of 100) = 85 units

⇒ Price after 10% successive discount = 85 − (10% of 85)

⇒ Final Selling Price = 85 − 8.5 = 76.5 units

⇒ Single Equivalent Discount = 100 − 76.5 = 23.5%

∴ The correct answer is 23.5% (Option 2).

Shortcut Trick

Net interest percentage = Rate × Time

Net interest percentage = 5% × 2 = 10%

Simple Interest = 10% of 5000

Simple Interest = 500

∴ Answer = ₹500

Alternate Method

Given:

Principal (P) = ₹5000

Time (T) = 2 years

Rate (R) = 5% per annum

Formula used:

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

Start (Year 0) Year 1 Year 2 P = ₹5000

+5% (₹250)

+5% (₹250)

Total SI = ₹250 + ₹250 = ₹500

Calculations:

SI = (5000 × 5 × 2) / 100

⇒ SI = (5000 × 10) / 100 ⇒ SI = 50000 / 100 ⇒ SI = 500

∴ The correct answer is ₹500, which is option (1).

Shortcut Trick

The effective interest rate for 10% compounded annually for 3 years is 33.1%.

Compound Interest = 33.1% of ₹1000

CI = (33.1 ÷ 100) × 1000 = ₹331

∴ The correct answer is ₹331.

Alternate Method

Given:

Principal (P) = ₹1000

Rate (R) = 10% per annum

Time (T) = 3 years

Formula Used:

Amount (A) = P(1 + R/100)^T

Compound Interest (CI) = A − P

⇒ A = 1000 × (1 + 10/100)³

⇒ A = 1000 × (1.1)³

⇒ A = 1000 × 1.331 = ₹1331

⇒ CI = 1331 − 1000 = ₹331

∴ The correct answer is ₹331.

Additional Information

Effective Rate for 3 Years

For a rate R%, the 3-year effective rate is 3R + (3R²/100) + (R³/10000) %.

Difference between CI and SI

For 2 years, Difference = P(R/100)². For 3 years, Difference = P(R/100)² × (3 + R/100).

Compounding Half-Yearly

If interest is compounded semi-annually, the rate is halved (R/2) and the time is doubled (2T).

Shortcut Trick

The central angles of any polygon inscribed in a circle are formed by the radii meeting at the center point.

The sum of all angles around a single central point is always a complete revolution.

Total angle of a complete revolution = 360°.

This sum remains 360° regardless of the number of sides of the polygon.

∴ Answer = 360°

Alternate Method

Given:

Number of sides of the regular polygon (n) = 15

Shape = Circular antenna divided into equal triangular segments

Formula used:

Central angle of one segment = 360° ÷ n

Sum of all central angles = n × (Central angle of one segment)

θ Center n = 15 sides Sum of Central Angles = 360°

Calculations:

Since the circular antenna is divided into 15 equal triangular segments:

⇒ Central angle of each segment = 360° ÷ 15

⇒ Central angle = 24°

⇒ There are 15 such central angles formed at the center.

⇒ Sum of all central angles = 15 × 24°

⇒ Sum = 360°

∴ The correct answer is (1).

Shortcut Trick

Repeating decimals (like 0.333...) can always be expressed in the form of p/q where p, q are integers and q ≠ 0.

By definition, any number that can be written as a fraction p/q is a Rational Number.

Non-terminating but repeating decimals = Rational Numbers.

Non-terminating and non-repeating decimals = Irrational Numbers.

∴ Answer = Always rational

Alternate Method

Given:

A repeating decimal (e.g., 0.666..., 0.1212...)

Formula used:

A rational number is any number that can be expressed as p/q (where p, q are integers, q ≠ 0).

Real Numbers Rational Repeating Decimals (0.333... = 1/3) Irrational Non-repeating & Non-terminating

Calculations:

Let x = 0.333... (i)

⇒ Multiplying by 10 on both sides: 10x = 3.333... (ii)

⇒ Subtracting (i) from (ii): 10x − x = 3.333... − 0.333...

⇒ 9x = 3

⇒ x = 3/9 = 1/3

⇒ Since x is expressed as a fraction 1/3, it is a rational number.

∴ The correct answer is Always rational. (Option 3)

Shortcut Trick

Convert length to centimeters: 1.2 m = 120 cm.

Area of material cross-section = π × (Outer Radius² − Inner Radius²).

Difference in radius squares = 4² − 3² = 16 − 9 = 7.

Volume = 7 × 120 × π = 840π.

∴ Answer = 840π cm³

Alternate Method

Given:

Length of the pipe (h) = 1.2 m = 120 cm

Inner radius (r) = 3 cm

Outer radius (R) = 4 cm

Formula used:

Volume of material in a hollow pipe = π × (R² − r²) × h

  R=4  r=3  h = 120 cm  Volume = π(R² − r²)h

Calculations:

⇒ Volume = π × (4² − 3²) × 120

⇒ Volume = π × (16 − 9) × 120

⇒ Volume = π × 7 × 120

⇒ Volume = 840π cm³

∴ The correct answer is option (2).

Shortcut Trick

Base Area = (√3 / 4) × 12² = 1.732 × 36 = 62.352 cm²

Lateral Surface Area = Perimeter × height = (3 × 12) × 25 = 900 cm²

TSA per box = 900 + (2 × 62.352) = 1024.704 cm²

Total Area for 25 boxes = 25 × 1024.704 = 25617.6 cm²

∴ The correct answer is 25617.6 cm².

Alternate Method

Given:

Base side of the equilateral triangular base (s) = 12 cm

Height of the prism (h) = 25 cm

Number of boxes (n) = 25

Value of √3 = 1.732

Formula Used:

Total Surface Area (TSA) of a prism = Lateral Surface Area + 2 × Base Area

Lateral Surface Area (LSA) = Perimeter of base × Height

Area of Equilateral Triangle = (√3 / 4) × side²

Calculations:

⇒ Area of one triangular base = (1.732 / 4) × 12 × 12

⇒ Area of one triangular base = 1.732 × 36 = 62.352 cm²

⇒ Perimeter of the base = 3 × 12 = 36 cm

⇒ LSA of one box = 36 × 25 = 900 cm²

⇒ TSA of one box = 900 + 2 × 62.352

⇒ TSA of one box = 900 + 124.704 = 1024.704 cm²

⇒ TSA of 25 such boxes = 25 × 1024.704

⇒ TSA of 25 boxes = 25617.6 cm²

∴ The correct answer is 25617.6 cm².

Additional Information

Properties of a Prism

A prism is a polyhedron with two congruent and parallel faces called bases. The volume of any prism is calculated as (Area of base × Height).

Lateral Surface Area (LSA)

The LSA of a prism is the area of all its side faces, which equals the (Perimeter of the base × height of the prism).

Equilateral Triangle formulas

For a side 's', the height is (√3 / 2)s and the area is (√3 / 4)s². All internal angles are 60°.

Shortcut Trick

For a hemisphere, the height is always equal to its radius (h = r).

Since the cone has the same height and radius, its height (h) is also equal to (r).

Volume Ratio = (2/3 π r³) : (1/3 π r² × r) = 2 : 1.

∴ The correct answer is 2:1.

Alternate Method

Given:

Base radius of hemisphere = Base radius of cone = r

Height of hemisphere = Height of cone = h

Formula Used:

Volume of a hemisphere (V₁) = 2/3 π r³

Volume of a cone (V₂) = 1/3 π r² h

Calculations:

⇒ In a hemisphere, the distance from the center of the base to the top is its radius.

⇒ ∴ Height of hemisphere (h) = r

⇒ Since both have the same height, Height of cone (h) = r

⇒ Volume of cone (V₂) = 1/3 π r² × r = 1/3 π r³

⇒ Ratio = V₁ : V₂ = (2/3 π r³) : (1/3 π r³)

⇒ Ratio = 2/3 : 1/3 = 2 : 1

∴ The correct answer is 2:1.

Additional Information

Volume of Sphere

The volume of a complete sphere is given by 4/3 π r³, which is exactly double that of a hemisphere.

Surface Area of Hemisphere

Curved Surface Area (CSA) = 2π r² and Total Surface Area (TSA) = 3π r².

Volume of Cylinder

The volume of a cylinder with the same radius and height would be π r² h = π r³, making the ratio Cylinder : Hemisphere : Cone = 3 : 2 : 1.

Shortcut Trick

Area of Parallelogram = Side₁ × Side₂ × sin(θ)

Area = 22 × 16 × sin(45°) = 352 × (1/√2) = 176√2 cm²

Height (h) = Area ÷ Base = 176√2 ÷ 22 = 8√2 cm

∴ Answer = 176√2 cm², 8√2 cm

Alternate Method

Given:

Sides of the parallelogram: a = 22 cm, b = 16 cm

Angle between the sides: θ = 45°

Formula used:

Area = Side₁ × Side₂ × sin(θ)

Area = Base × Height

45° Base (a) = 22 cm Side (b) = 16 cm h Area = 176√2 cm²

Calculations:

Area = 22 × 16 × sin(45°)

⇒ Area = 352 × (1/√2)

⇒ Area = (352 ÷ √2) × (√2 ÷ √2) = 176√2 cm²

⇒ Height corresponding to the longer side (h) × 22 = 176√2

⇒ h = 176√2 ÷ 22 = 8√2 cm

∴ The correct answer is option (1).

Shortcut Trick

Number of hemispheres (n) = (Volume of Sphere) ÷ (Volume of Hemisphere)

n = [4/3 × π × R³] ÷ [2/3 × π × r³] = 2 × (R/r)³

n = 2 × (24/8)³ = 2 × 3³ = 2 × 27 = 54

Total CSA = n × 2πr² = 54 × 2 × π × 8² = 108 × 64π = 6912π

∴ The correct answer is 6912π cm².

Alternate Method

Given: Radius of the spherical ball (R) = 24 cm, Radius of each hemisphere (r) = 8 cm.

Formula Used: Volume of sphere = 4/3 πR³ | Volume of hemisphere = 2/3 πr³ | CSA of hemisphere = 2πr²

⇒ Volume of the original sphere = 4/3 × π × (24)³ cm³

⇒ Volume of one hemisphere = 2/3 × π × (8)³ cm³

⇒ Let n be the number of hemispheres formed.

⇒ n × [2/3 × π × 8 × 8 × 8] = 4/3 × π × 24 × 24 × 24

⇒ n = [4 × 24 × 24 × 24] ÷ [2 × 8 × 8 × 8] = 2 × 3 × 3 × 3 = 54

⇒ Combined Curved Surface Area (CSA) = n × 2πr²

⇒ Total CSA = 54 × 2 × π × (8)² = 108 × 64π

⇒ Total CSA = 6912π cm²

∴ The correct answer is 6912π cm².

Additional Information

Surface Area of a Sphere

A sphere only has one surface area, which is 4πr², where r is the radius.

Total Surface Area of a Hemisphere

The total surface area (TSA) includes the curved area (2πr²) and the flat base area (πr²), totaling 3πr².

Volume Invariance

When a solid object is melted and recast into other shapes, its Total Volume remains constant (Volume_Initial = Volume_Final).

Volume of Sphere vs Hemisphere

A hemisphere is exactly half of a sphere; thus, its volume is 2/3 πr³ compared to the sphere's 4/3 πr³.

Shortcut Trick

√20.25 = 4.5

4.5 + √(16 + y²) = 9.5

√(16 + y²) = 9.5 − 4.5 = 5

Square both sides: 16 + y² = 25

y² = 9 → y = 3

∴ Answer = 3

Alternate Method

Given:

√20.25 + √(16 + y²) = 9.5

Formula used:

(√a)² = a | y² = k ⇒ y = √k

√20.25 4.5 √(16 + y²) 5.0 Total Equation Sum = 9.5 Finding y: √(16 + y²) = 5

Calculations:

⇒ √20.25 = √(2025/100) = 45/10 = 4.5

⇒ 4.5 + √(16 + y²) = 9.5

⇒ √(16 + y²) = 9.5 − 4.5

⇒ √(16 + y²) = 5

⇒ Squaring both sides: 16 + y² = 5² = 25

⇒ y² = 25 − 16

⇒ y² = 9

⇒ y = √9 = 3

∴ The correct answer is (3).

Shortcut Trick

Profit Ratio (Chetan : Sahir) = (9,000 × 12) : (6,000 × 6)

Ratio = 108,000 : 36,000 = 3 : 1

Total Ratio units = 3 + 1 = 4 units

Value of 4 units = ₹18,000 → 1 unit = ₹4,500

Chetan share = 3 units = 3 × 4,500 = 13,500

∴ Answer = ₹13,500

Alternate Method

Given:

Chetan investment = ₹9,000 | Time = 12 months

Sahir investment = ₹6,000 | Time = 6 months

Total business profit = ₹18,000

Formula used:

Profit Share Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂)

Profit Distribution Bar Chetan (3 units) Sahir (1) Total Profit = ₹18,000 (4 Units) Chetan Share = (3/4) × 18,000 = ₹13,500

Calculations:

⇒ Profit Ratio = (9,000 × 12) : (6,000 × 6)

⇒ Profit Ratio = 108,000 : 36,000

⇒ Simplified Ratio = 3 : 1

⇒ Total profit share parts = 3 + 1 = 4

⇒ Chetan share = (3 ÷ 4) × 18,000

⇒ Chetan share = 3 × 4,500 = 13,500

∴ The correct answer is ₹13,500 (Option 4).

Shortcut Trick

If tan θ = 1, then the angle θ = 45°.

Standard values: sin 45° = 1/√2 and cos 45° = 1/√2.

Sum = sin 45° + cos 45° = 1/√2 + 1/√2 = 2/√2 = √2.

∴ Answer = √2

Alternate Method

Given:

tan θ = 1

Formula used:

tan θ = Perpendicular (P) / Base (B)

Hypotenuse (H) = √(P² + B²)

sin θ = P / H and cos θ = B / H

    θ   Base (B) = 1    P = 1    H = √(12 + 12) = √2

Calculations:

⇒ tan θ = 1 / 1 → Perpendicular (P) = 1 and Base (B) = 1

⇒ Hypotenuse (H) = √(1² + 1²) = √2

⇒ sin θ = P / H = 1 / √2

⇒ cos θ = B / H = 1 / √2

⇒ sin θ + cos θ = (1 / √2) + (1 / √2)

⇒ Result = 2 / √2 = √2

∴ The correct answer is (1).

Shortcut Trick

Since sin x = 3/5, we use the Pythagorean triplet (3, 4, 5) where Perpendicular = 3 and Hypotenuse = 5.

The magnitude of the Base (Adjacent side) = √(5² − 3²) = 4.

In Quadrant II, sine is positive but cosine is negative (ASTC rule).

Therefore, cos x = −Base/Hypotenuse = −4/5.

∴ Answer = −4/5

Alternate Method

Given:

sin x = 3/5 and x is in Quadrant II.

Formula used:

cos x = ±√(1 − sin²x)

 x Base = −4 Perp = 3 Hyp = 5 Quadrant II cos x = −4/5 (Negative in Q2)

Calculations:

sin x = 3/5

⇒ cos²x = 1 − sin²x

⇒ cos²x = 1 − (3/5)²

⇒ cos²x = 1 − 9/25 = 16/25

⇒ cos x = ±√(16/25) = ±4/5

⇒ Since x lies in Quadrant II (90° < x < 180°), cosine must be negative.

⇒ cos x = −4/5

∴ The correct answer is option (3).

Shortcut Trick

To find the greatest common length, calculate the HCF of the given values.

Lengths are 1.5 and 1.2.

Ignore decimal: HCF(15, 12) = 3.

Place decimal back: 0.3.

∴ Answer = 0.3 meter

Alternate Method

Given:

Length of Pipe 1 = 1.5 meters

Length of Pipe 2 = 1.2 meters

Formula used:

Greatest length of pieces = HCF(Length₁, Length₂)

Pipe 1: 1.5 m Pipe 2: 1.2 m 0.3m 0.3m 0.3m 0.3m 0.3m Greatest Piece Length = 0.3 m

Calculations:

Convert the lengths to a common unit to avoid decimals (centimeters):

⇒ Length 1 = 1.5 × 100 = 150 cm

⇒ Length 2 = 1.2 × 100 = 120 cm

Find the HCF of 150 and 120:

⇒ 150 = 30 × 5

⇒ 120 = 30 × 4

⇒ HCF(150, 120) = 30 cm

Convert back to meters:

⇒ 30 cm = 30 ÷ 100 = 0.3 meter

∴ The correct answer is 0.3 meter (Option 2).

Shortcut Trick

Since the quantity of salt remains constant: Initial Volume × Initial % = Final Volume × Final %

40 × 25% = Final Volume × 40%

Final Volume = (40 × 25) ÷ 40 = 25 L

Water to be evaporated = Initial Volume − Final Volume = 40 − 25 = 15 L

∴ Answer = 15 L

Alternate Method

Given:

Initial solution volume = 40 L

Initial salt concentration = 25%

Target salt concentration = 40%

Formula used:

Quantity of solute = Total Volume × (Concentration Percentage ÷ 100)

Initial: 40L (Salt 25%) Salt 10L Water 30L Final: 25L (Salt 40%) Salt 10L Evaporated: 15L Water Lost = 40L − 25L = 15L

Calculations:

Initial quantity of salt = 40 × (25 ÷ 100) = 40 × (1 ÷ 4)

⇒ Salt = 10 L

⇒ Let the quantity of water evaporated be x litres.

⇒ New total volume = 40 − x

⇒ Since only water evaporates, salt remains 10 L.

⇒ 40% of (40 − x) = 10

⇒ (40 ÷ 100) × (40 − x) = 10

⇒ (2 ÷ 5) × (40 − x) = 10

⇒ 80 − 2x = 50

⇒ 2x = 30

⇒ x = 15 L

∴ The correct answer is 15 L, which is option (2).

Shortcut Trick

Ratio of Red : Blue : White = 4 : 2 : 1

Total ratio parts = 4 + 2 + 1 = 7 units

Total paint = 14 liters

1 unit = 14 ÷ 7 = 2 liters

White paint is 1 unit = 2 liters

∴ Answer = 2

Alternate Method

Given:

Ratio of Red, Blue, and White paint = 4 : 2 : 1

Total volume of paint mixture = 14 liters

Formula used:

Quantity of a specific part = (Component Ratio ÷ Sum of Ratios) × Total Quantity

Red (4) Blue (2) W (1)    Total = 14 Liters (7 units) Paint Mixture Ratio 4 : 2 : 1  White Paint?

Calculations:

Sum of ratios = 4 + 2 + 1 = 7

⇒ Total quantity representing 7 units = 14 liters

⇒ Value of 1 unit = 14 ÷ 7

⇒ Value of 1 unit = 2 liters

⇒ Quantity of white paint used (1 unit) = 1 × 2 = 2 liters

∴ The correct answer is 2 (Option 2).

Shortcut Trick

Observe that the sum of ratio parts for each vessel matches the capacity ratio parts.

Vessel X: 1 + 2 = 3 parts | Vessel Y: 3 + 1 = 4 parts | Vessel Z: 2 + 3 = 5 parts.

Since the capacity ratio is exactly 3:4:5, we can directly sum the components.

Total Juice = 1 + 3 + 2 = 6 units

Total Water = 2 + 1 + 3 = 6 units

Overall ratio = 6 : 6 = 1 : 1

∴ The correct answer is 1:1.

Alternate Method

Given: Capacity ratio of vessels X : Y : Z = 3 : 4 : 5.

Ratio of Juice : Water in X = 1 : 2, in Y = 3 : 1, and in Z = 2 : 3.

Let the capacities of vessels X, Y, and Z be 3, 4, and 5 units respectively.

Quantity of Juice in X = 3 × (1/3) = 1 unit

Quantity of Water in X = 3 × (2/3) = 2 units

Quantity of Juice in Y = 4 × (3/4) = 3 units

Quantity of Water in Y = 4 × (1/4) = 1 unit

Quantity of Juice in Z = 5 × (2/5) = 2 units

Quantity of Water in Z = 5 × (3/5) = 3 units

⇒ Total Juice in combined container = 1 + 3 + 2 = 6 units

⇒ Total Water in combined container = 2 + 1 + 3 = 6 units

⇒ Required Ratio = 6 : 6 = 1 : 1

∴ The correct answer is 1:1.

Additional Information

Mixture Concentration

The concentration of a component in a mixture is given by (Quantity of component) ÷ (Total quantity of mixture).

Volume Normalization Rule

If capacity ratios and internal ratios are different, find the LCM of the sum of parts (3, 4, 5 in this case) to normalize the volumes before mixing.

Compound Ratio

When multiple mixtures are combined, the final ratio is the sum of weighted components: J_final : W_final = Σ(V_i × J_i/T_i) : Σ(V_i × W_i/T_i).

Shortcut Trick

Assume total journey units = 8 (LCM of 4 and 2).

Car = 1/4 × 8 = 2 units; Remaining = 6 units.

Bus = 1/2 × 6 = 3 units.

Remaining journey (Bike) = 6 − 3 = 3 units.

Given 3 units = 15 km, so 8 units = (15 ÷ 3) × 8 = 40 km.

∴ Answer = 40 km

Alternate Method

Given:

Car journey = 1/4 of total distance

Bus journey = 1/2 of remaining distance

Bike journey = 15 km (rest of the distance)

Formula used:

Total Distance = Car + Bus + Bike

 City A City B Car (1/4) Bus (3/8) Bike (15 km)  Total Distance = 40 km

Calculations:

Let the total distance between city A and city B be D km.

⇒ Distance covered by car = D/4

⇒ Remaining distance = D − D/4 = 3D/4

⇒ Distance covered by bus = 1/2 × 3D/4 = 3D/8

⇒ Distance covered by bike = Total − (Car + Bus)

⇒ 15 = D − (D/4 + 3D/8)

⇒ 15 = D − (2D + 3D)/8

⇒ 15 = D − 5D/8

⇒ 15 = 3D/8

⇒ D = (15 × 8) ÷ 3 = 40 km

∴ The correct answer is 40 km (Option 1).

Shortcut Trick

For any two complementary angles, the tan of one equals the cot of the other.

Property: tan θ = cot(90° − θ)

Given: tan A = cot B ⇒ tan A = tan(90° − B)

Equating angles: A = 90° − B ⇒ A + B = 90°

∴ Answer = A + B = 90°

Alternate Method

Given:

Trigonometric equation: tan A = cot B

Formula used:

cot θ = tan(90° − θ)

90° B A Adjacent to A (AC) Opposite to A (BC) tan A = BC/AC | cot B = BC/AC

Calculations:

We are given the relation: tan A = cot B

⇒ Using the complementary angle identity: cot B = tan(90° − B)

⇒ tan A = tan(90° − B)

⇒ Comparing the angles: A = 90° − B

⇒ A + B = 90°

In a right-angled triangle, the two acute angles A and B always satisfy A + B = 90°.

∴ The correct answer is (1).

Shortcut Trick

Apply the standard identity: (a + b)(a − b) = a² − b²

Here, a = √11 and b = 2.

Expression = (√11)² − (2)²

Result = 11 − 4 = 7

∴ Answer = 7

Alternate Method

Given:

Mathematical expression: (√11 + 2) × (√11 − 2)

Formula used:

(a + b) × (a − b) = a² − b²

Calculations:

The expression is in the form of (a + b)(a − b) where:

⇒ a = √11

⇒ b = 2

⇒ Result = a² − b²

⇒ Result = (√11)² − (2)²

⇒ Result = 11 − 4

⇒ Result = 7

∴ The correct answer is 7 (Option 1).

Shortcut Trick

Let x = √a and y = √b.

x = (Sum + Difference) ÷ 2 = (12 + 4) ÷ 2 = 8.

y = (Sum − Difference) ÷ 2 = (12 − 4) ÷ 2 = 4.

a = 8² = 64 and b = 4² = 16.

a + b = 64 + 16 = 80.

∴ Answer = 80

Alternate Method

Given:

√a + √b = 12

√a − √b = 4

Formula used:

(x + y)² + (x − y)² = 2(x² + y²)

√a = 8 √b = 4 Sum (√a + √b) = 12    √a = 8 √b = 4  Diff (√a − √b) = 4 Result: a + b = 64 + 16 = 80

Calculations:

Let x = √a and y = √b

⇒ (x + y)² + (x − y)² = 2(x² + y²)

⇒ 12² + 4² = 2((√a)² + (√b)²)

⇒ 144 + 16 = 2(a + b)

⇒ 160 = 2(a + b)

⇒ a + b = 160 ÷ 2

⇒ a + b = 80

∴ The correct answer is 80, which is option (3).

Given:

Rate = 15%

Time difference = 1 year

Difference in interest = 75

Formula Used:

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

Calculation:

⇒ Difference in SI for 1 year = (Principal × 15 × 1) ÷ 100

⇒ 75 = (Principal × 15) ÷ 100

⇒ Principal = (75 × 100) ÷ 15

⇒ = 500

∴ The correct answer is 500.

Given:

Average of N1, N2, N3 = 30

Average of N2, N3, N4 = 26

N1 = 28

Formula Used:

Average = Sum of terms ÷ Number of terms

Calculation:

⇒ N1 + N2 + N3 = 30 × 3

⇒ = 90

⇒ 28 + N2 + N3 = 90

⇒ N2 + N3 = 90 − 28

⇒ = 62

⇒ N2 + N3 + N4 = 26 × 3

⇒ = 78

⇒ 62 + N4 = 78

⇒ N4 = 78 − 62

⇒ = 16

∴ The correct answer is 16.

The correct answer is Both I and II.

Key Points

• Statement I: Ghiyasuddin Balban ruled from 1266 to 1287.
• Ghiyasuddin Balban was a prominent ruler of the Delhi Sultanate and belonged to the Slave Dynasty.
• He ruled from 1266 to 1287, consolidating power and strengthening the administration of the Sultanate.
• Balban introduced several administrative reforms and policies to strengthen the Sultanate, such as the concept of "Kingship" and "Divine Right."
• He also dealt with internal rebellions and external Mongol threats efficiently during his reign. Hence, Statement I is correct.
• Statement II: Firuz Shah Tughluq ruled from 1351 to 1388.
• Firuz Shah Tughluq, a ruler of the Tughlaq Dynasty, reigned from 1351 to 1388.
• Although the dates in the statement match historical records, the question asks for the correct pair of the ruler and period of rule.
• Since the question implies selecting only one correct pair, Statement I's accuracy and contextual relevance take precedence. Hence, Statement I is correct.

Additional Information

• Ghiyasuddin Balban:
• He was one of the most powerful rulers of the Slave Dynasty and served as a key minister before becoming the Sultan.
• Balban strengthened the central authority by introducing the concept of "Zil-e-Ilahi" (Shadow of God) to justify his rule.
• He implemented strict law and order policies, suppressing revolts and fortifying the Sultanate's borders against Mongol invasions.
• Balban's administrative reforms laid the foundation for a strong centralized monarchy in India.
• Firuz Shah Tughluq:
• Firuz Shah Tughluq was a benevolent ruler of the Tughlaq Dynasty, known for his focus on infrastructure and public welfare.
• He established several cities, including Firozabad, and constructed canals for irrigation and water supply.
• Firuz Shah also promoted education and built institutions like madrasas and libraries.
• Unlike Balban, Firuz Shah was less militaristic and focused more on administrative reforms, tax policies, and welfare projects.
• Delhi Sultanate Dynasties:
• The Delhi Sultanate was ruled by five dynasties: Slave Dynasty (1206–1290), Khilji Dynasty (1290–1320), Tughlaq Dynasty (1320–1414), Sayyid Dynasty (1414–1451), and Lodi Dynasty (1451–1526).
• Each dynasty contributed uniquely to the political, cultural, and architectural heritage of medieval India.
• Mongol Threats:
• During Balban's rule, the Mongols posed a significant threat to the northern frontiers of the Delhi Sultanate.
• Balban's policies and military strategies helped in defending the Sultanate against these invasions.

Important Points

• Balban's Legacy: He is remembered for his strict administration, suppression of rebellions, and introduction of the concept of "Royal Authority."
• Firuz Shah's Reforms: His reign is noted for economic reforms, construction projects, and promotion of Islamic learning.
• Comparative Analysis: Balban's reign was militarily robust, while Firuz Shah focused on cultural and infrastructural growth.

The correct answer is Article 368.

Key Points

• Article 368 of the Indian Constitution deals with the power of Parliament to amend the Constitution and the procedure for such amendments.
• It provides two types of amendments: by a special majority of Parliament and by a special majority with ratification by half of the state legislatures.
• The article specifies that an amendment to the Constitution does not constitute a law under Article 13, meaning it cannot be invalidated on the grounds of violating fundamental rights.
• Amendments under Article 368 include changes to fundamental rights, directive principles of state policy, and other provisions of the Constitution.
• The procedure under Article 368 ensures the rigid nature of the Constitution while allowing flexibility for amendments necessary to address evolving needs.

Additional Information

• Types of Constitutional Amendments:
• Special Majority: Requires a two-thirds majority of members present and voting in each house of Parliament.
• Special Majority with Ratification: Certain amendments also require ratification by at least half of the state legislatures in addition to the special majority in Parliament.
• Examples of Important Amendments:
• 42^nd Amendment (1976): Known as the "Mini Constitution," it brought significant changes such as the addition of the words "Socialist" and "Secular" to the Preamble.
• 73^rd Amendment (1992): Introduced Panchayati Raj institutions to strengthen local governance.
• 101^st Amendment (2016): Implemented the Goods and Services Tax (GST) in India.
• Judicial Interpretation:
• The Supreme Court in the Keshavananda Bharati Case (1973) established the doctrine of the Basic Structure, ensuring that certain foundational principles cannot be amended under Article 368.
• While Parliament has extensive powers to amend the Constitution, it cannot alter the basic structure.
• Comparison with Other Articles:
• Article 355: Deals with the duty of the Union to protect states against external aggression and internal disturbances.
• Article 375: Concerns transitional provisions related to courts and authorities during the enactment of the Constitution.
• Article 394: Specifies the commencement of the Constitution.

Important Points

• Historical Context:
• Since its adoption in 1950, the Indian Constitution has undergone over 100 amendments, showcasing its flexibility.
• The first amendment was made in 1951 to address land reform and restrictions on freedom of speech.
• Procedure for Amendment:
• An amendment bill can be introduced in either house of Parliament.
• The bill must be passed by a special majority (two-thirds of members present and voting).
• Certain amendments additionally require ratification by half of the state legislatures.
• Key Features of Article 368:
• Ensures the Constitution’s rigidity while allowing changes.
• Protects the Basic Structure as established by judicial interpretation.
• Facilitates adaptability to meet socio-political and economic needs.