SSC CHSL 2025 Tier-1 (Held On: 18 Nov, 2025 Shift 3) (Previous Year Paper)

The correct answer is '3' i.e. were unanimous in its decision .

Key Points

• The subject of the sentence is "The board", which is treated as a singular collective noun in standard English usage.
• Therefore, the verb used with it must also be singular to maintain subject-verb agreement.
• However, in the given sentence, the verb "were" is plural, which causes a grammatical error.
• The correct singular verb should be "was" instead of "were".

Correct sentence: The board, in a rare moment of complete agreement, was unanimous in its decision to fire the CEO, which came as a surprise.

Additional Information

• Collective Nouns:
• Collective nouns like "board," "team," "committee" are usually treated as singular in American English and take singular verbs.
• Example: The team is preparing for the big game.
• However, in British English, they are sometimes treated as plural if the focus is on the members of the group acting individually.
• Subject-Verb Agreement:
• It is crucial to ensure that the verb matches the subject in both number and form.
• Example: The committee has made its decision (singular).

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

Key Points

• The phrase "Despite of" is grammatically incorrect. The correct usage is simply "Despite".
• "Despite" is a preposition that does not require the addition of "of" to indicate contrast or opposition.
• In the given sentence, the word "Despite" should be used to introduce the contrast between the low score in the test and the ability to pass the course.

Correct sentence: Despite his low score in the test, he was able to pass the course.

Additional Information

• Common Usage of "Despite":
• Correct: Despite the rain, they went for a walk.
• Incorrect: Despite of the rain, they went for a walk.
• Other Words for Contrast:
• Although: Although he was tired, he finished his work.
• However: He wanted to go out; however, it was too late.

The correct answer is '3' i.e. into .

Key Points

• The preposition "into" is used to indicate movement or transition from one state or position to another. In this case, it indicates dividing something (students) into groups.
• The preposition "among" is used when distributing something between multiple entities, but it doesn’t fit here because we are dividing the students, not distributing something among them.
• The preposition "in" refers to a location or position and does not convey the idea of dividing.
• The preposition "between" is used when referring to two entities, but here the sentence refers to four groups, making it incorrect in this context.

Correct sentence: The teacher divided the students into four groups for the activity.

Additional Information

• Usage of "into":
• Example: The cake was cut into equal slices.
• Explanation: Indicates division or transformation.
• Usage of "among":
• Example: The prize was distributed among the participants.
• Explanation: Refers to distribution within a group.
• Usage of "in":
• Example: The students are sitting in the classroom.
• Explanation: Refers to a specific location or position.
• Usage of "between":
• Example: The debate was held between two candidates.
• Explanation: Refers to a relationship or comparison involving two entities.

The correct answer is '1' i.e. on .

Key Points

• The verb "reflect" is commonly followed by the preposition "on", which means to think carefully or deeply about something.
• In this context, the sentence discusses the poet contemplating or thinking deeply about the impermanence of beauty and the inevitability of decay. Therefore, "on" is the most appropriate preposition.
• The other options do not fit the context of the sentence:
• "over" suggests physical movement or position, which is not relevant here.
• "under" implies being beneath something, which also does not make sense in this context.
• "until" indicates time duration, which is unrelated to the act of reflection.

Correct sentence: The poet reflects on the impermanence of beauty and the inevitability of decay.

Additional Information

• Common Collocations with "Reflect":
• Reflect on: To think deeply about something. Example: She reflected on her past decisions.
• Reflect in: To show an image or representation. Example: The mountains were reflected in the lake.
• Reflect upon: Similar to "reflect on," used in a more formal context. Example: The speech gave him time to reflect upon his values.

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

Key Points

• The word Bellicose means demonstrating aggression or willingness to fight.
• The correct synonym of Bellicose is Warlike, which also refers to being combative or eager to engage in conflict.
• The other options do not match the meaning of the given word:
• Peaceful: Opposite in meaning to Bellicose.
• Amiable: Means friendly and pleasant, which is unrelated to aggression.
• Timid: Refers to being shy or lacking confidence, which is also opposite in meaning to Bellicose.

Correct Sentence: The most appropriate synonym of Bellicose is Warlike.

Additional Information

• Synonyms: Words with similar meanings.
• Example: Angry - Furious, Mad, Irritated.
• Antonyms: Words with opposite meanings.
• Example: Happy - Sad, Miserable, Upset.

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

Key Points

• The word INTEGRITY refers to the quality of being honest and having strong moral principles.
• It is synonymous with Honesty, which reflects uprightness and truthfulness in behavior or actions.
• The other options do not match the meaning of INTEGRITY:
• Corruption: Refers to dishonest or unethical conduct, opposite to integrity.
• Negligence: Refers to failure to take proper care, unrelated to moral uprightness.
• Greed: Refers to an excessive desire for wealth or power, contrary to moral principles.

Correct sentence: The most appropriate synonym of INTEGRITY is Honesty.

Additional Information

• Synonyms: Words that have a similar meaning to a given word.
• Example: Brave – Courageous
• Antonyms: Words that have an opposite meaning to a given word.
• Example: Honest – Dishonest

The correct answer is '3' i.e. In small, irregular amounts .

Key Points

• The idiom "in dribs and drabs" refers to something happening or arriving in small, irregular amounts rather than all at once or in a continuous flow.
• It conveys the idea of something being inconsistent or sporadic in quantity or frequency.
• For example, "The donations for the fundraiser came in dribs and drabs, making it difficult to meet the target quickly."

Correct meaning: The phrase "in dribs and drabs" means in small, irregular amounts.

Additional Information

• Incorrect options:
• Option 1: "In large quantities" is incorrect as the idiom specifically refers to small and irregular amounts.
• Option 2: "In a continuous flow" is incorrect because the meaning is opposite to the sporadic nature implied by the idiom.
• Option 4: "In an unorganized manner" is incorrect because the idiom does not necessarily imply disorganization, only irregularity in quantity or frequency.
• Tips for understanding idioms:
• Idioms often have figurative meanings that differ from their literal meanings.
• Understanding idioms requires familiarity with their usage in context.

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

Key Points

• The word Minute means something very small or tiny in size, quantity, or importance.
• The question asks for the antonym, which is a word opposite in meaning.
• The correct antonym of "Minute" is Enormous, which means something very large or great in size or extent.
• Other options:
• Tiny: Synonym of "Minute," meaning very small.
• Small: Synonym of "Minute," meaning not large in size.
• Insignificant: Related word but not an antonym; refers to something unimportant or trivial.

Correct sentence: The most appropriate antonym of the word Minute is Enormous.

Additional Information

• Understanding Antonyms:
• An antonym is a word that has a meaning opposite to that of another word.
• For example, the antonym of "happy" is "sad," and the antonym of "big" is "small."
• Synonyms vs Antonyms:
• Synonyms are words with similar meanings, while antonyms are words with opposite meanings.
• Example:
• Synonym of "Minute": Small, Tiny
• Antonym of "Minute": Enormous

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

Key Points

• The given word is "Extinguished," which means to put out a fire or light, or to bring something to an end.
• To find the antonym, we need to look for a word that means the opposite, i.e., something that starts or lights a fire.
• Among the options, "Ignited" is the correct antonym, as it means to set fire to something or to light something up.

Correct sentence: The antonym of "Extinguished" is "Ignited", which signifies the act of lighting or starting a fire..

Additional Information

• Option Analysis:
• Option 1: Ignited - Correct. Opposite of extinguished as it refers to lighting a fire.
• Option 2: Stopped - Incorrect. While "Stopped" could imply an ending, it does not specifically relate to fire or light.
• Option 3: Quenched - Incorrect. Similar in meaning to "Extinguished," as it refers to putting out a fire.
• Option 4: Burnt - Incorrect. Refers to something that has already been consumed by fire, not the act of lighting it.
• Understanding antonyms is crucial for vocabulary building and comprehension skills.

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

Key Points

• An Atheist is someone who denies or does not believe in the existence of God or any deities.
• On the other hand:
• Agnostic: Someone who believes that the existence of God is unknown or unknowable.
• Deist: A person who believes in the existence of God based on reason and nature but rejects organized religion.
• Pantheist: Someone who believes that God and the universe are identical or that God exists in all aspects of the universe.

Correct sentence: A person who denies the existence of God is called an Atheist.

Additional Information

• These terms are often confused due to overlapping ideas, but they represent distinct philosophical and theological positions.
• Atheism focuses specifically on the rejection of belief in God or gods, while Agnosticism addresses the uncertainty or lack of knowledge regarding God's existence.
• Understanding the nuances of these terms is crucial to using them accurately in discussions or writing.

The correct answer is '3' i.e. After her powerful lecture, the students had given the renowned professor a standing ovation .

Key Points

• The given sentence is in the passive voice, where the subject (the renowned professor) is the receiver of the action.
• To convert the sentence to the active voice, we need to make the doer of the action (students) the subject of the sentence.
• The original sentence is: The renowned professor had been given a standing ovation by the students after her powerful lecture.
• In the active voice, the sentence becomes: After her powerful lecture, the students had given the renowned professor a standing ovation.
• This rearranges the sentence to correctly follow the structure of an active voice sentence: Subject (students) + verb (had given) + object (the renowned professor).

Correct sentence: After her powerful lecture, the students had given the renowned professor a standing ovation.

Additional Information

• Active Voice:
• Structure: Subject + verb + object.
• Example: The students wrote an essay.
• Usage: The subject performs the action.
• Passive Voice:
• Structure: Object + verb (to be) + past participle + by + subject.
• Example: An essay was written by the students.
• Usage: The focus is on the action or the receiver of the action.

The correct answer is '1' i.e. He said that he would be working on the project .

Key Points

• The given sentence is an example of converting a sentence from direct speech to indirect speech.
• When converting to indirect speech, the tense of the verb in the reported clause usually changes according to the rules of sequence of tenses.
• In this case, the direct speech sentence uses "will," which changes to "would" in the indirect speech.
• The original sentence says, "He said, 'I will be working on the project.'" After conversion, it becomes, "He said that he would be working on the project."

Correct sentence: He said that he would be working on the project.

Additional Information

• Rules for Tense Changes in Indirect Speech:
• Present Simple → Past Simple
• Present Continuous → Past Continuous
• Will → Would
• Can → Could
• Example:
• Direct: She said, "I am reading a book."
• Indirect: She said that she was reading a book.

The correct answer is '3' i.e. He seegued into a completely different subject halfway through. .

Key Points

• The word "segue" is a verb that means to transition smoothly from one topic or section to another.
• In the sentence provided in option 3, the word "seegued" is misspelled. The correct spelling is "segued".
• This makes option 3 the sentence containing the misspelled word.

Correct sentence: He segued into a completely different subject halfway through.

Additional Information

• Common Context for "Segue":
• The word is often used in speeches, presentations, and conversations to describe a smooth transition.
• Example: The speaker seamlessly segued from one topic to another.
• Other Forms:
• Present tense: segue
• Past tense: segued
• Continuous tense: segueing

The correct answer is '2' i.e. He didn't want to embarrass himself at the start of the new millenium. .

Key Points

• The word "millennium" is misspelled in option 2 as "millenium" (missing one 'n').
• The correct spelling of the word is "millennium", which has two 'n's.
• All other options have no spelling errors, making option 2 the correct choice.

Correct sentence: He didn't want to embarrass himself at the start of the new millennium.

Additional Information

• Commonly Confused Words:
• Millennium: Correct spelling for a period of 1,000 years.
• Millenium: Incorrect spelling, often due to the omission of one 'n'.
• Tips to Avoid Spelling Errors:
• Break the word into syllables (mil-len-ni-um) to help remember the double 'n'.
• Practice writing commonly misspelled words to reinforce correct spelling.

The correct answer is '4' i.e. All of the water in the bottles is over and you have to refill it .

Key Points

• The subject of the sentence is "all the water", which is singular because the word "water" is an uncountable noun.
• When the subject is singular, the verb should also be singular. Therefore, the correct verb form is "is", not "are".
• The pronoun "it" correctly refers back to the singular noun "water," as "water" is treated as a single entity.
• The correct sentence ensures proper subject-verb agreement and maintains grammatical accuracy.

Correct sentence: All of the water in the bottles is over and you have to refill it.

Additional Information

• Common Mistakes:
• Using "are" instead of "is" for uncountable nouns like "water."
• Referring back to an uncountable noun with a plural pronoun like "them" instead of "it."
• Examples for clarity:
• Correct: The milk in the fridge is spoiled.
• Incorrect: The milk in the fridge are spoiled.
• Correct: All of the rice is cooked and ready to serve.
• Incorrect: All of the rice are cooked and ready to serve.

The correct answer is '3' i.e. Three hours is the duration of the exam .

Key Points

• The subject of the sentence is "Three hours", which refers to a specific duration of time.
• In English, when a unit of time, distance, or money is used as a single entity or measure, it is treated as singular, and the verb must agree accordingly.
• Hence, the correct verb to use with "Three hours" in this context is "is" (singular form).

Correct sentence: Three hours is the duration of the exam.

Additional Information

• Subject-Verb Agreement:
• When a subject refers to a collective unit, such as "time, distance, or money," it is considered singular, regardless of plurality in its form.
• Example: Ten dollars is enough for lunch.
• Common Mistake:
• It is incorrect to use a plural verb like "are" or "were" with time expressions treated as singular units.
• Example of incorrect usage: "Three hours are the duration of the exam."

The correct answer is '1' i.e. The bridge will have been built by them by next year .

Key Points

• The given sentence is in the future perfect tense, which describes actions that will be completed before a specific point in the future.
• The passive voice transformation of a sentence in the future perfect tense follows the structure: Object + will have been + past participle + (by + subject).
• Here, the active sentence is: "They will have built the bridge by next year."
• In the passive voice:
• The object of the active sentence, "the bridge," becomes the subject of the passive sentence.
• The verb "will have built" changes to "will have been built" to indicate the passive voice.
• The subject of the active sentence, "they," is included in the passive sentence with "by them."

Correct sentence: The bridge will have been built by them by next year.

Additional Information

• Active voice to passive voice transformation rules:

• Identify the object of the active sentence and make it the subject of the passive sentence.

• Change the verb form according to the passive voice structure, keeping the tense intact.

• Include the subject of the active sentence after the verb, preceded by "by," if necessary.

• Examples of future perfect tense transformation:

• Active: She will have completed the project by tomorrow.
  Passive: The project will have been completed by her by tomorrow.

• Active: They will have finished the homework.
  Passive: The homework will have been finished by them.

The correct answer is '2' i.e. Colorful decorations are being made by the children for the upcoming school festival.

Key Points

• The given sentence is in the present continuous tense, as indicated by the use of "are making."
• To convert a sentence from active to passive voice in the present continuous tense:
• The structure changes to: Object + is/are/am + being + past participle + by + subject.
• In the given sentence:
• Active voice: The children are making colorful decorations for the upcoming school festival.
• Object: Colorful decorations
• Verb: are making → are being made (in passive voice)
• Subject: The children → by the children

Correct sentence: Colorful decorations are being made by the children for the upcoming school festival.

Additional Information

• Passive voice structure for tenses:
• Present Simple: Object + is/are/am + past participle
• Example: The letter is written by John.
• Present Continuous: Object + is/are/am + being + past participle
• Example: The book is being read by Mary.
• Present Perfect: Object + has/have + been + past participle
• Example: The homework has been completed by the students.

The correct answer is '2' i.e. "Although the governments have been discussing the issue for years, they haven't yet implemented any effective measures, and I believe that time is running out," the environmentalist said.

Key Points

• The sentence given uses reported speech, which requires accuracy in terms of tense, pronouns, and structure.
• Since the environmentalist is quoted directly, the sentence requires appropriate use of present perfect progressive tense to indicate an action that started in the past and is still ongoing.
• Option 2 correctly employs the present perfect progressive tense ("have been discussing") to reflect the ongoing nature of the governments' discussion and aligns well with the quote format.
• Additionally, the phrase "haven't yet implemented" is grammatically correct and indicates that no effective measures have been taken yet.

Correct sentence: "Although the governments have been discussing the issue for years, they haven't yet implemented any effective measures, and I believe that time is running out," the environmentalist said.

Additional Information

• Why not Option 1?
• Option 1 uses "were discussing" (past continuous), which is incorrect because it doesn’t align with the ongoing nature of the governments' actions.
• Why not Option 3?
• Option 3 uses "had been discussing" (past perfect progressive), which is incorrect because it implies the action of discussing was completed before another past action.
• Why not Option 4?
• Option 4 incorrectly mixes tenses by combining "had been discussing" with "have not yet implemented," leading to inconsistency in tense usage.

The correct answer is Option 2.

Key Points

• The phrase begins with "allowing," which is a present participle (a verb ending in -ing that acts as an adjective).
• In this sentence, the phrase "allowing remote control..." modifies the noun phrase "Smart lighting systems." It provides additional information about what these systems do or what their characteristics are.
• Why other options are incorrect:
• Option 1 (Gerund phrase): A gerund also ends in -ing but functions as a noun (e.g., "Allowing remote control is a great feature"). In the passage, it is describing a noun, not acting as one.
• Option 3 (Infinitive phrase): An infinitive phrase starts with "to" plus a verb (e.g., "to allow").
• Option 4 (Absolute phrase): An absolute phrase modifies the entire sentence and usually consists of a noun followed by a participle (e.g., "The technology allowing remote control, users felt empowered"). This phrase is specifically tied to the subject "Smart lighting systems."

Therefore, the correct answer is 2.

Analytical Insight: In competitive exams, distinguishing between a Gerund and a Present Participle is a common trap. If the '-ing' word describes a noun (adjective function), it's a Participle. If it is the subject or object of a sentence (noun function), it's a Gerund.

Additional Information

• Luminosity: The quality of being bright or emitting light.
• Incandescent: Emitting light as a result of being heated.
• Convergence: The process of moving toward union or uniformity.
• Contemporary: Belonging to or occurring in the present.

The correct answer is Option 1.

Key Points

• The phrase "has evolved" follows the structure of the Present Perfect Tense.
• The formula for Present Perfect is: Subject + Has/Have + Past Participle (V3).
• Subject: lighting
• Auxiliary Verb: has
• Past Participle: evolved
• The Present Perfect is used here because the action (evolution) started in the past and has a connection to the present—lighting is currently in this "converged" state.
• Why other options are incorrect:
• Option 2 (Past perfect): This would use "had evolved," indicating an action completed before another past action.
• Option 3 (Present continuous): This would use "is evolving," indicating an action currently in progress.
• Option 4 (Simple present): This would use "evolves," indicating a general fact or habit.

Therefore, the correct answer is 1.

Analytical Insight: In competitive exams, identifying tenses often requires looking for the specific auxiliary verb. Whenever you see "has/have" paired with a V3 verb, it is a guaranteed indicator of the Present Perfect family.

Additional Information

• Convergence: The state of separate elements joining or coming together.
• Sustainability: The ability to be maintained at a certain rate or level, often regarding the environment.
• Indispensable: Absolutely necessary.
• Facet: A particular aspect or feature of something.

The correct answer is Option 2.

Key Points

• In the context of the passage, "luminosity" is used to describe the quality of early light sources like torches and oil lamps. The text states they were "limited in luminosity" but still "extended productive hours beyond daylight."
• The root word is "lumen" (Latin for light). In physics and general English, luminosity refers to the amount of light emitted by an object; hence, brightness is the closest synonym.
• Why other options are incorrect:
• Option 1 (Heat production): While early lamps did produce heat, the passage is discussing their function as lighting tools.
• Option 3 (Lifespan): The text uses the word "longevity" later on to describe how long a light source lasts (specifically regarding LEDs).
• Option 4 (Complexity): The passage describes early sources as "rudimentary" (simple), not complex.

Therefore, the correct answer is 2.

Analytical Insight: In competitive exams, vocabulary questions often use words that share a "domain." Heat, brightness, and lifespan are all related to lightbulbs, but you must look at the etymology (Lumen = Light) to pick the specific meaning.

Additional Information

• Rudimentary: Involving or limited to basic principles; primitive.
• Heralded: Signaled the appearance of; ushered in.
• Albeit: Though; even though.
• Indispensable: Absolutely necessary; something one cannot do without.

The correct answer is Option 2.

Key Points

• In the context of the sentence, "heralded" is used to describe the impact of the incandescent bulb: it "heralded a transformative era."
• To herald something means to be a sign that it is about to happen or to announce its arrival. In this historical context, the invention of the bulb signified the beginning of a major shift in how humans lived.
• Why other options are incorrect:
• Option 1 (Criticised): The passage treats the invention of the bulb as a positive "transformative" event, not a negative one to be attacked.
• Option 3 (Hidden): An invention that changes the world is the opposite of something hidden; it is highly visible and impactful.
• Option 4 (Delayed): The text suggests the invention started the era immediately, rather than pushing it back or slowing it down.

Therefore, the correct answer is 2.

Analytical Insight: In competitive exams, the word "herald" often appears in historical or scientific passages. It acts as a "transition" verb, moving the narrative from an old state to a new, often better, one.

Additional Information

• Pioneered: To be among the first to explore or develop a new method or area.
• Transformative: Causing a marked change in someone or something.
• Albeit: A conjunction meaning "even though" or "notwithstanding."
• Advent: The arrival of a notable person, thing, or event.

The correct answer is Option 4.

Key Points

• The passage explicitly identifies Light Emitting Diodes (LEDs) as the innovation that "combine minimal energy consumption with exceptional longevity."
• In this context, "longevity" is a direct synonym for "lifespan," confirming that Option 4 is the correct choice based on the text.
• Why other options are incorrect:
• Option 1 (Incandescent bulb): These are described as the first transformative era but are not noted for energy efficiency or long lifespans (they rely on heated filaments).
• Option 2 (Fluorescent light): While more efficient than incandescent bulbs, the passage does not attribute the specific combination of "minimal energy" and "exceptional longevity" to them.
• Option 3 (Halogen lamp): These are "prized for their compact size and enhanced brightness," but not specifically for their energy savings or lifespan in this text.

Therefore, the correct answer is 4.

Analytical Insight: In competitive exams, questions often use synonyms to test your comprehension. Recognizing that "longevity" in the passage refers to "lifespan" in the question is the key to identifying the correct data point.

Additional Information

• Longevity: Long life; the length of time that something lasts.
• Albeit: Although; even though.
• Luminosity: The state or quality of being bright or luminous.
• Advent: The arrival of a notable person, thing, or event.

The correct answer is '4' i.e. affect, effect .

Key Points

• The given sentence requires two homonyms (words that sound similar but have different meanings) to fill the blanks appropriately.
• The first blank refers to the impact or influence of the medication, which is denoted by the verb "affect."
• The second blank refers to the result or outcome of the medication, which is denoted by the noun "effect."
• Therefore, the correct pair of homonyms to fit the context is "affect" and "effect."

Correct sentence: The new medication did not affect the patient’s symptoms as expected, so the doctor questioned its overall effect.

Additional Information

• Difference between "Affect" and "Effect":
• Affect (Verb): Refers to the action of influencing something. Example: The weather affects my mood.
• Effect (Noun): Refers to the result or outcome of an action. Example: The effect of the medication was immediate.
• Use "affect" when describing an action or influence, and "effect" when describing a result or outcome.

The logic followed here is:

Logic: All numbers are perfect squares except 30.

4 → 2²

9 → 32

16 → 42

25 → 52

30 → Not a perfect square

36 → 62

Thus, 30 is the odd one out.

Hence, the correct answer is "Option 3".

Given:

Pipe P fills tank in 12 hours

Pipe Q empties tank in 18 hours

Formula used:

LCM = Total work

Efficiency = Work / Time

Calculation:

⇒ LCM of 12 and 18 = 36 (Total work)

⇒ P efficiency = 36 / 12 = 3 units/hour

⇒ Q efficiency = 36 / 18 = 2 units/hour (emptying)

⇒ Net efficiency = 3 − 2 = 1 unit/hour

⇒ Time = 36 / 1 = 36 hours

∴ Tank will be full in 36 hours

Given:

x = 8

y = 3

Formula used:

Expression: 3x - 2y + 5

Calculation:

Expression = 3x - 2y + 5

⇒ 3(8) - 2(3) + 5

⇒ 24 - 6 + 5

⇒ 23

∴ The correct answer is option 2 (23).

Shortcut Trick

Ratio of Cost Price (CP) to Selling Price (SP) = 500 : 650 = 10 : 13.

Profit units = 13 − 10 = 3 units.

Profit Percentage = (Profit Units / CP Units) × 100 = (3 / 10) × 100 = 30%.

∴ The correct answer is 30%.

Alternate Method

Given:

Cost Price (CP) of the item = ₹500

Selling Price (SP) of the item = ₹650

Formula Used:

Profit = Selling Price − Cost Price

Profit Percentage = (Profit / Cost Price) × 100

Calculations:

⇒ Profit = ₹650 − ₹500

⇒ Profit = ₹150

⇒ Profit % = (150 / 500) × 100

⇒ Profit % = 150 / 5

⇒ Profit % = 30%

∴ The correct answer is 30%.

Additional Information

Loss Percentage

When SP is less than CP, Loss % = [(CP − SP) / CP] × 100.

Selling Price Formula

To find SP when CP and Profit % are known: SP = [CP × (100 + Profit %)] / 100.

Cost Price Formula

To find CP when SP and Profit % are known: CP = [SP × 100] / (100 + Profit %).

Given:

Row 1 lamps = 4

Increment per row = 3

Number of rows = 8

Formula used:

Lamps in nth row = First row lamps + (n - 1) × Increment per row

Calculation:

Lamps in 8th row = 4 + (8 - 1) × 3

⇒ Lamps in 8th row = 4 + 7 × 3

⇒ Lamps in 8th row = 4 + 21

⇒ Lamps in 8th row = 25

∴ The correct answer is option 2 (25).

Given:

Milk: Water = 5:1

Milk = 30 liters

Formula used:

Total mixture = Milk + Water

From the ratio, Milk/Water = 5/1

⇒ Water = Milk/5

Calculation:

Water = 30 ÷ 5

⇒ Water = 6 liters

Total mixture = Milk + Water

⇒ Total mixture = 30 + 6

⇒ Total mixture = 36 liters

∴ The correct answer is option 2 (36 liters).

Given:

A + B = 12 days

A = 20 days

Calculation:

Let total work = LCM of 12 and 20 = 60

⇒ (A + B) efficiency = 60 / 12 = 5 units/day

⇒ A efficiency = 60 / 20 = 3 units/day

⇒ B efficiency = 5 − 3 = 2 units/day

⇒ Time taken by B = 60 / 2 = 30 days

∴ B alone will complete the work in 30 days

Given: A man starts walking from point A and walks 4 km east, then 3 km south, and finally 4 km west.

Thus, the person is 3 km from point A.

Hence, the correct answer is "Option 3".

Given: A person walks 7 km east, then 5 km north, and finally 7 km west.

Thus, the person is 5 km far from his starting point.

Hence, the correct answer is "Option 1".

The position and positional values or English Alphabets are:

Given: D, G, K, P, ?

The logic followed here is:

Thus, V can replace question mark.

Hence, the correct answer is "Option 1".

BODMAS Rule:

Given equation: 2 x 4 + 5 - 3 = 15

Let's check each option one by one.

1. Interchange 4 and 5

Given equation: 2 x 4 + 5 - 3 = 15

After Interchanging 4 and 5, the equation becomes:

⇒ 2 x 5 + 4 - 3 = 15

⇒ 10 + 4 - 3 = 15

⇒ 14 - 3 = 15

⇒ 11 ≠ 15

⇒ LHS ≠ RHS

2. Interchange x and +

Given equation: 2 x 4 + 5 - 3 = 15

After Interchanging x and +, the equation becomes:

⇒ 2 + 4 x 5 - 3 = 15

⇒ 2 + 20 - 3 = 15

⇒ 22 - 3 = 15

⇒ 19 ≠ 15

⇒ LHS ≠ RHS

3. Interchange 5 and 3

Given equation: 2 x 4 + 5 - 3 = 15

After Interchanging 4 and 5, the equation becomes:

⇒ 2 x 4 + 3 - 5 = 15

⇒ 8 + 3 - 5 = 15

⇒ 11 - 5 = 15

⇒ 6 ≠ 15

⇒ LHS ≠ RHS

4. Interchange 2 and 3

Given equation: 2 x 4 + 5 - 3 = 15

After Interchanging 4 and 5, the equation becomes:

⇒ 3 x 4 + 5 - 2 = 15

⇒ 12 + 5 - 2 = 15

⇒ 17 - 2 = 15

⇒ 15 = 15

⇒ LHS = RHS

Hence, the correct answer is "Option 4".

A palindromic number reads the same forward and backward.

Checking each option:

1. 1991 → same both ways
2. 13431 → same both ways 
3. 3983 → reverse is 3893 (not same)
4. 12321 → same both ways 

Thus, 3983 is not a palindromic number.

Hence, the correct answer is "Option 3".

The position and positional values or English Alphabets are:

Given: B3, D6, F9, H12, ?

The logic followed here is:

Thus, J15 will replace the question mark (?) in the given series.

Hence, the correct answer is "Option 1".

The position and positional values or English Alphabets are:

Given: Z1, Y4, X9, W16, ?

The logic followed here is:

Thus, V25 will replace the question mark (?) in the given series.

Hence, the correct answer is "Option 1".

The position and positional values or English Alphabets are:

Given: A1, C1, E2, G3, 15, ?

The logic followed here is:

Logic: Letters increase by +2 positions and numbers follow a Fibonacci pattern.

Letter series:

Numbers: 1, 1, 2, 3, 5

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8

Thus, the next term is: K8.

Hence, the correct answer is "Option 1".

Given: RETAIN is coded as 24, BESIDES is coded as 35 and PROCEDURE is coded as 63.

The logic followed here is:

Logic: Number of letters in the word × (Number of letters in the word - 2) = Code of the Word

RETAIN → 6 letters → 6 × (6 - 2) = 6 × 4 = 24

BESIDES → 7 letters → 5 × (7 - 2) = 7 × 5 = 35

PROCEDURE → 9 letters → 9 × (9 - 2) = 9 × 7 = 63

Similarly,

GIVEN → 5 letters → 5 × (5 - 2) = 5 × 3 = 15

Thus, 15 is the code for GIVEN.

Hence, the correct answer is "Option 2".

Family Chart:

Decoding the Symbols:

1.T%K$B#C#V

It means: T is the husband of K, K is the sister of B, B is the father of C, C is the father of V.

K is not the Paternal Aunt of V.

2. T%B$K#C%V 

It means: T is the husband of B, B is the sister of K, K is the father of C, C is the husband of V.

K is not the Paternal Aunt of V.

3. T%K$C#V$B

It means: T is the husband of K, K is the sister of C, C is the father of V, V is the sister of B.

K is the Paternal Aunt of V.

4. T#K$B\%C$V

It means: T is the father of K, K is the sister of B, B is the husband of C, C is the sister of V.

K is not the Paternal Aunt of V.

Hence, the correct answer is "Option 3".

Given date: 17 September, 2012

Now,

Till 2012 → 2000 + 12

In 2000 Years the odd day is 0,

From 2001 to 2011 (11 years):

In 11 Years (2 Leap Years and 9 Ordinary Years):

2 × 2 + 9 × 1 = 4 + 9 = 13 odd days

⇒ 13 odd days.

From 1st Jan 2012 to 17th Sept 2012:

(2012 is a leap year)

⇒ 31 (Jan) + 29 (Feb) + 31 (Mar) + 30 (Apr) + 31 (May) + 30 (June) + 31 (July) + 31 (Aug) + 17 (Sept)

= 31 + 29 + 31 + 30 + 31 + 30 + 31 + 31 + 17 = 261 days

Total odd days → (261 + 13) ÷ 7

= 274 ÷ 7

= 39 weeks and 1 odd days.

→ 1 represents Monday.

So, 17 September, 2012 is Monday.

Hence, the correct answer is "Option 4".

Thus, option 1 is exactly the same as the one given.

Hence, the correct answer is "Option 1".

Thus, option 1 is exactly the same as the one given.

Hence, the correct answer is "Option 1".

Thus, option 3 is exactly the same as the one given.

Hence, the correct answer is "Option 3".

Given: 100, 90, 80, 70, ?

The logic followed here is:

Thus, 60 comes next in the series.

Hence, the correct answer is "Option 1".

The logic followed here is:

Thus, 27 comes next in the series.

Hence, the correct answer is "Option 1".

The logic followed here is:

Column 1: (2 × 4 × 5) − 1 = 40 − 1 = 39

Column 2: (3 × 3 × 6) − 1 = 54 − 1 = 53

Similarly

Column 3: (7 × 2 × 3) − 1 = 42 − 1 = 41

Thus, 41 can be placed at the sign of question mark.

Hence, the correct answer is "Option 1".

The logic followed here is:

Column 1: (4 × 5 × 6) × 10 = 120 × 10 = 1200

Column 2: (7 × 8 × 5) × 10 = 280 × 10 = 2800

Similarly,

Column 3: (4 × 4 × 8) × 10 = 128 × 10 = 1280

Thus, 1280 can be placed at the sign of question mark (?).

Hence, the correct answer is "Option 1".

Given:

x is irrational

y is irrational

Formula Used:

Sum of two irrational numbers may be rational or irrational

Calculation:

⇒ Let x = √2

⇒ Let y = -√2

⇒ x + y = √2 + ( -√2 ) = 0

⇒ 0 is rational

⇒ Let x = √2

⇒ Let y = √3

⇒ x + y = √2 + √3

⇒ √2 + √3 is irrational

∴ The correct answer is may be rational or irrational.

Given:

AB = 7

BC = 24

AC = 25

Formula Used:

In right triangle: sinθ = Perpendicular ÷ Hypotenuse

tanθ = Perpendicular ÷ Base

cotθ = Base ÷ Perpendicular

Calculation:

⇒ 7² + 24² = 49 + 576 = 625 = 25²

⇒ Triangle is right-angled with hypotenuse = 25

⇒ For angle C: opposite = AB = 7, adjacent = BC = 24

⇒ tanC = 7 ÷ 24

⇒ sinC = 7 ÷ 25

⇒ For angle A: opposite = BC = 24, adjacent = AB = 7

⇒ cotA = 7 ÷ 24

⇒ tanC + sinC + 2cotA = 7 ÷ 24 + 7 ÷ 25 + 2 × 7 ÷ 24

⇒ = 7 ÷ 24 + 7 ÷ 25 + 14 ÷ 24

⇒ = 21 ÷ 24 + 7 ÷ 25

⇒ = 7 ÷ 8 + 7 ÷ 25

⇒ = (175 + 56) ÷ 200

⇒ = 231 ÷ 200

⇒ 1.155

∴ The correct answer is 1.155.

Given:

Sonu + Monu time = 30

Sonu efficiency = 80% of Monu

Required work = 40%

Formula Used:

Efficiency ∝ 1 ÷ Time

Work = Efficiency × Time

Calculation:

⇒ Let Monu efficiency = 5x

⇒ Sonu efficiency = 4x

⇒ Combined efficiency = 9x

⇒ 9x = 1 ÷ 30

⇒ x = 1 ÷ 270

⇒ Sonu efficiency = 4x = 4 ÷ 270 = 2 ÷ 135

⇒ Time taken by Sonu for full work = 1 ÷ (2 ÷ 135) = 135 ÷ 2

⇒ Time for 40% work = 135 ÷ 2 × 40 ÷ 100

⇒ Time = 135 ÷ 2 × 2 ÷ 5

⇒ Time = 135 ÷ 5

⇒ Time = 27

∴ The correct answer is 27.

Given:

Angle at center = 90

Chord length = 8

Formula Used:

Chord length = 2 × Radius × sin(θ ÷ 2)

Calculation:

⇒ 8 = 2 × r × sin(90 ÷ 2)

⇒ 8 = 2 × r × sin45

⇒ sin45 = 1 ÷ √2

⇒ 8 = 2 × r × 1 ÷ √2

⇒ 8 = √2 × r

⇒ r = 8 ÷ √2

⇒ r = 8√2 ÷ 2

⇒ r = 4√2

∴ The correct answer is 4√2.

Given:

Radius = 13

Distance from center = 5

Formula Used:

Chord length = 2 × √(Radius² - Distance²)

Calculation:

⇒ Chord length = 2 × √(13² - 5²)

⇒ = 2 × √(169 - 25)

⇒ = 2 × √144

⇒ = 2 × 12

⇒ = 24

∴ The correct answer is 24.

Given:

Angle at center = 120°

Formula Used:

Angle at circumference = (1 ÷ 2) × Angle at center

Angle between tangent and chord = Angle in opposite arc

Calculation:

⇒ Angle at circumference = (1 ÷ 2) × 120 = 60°

⇒ Angle between tangent and chord = 60°

∴ The correct answer is 60°.

Given:

CSA : TSA = 7 : 10

Volume = 12672 cm³

Formula Used:

CSA of cylinder = 2 × π × r × h

TSA of cylinder = 2 × π × r × (h + r)

Volume = π × r² × h

Calculation:

⇒ (2 × π × r × h) ÷ [2 × π × r × (h + r)] = 7 ÷ 10

⇒ h ÷ (h + r) = 7 ÷ 10

⇒ 10h = 7h + 7r

⇒ 3h = 7r

⇒ h = (7 ÷ 3)r

⇒ Volume = π × r² × (7r ÷ 3)

⇒ 12672 = (7 ÷ 3) × π × r³

⇒ Using π = 22 ÷ 7

⇒ 12672 = (22 ÷ 3) × r³

⇒ r³ = (12672 × 3) ÷ 22 = 1728

⇒ r = 12

⇒ h = (7 ÷ 3) × 12 = 28

⇒ CSA = 2 × (22 ÷ 7) × 12 × 28

⇒ CSA = 2112 cm²

∴ The correct answer is 2112 cm².

Given:

PQ = QR + 5

PQ = PR + 2

Perimeter = 32 cm

Formula Used:

Perimeter of triangle = PQ + QR + PR

Calculation:

⇒ QR = PQ − 5

⇒ PR = PQ − 2

⇒ Perimeter = PQ + (PQ − 5) + (PQ − 2)

⇒ 32 = 3PQ − 7

⇒ 3PQ = 39

⇒ PQ = 13

⇒ PR = 13 − 2 = 11

∴ The correct answer is 11.

Given:

Rate = 5%

Time for A = 4 years

Time for B = 6 years

B's investment = A − 12000

Formula Used:

Simple Interest = (P × R × T) ÷ 100

Calculation:

⇒ (A × 5 × 4) ÷ 100 = [(A − 12000) × 5 × 6] ÷ 100

⇒ A × 20 = (A − 12000) × 30

⇒ 20A = 30A − 360000

⇒ 10A = 360000

⇒ A = 36000

∴ The correct answer is 36000.

Given:

P investment = 50000

Q investment = 60000

R investment = 70000

Total profit = 24000

Formula Used:

Profit share ∝ Investment

Individual share = (Individual investment ÷ Total investment) × Total profit

Calculation:

⇒ Total investment = 50000 + 60000 + 70000 = 180000

⇒ Q's share = (60000 ÷ 180000) × 24000

⇒ Q's share = (1 ÷ 3) × 24000

⇒ Q's share = 8000

∴ The correct answer is 8000.

Given:

Ratio = 5 : 8

New ratio = 11 : 17

Formula Used:

Numbers = 5x and 8x

Ratio = (a ÷ b)

Calculation:

⇒ (5x + 12) ÷ (8x + 12) = 11 ÷ 17

⇒ 17(5x + 12) = 11(8x + 12)

⇒ 85x + 204 = 88x + 132

⇒ 204 − 132 = 88x − 85x

⇒ 72 = 3x

⇒ x = 24

⇒ Numbers = 5x = 120 and 8x = 192

⇒ Sum = 120 + 192 = 312

∴ The correct answer is 312.

Given:

Number = 1812

Divisors = 7, 11, 14

Formula Used:

LCM of numbers

Required number = Next multiple of LCM − Given number

Calculation:

⇒ LCM of 7, 11, 14 = 154

⇒ 1812 ÷ 154 = 11 remainder 118

⇒ Required addition = 154 − 118 = 36

∴ The correct answer is 36.

Given:

Sum = 84

HCF = 12

LCM : HCF = 12 : 1

Formula Used:

Product of two numbers = HCF × LCM

Numbers = HCF × m and HCF × n where gcd(m, n) = 1

Calculation:

⇒ LCM = 12 × 12 = 144

⇒ Product = 12 × 144 = 1728

⇒ Let numbers = 12m and 12n

⇒ Sum = 12(m + n) = 84

⇒ m + n = 7

⇒ mn = (Product) ÷ 12² = 1728 ÷ 144 = 12

⇒ m, n = 3 and 4

⇒ Numbers = 12 × 3 = 36 and 12 × 4 = 48

∴ The correct answer is 36 and 48.

Shortcut Trick

If every number in a data set is increased, decreased, multiplied, or divided by a constant k, the average of the set changes in the same way.

New Average = Old Average − Decrease Value

New Average = 45 − 7 = 38

∴ The correct answer is 38.

Alternate Method

Given:

Total observations = 20

Original Average = 45

Constant decrease (k) = 7

⇒ Total Sum of 20 numbers = 20 × 45 = 900

⇒ Total reduction in sum = 20 × 7 = 140

⇒ New Total Sum = 900 − 140 = 760

⇒ New Average = New Sum ÷ Total numbers

⇒ New Average = 760 ÷ 20 = 38

∴ The correct answer is 38.

Additional Information

Arithmetic Mean Properties

If every value in a set is multiplied by a constant x, the average also becomes x times the original average.

Summation Formula

The Sum of all observations is calculated as Average × Number of items.

Effect of Addition

If each observation is increased by k, the new average is Original Average + k.

Shortcut Trick

Excess contribution by the new employee = 50,000 − 20,000 = ₹30,000.

This excess is distributed to increase the average of everyone by ₹500.

Total employees (after join) = 30,000 ÷ 500 = 60.

Original employees = 60 − 1 = 59.

∴ The correct answer is 59.

Alternate Method

Given: Original average = ₹20,000 | New salary = ₹50,000 | Increase in average = ₹500.

Formula Used: Total Sum = Average × Number of items.

Let n be the original number of employees.

⇒ Total salary initially = 20,000 × n

⇒ New total salary = 20,000n + 50,000

⇒ New average = 20,000 + 500 = 20,500

⇒ (20,000n + 50,000) ÷ (n + 1) = 20,500

⇒ 20,000n + 50,000 = 20,500(n + 1)

⇒ 20,000n + 50,000 = 20,500n + 20,500

⇒ 20,500n − 20,000n = 50,000 − 20,500

⇒ 500n = 29,500

⇒ n = 29,500 ÷ 500 = 59

∴ The correct answer is 59.

Additional Information

Inclusion Formula

Value of new person = Old Average + (Total count × Increase in Average).

Weighted Average

Combined Average = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂), where n is count and a is average.

Deviation Method

Sum of deviations from the average is always zero. Net gain by new person = Net loss distributed among others.

Given:

B = 100

A is 50% more than B

C is 30% less than (A + B)

Formula Used:

Percentage increase = (Increase ÷ Original) × 100

Percentage decrease = (Decrease ÷ Original) × 100

Percentage = (Part ÷ Whole) × 100

Calculation:

⇒ A = 100 + 50 = 150

⇒ A + B = 150 + 100 = 250

⇒ C = 250 × (70 ÷ 100) = 175

⇒ Required % = (175 ÷ 150) × 100

⇒ = 116.67%

∴ The correct answer is 116.67%.

Given:

Distance₁ = 100 km

Speed₁ = 50 km/h

Distance₂ = 60 km

Speed reduced by 40%

Formula Used:

Time = Distance ÷ Speed

New speed = Original speed × (100 − reduction%) ÷ 100

Calculation:

⇒ Time₁ = 100 ÷ 50 = 2 hours

⇒ New speed = 50 × (60 ÷ 100) = 30 km/h

⇒ Time₂ = 60 ÷ 30 = 2 hours

⇒ Total time = 2 + 2 = 4 hours

∴ The correct answer is 4 hours.

Given:

Men = 18

Total days = 20

Work done in 10 days

Remaining men = 12

Formula Used:

Total work = Men × Days

Remaining work = Total work − Work done

Days = Remaining work ÷ Remaining men

Calculation:

⇒ Total work = 18 × 20 = 360

⇒ Work done in 10 days = 18 × 10 = 180

⇒ Remaining work = 360 − 180 = 180

⇒ Days required = 180 ÷ 12 = 15

∴ The correct answer is 15.

Given:

Cost of items = ₹2050

Discount rate = 26%

Formula Used:

Total savings = (Cost of items × Discount rate) ÷ 100

Calculation:

⇒ Total savings = (₹2050 × 26) ÷ 100

⇒ Total savings = ₹53300 ÷ 100

⇒ Total savings = ₹533

∴ The correct answer is ₹533.

Given:

Selling price after 25% discount = 7200

New discount = 30%

Formula Used:

Selling price = Marked price × (100 − discount%) ÷ 100

Calculation:

⇒ 7200 = MP × (75 ÷ 100)

⇒ MP = 7200 × (100 ÷ 75) = 9600

⇒ New selling price = 9600 × (70 ÷ 100)

⇒ New selling price = 6720

∴ The correct answer is 6720.

Given:

Container A = 20 litres, ratio = 3 : 2

Container B = 30 litres, ratio = 4 : 1

Formula Used:

Quantity = Total × (part ÷ sum of ratio)

Calculation:

⇒ Milk in A = 20 × (3 ÷ 5) = 12

⇒ Water in A = 20 × (2 ÷ 5) = 8

⇒ Milk in B = 30 × (4 ÷ 5) = 24

⇒ Water in B = 30 × (1 ÷ 5) = 6

⇒ Total milk = 12 + 24 = 36

⇒ Total water = 8 + 6 = 14

⇒ Ratio = 36 : 14

⇒ Simplified ratio = 18 : 7

∴ The correct answer is 18 : 7.

Given:

Numbers = 2^{1 ÷ 3}, 3^{1 ÷ 2}, 5^{1 ÷ 6}

Formula Used:

If a^m and bⁿ, compare by taking common power

Calculation:

⇒ LCM of 3, 2, 6 = 6

⇒ (2^{1 ÷ 3})⁶ = 2² = 4

⇒ (3^{1 ÷ 2})⁶ = 3³ = 27

⇒ (5^{1 ÷ 6})⁶ = 5

⇒ 27 > 5 > 4

∴ The correct answer is √3.

Shortcut Trick

Identify the slope m = −2 and the point (1, −3).

Use the Slope-Intercept form: y = mx + c.

Substitute the coordinates: −3 = (−2 × 1) + c.

⇒ −3 = −2 + c ⇒ c = −1.

The required equation is y = −2x − 1.

∴ The correct answer is y = − 2x − 1.

Alternate Method

Given:

Slope (m) = −2

Point (x₁, y₁) = (1, −3)

Formula Used:

The Point-Slope form of a linear equation is: (y − y₁) = m(x − x₁)

Calculations:

⇒ y − (−3) = −2(x − 1)

⇒ y + 3 = −2(x) − (−2 × 1)

⇒ y + 3 = −2x + 2

⇒ y = −2x + 2 − 3

⇒ y = −2x − 1

∴ The correct answer is y = − 2x − 1.

Additional Information

Slope-Intercept Form

Defined as y = mx + c, where m represents the slope and c represents the y-intercept (the value of y when x = 0).

Slope Formula

If two points (x₁, y₁) and (x₂, y₂) are known, the slope m is calculated as (y₂ − y₁) ÷ (x₂ − x₁).

Parallel and Perpendicular Lines

Parallel lines have equal slopes (m₁ = m₂). Perpendicular lines have slopes whose product is −1 (m₁ × m₂ = −1).

Shortcut Trick

In similar triangles, the ratio of any corresponding linear segments (such as sides, perimeters, medians, altitudes, or angle bisectors) is always equal.

Ratio of perimeters = 3 : 4

Ratio of corresponding medians = Ratio of perimeters

∴ Ratio of medians = 3 : 4

∴ The correct answer is 3:4.

Alternate Method

Given: ΔPQR ∼ ΔXYZ and Perimeter(ΔPQR) : Perimeter(ΔXYZ) = 3 : 4.

Formula Used: For two similar triangles, Ratio of Perimeters = Ratio of Sides = Ratio of Medians = Ratio of Altitudes.

Calculations:

⇒ Let the sides of ΔPQR be a₁, b₁, c₁ and sides of ΔXYZ be a₂, b₂, c₂.

⇒ Perimeter of ΔPQR / Perimeter of ΔXYZ = 3 / 4

⇒ By the property of similarity, the ratio of corresponding sides is equal to the ratio of perimeters.

⇒ Ratio of sides = 3 / 4

⇒ Corresponding medians of similar triangles are in the same ratio as their corresponding sides.

⇒ Length of median from P / Length of median from X = Ratio of sides = 3 / 4

∴ The correct answer is 3:4.

Additional Information

Area Ratio Property

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding linear dimensions (sides, medians, or perimeters). Area Ratio = (3/4)² = 9/16.

Median Definition

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Every triangle has exactly three medians, which intersect at the centroid.

Similarity Criteria

Triangles are similar if their corresponding angles are equal (AA) or if their corresponding sides are in the same proportion (SSS or SAS).

Given:

AD = 5 cm

DB = 7 cm

AE = 10 cm

Formula Used:

If a line is parallel to one side of a triangle, then it divides the other two sides proportionally

AD ÷ DB = AE ÷ EC

Calculation:

⇒ 5 ÷ 7 = 10 ÷ EC

⇒ 5 × EC = 7 × 10

⇒ 5EC = 70

⇒ EC = 70 ÷ 5

⇒ EC = 14 cm

∴ The correct answer is 14.

The correct answer is European Union.

Key Points

• The European Union (EU) introduced the Carbon Border Adjustment Mechanism (CBAM) on October 1, 2023, as part of its broader commitment to reducing carbon emissions and addressing climate change.
• CBAM is a critical policy under the European Green Deal, aimed at ensuring that the cost of carbon emissions is factored into the price of imported goods.
• The mechanism applies to carbon-intensive products such as cement, aluminum, steel, fertilizers, electricity, and hydrogen, among others, imported into the European Union.
• The primary goal of CBAM is to prevent carbon leakage, which occurs when companies relocate their production to countries with less stringent climate policies, undermining global climate goals.
• Initially, the mechanism will operate in a transitional phase until 2026, focusing on reporting emissions without imposing financial obligations. Full implementation with a monetary carbon levy is set to begin thereafter.

Additional Information

• European Green Deal:
• Launched in 2019, the European Green Deal is the EU's roadmap to make Europe the first climate-neutral continent by 2050.
• It includes policies targeting clean energy, sustainable industry, and biodiversity, along with the CBAM to address carbon leakage.
• Carbon Leakage:
• Occurs when industries relocate production to regions with weaker climate policies, causing an increase in global emissions rather than reducing them.
• CBAM aims to level the playing field by imposing a carbon cost on imports equivalent to the EU’s carbon price.
• Implementation Process:
• During the transitional phase (2023-2026), importers are required to report the embedded emissions of their goods, but no financial payments are demanded.
• From 2026 onwards, importers will need to purchase CBAM certificates to account for the carbon emissions of imported goods.
• Global Implications:
• CBAM has raised concerns among developing countries and trade partners, as it could impact their export competitiveness.
• It encourages other countries to adopt similar carbon pricing mechanisms to align with global climate goals.
• Comparison with Other Initiatives:
• While CBAM is specific to the EU, similar initiatives are being discussed globally to address carbon emissions in trade.
• For example, the United States has proposed a Clean Competition Act with similar objectives.

The correct answer is Manu Bhakar.

Key Points

• Manu Bhakar is a renowned Indian sportsperson associated with the sport of shooting. She has represented India in various national and international shooting competitions.
• She gained prominence for her exceptional performance in the 10m Air Pistol and 25m Pistol events.
• Manu Bhakar won a gold medal at the 2018 ISSF World Cup, becoming one of the youngest Indian shooters to achieve this feat.
• She also clinched gold medals at the 2018 Commonwealth Games and the 2019 ISSF World Cup finals, solidifying her position as a top-tier shooter.
• Her achievements have made her a key figure in Indian shooting sports, and she continues to inspire young athletes in the country.

Additional Information

• D. Gukesh:
• D. Gukesh is an Indian chess prodigy and is not associated with shooting.
• He holds the title of Grandmaster in chess and is among the youngest to achieve this distinction.
• Gukesh has represented India in international chess tournaments and has won multiple accolades in the sport.
• Mithali Raj:
• Mithali Raj is a former captain of the Indian women’s cricket team and is not related to shooting.
• She is known for her exceptional batting skills and has been a leading figure in women’s cricket globally.
• Mithali is the highest run-scorer in women’s international cricket and has received numerous awards for her contributions to the sport.
• Dipa Karmakar:
• Dipa Karmakar is a renowned Indian gymnast and is not associated with shooting.
• She gained fame for her performance in the 2016 Rio Olympics, where she became the first Indian female gymnast to qualify for the Olympics final.
• Dipa is known for executing the Produnova vault, a highly challenging gymnastics move.
• Significance of Shooting in India:
• Shooting is a sport where India has achieved significant success on the international stage, including the Olympics, Commonwealth Games, and Asian Games.
• Notable Indian shooters include Abhinav Bindra (India’s first individual Olympic gold medalist), Gagan Narang, and Rahi Sarnobat.
• Organizations like the National Rifle Association of India (NRAI) play a key role in promoting and supporting shooting sports in the country.

The correct answer is Anusuiya Uikey.

Key Points

• Anusuiya Uikey was appointed as the Governor of Manipur in December 2024.
• She previously served as the Governor of Chhattisgarh, showcasing her extensive administrative experience.
• Her appointment as Governor of Manipur highlights the Government of India's focus on appointing experienced leaders to key gubernatorial roles in northeastern states.
• Manipur, being a state of strategic importance in the northeast, benefits from her leadership and administrative capabilities.
• Governors in India are appointed by the President of India under Article 155 of the Constitution, and they serve as the constitutional head of their respective states.

Additional Information

• Role of Governors in India:
• The Governor is the constitutional head of the state, acting on the advice of the Council of Ministers headed by the Chief Minister.
• They have the power to reserve certain bills for the consideration of the President under Article 200.
• The Governor also plays a critical role in ensuring the state’s administration is conducted per the provisions of the Constitution.
• Appointment of Governors:
• Governors are appointed by the President of India for a term of five years, but they serve at the pleasure of the President.
• They can be transferred between states and may also be reappointed for a second term.
• Manipur - Strategic Importance:
• Manipur is a northeastern state with significant geographical and cultural importance, sharing borders with Myanmar.
• The state plays a vital role in India's Act East Policy, enhancing trade and connectivity with Southeast Asia.
• It is known for its diverse cultural heritage, including traditional dances like Raas Leela and sports such as Polo, which originated here.
• Key Functions of the Governor:
• Appointing the Chief Minister and other ministers.
• Summoning, proroguing, and dissolving the state legislature.
• Granting pardons, reprieves, respites, or remissions of punishment under Article 161.
• Ensuring the constitutional machinery of the state is upheld, particularly under Article 356 in case of a constitutional crisis.

The correct answer is Rama Mohan Rao Amara.

Key Points

• Rama Mohan Rao Amara was appointed as the Managing Director (MD) of State Bank of India (SBI) in December 2024.
• He has extensive experience in the banking sector, having served in various roles in SBI over the years.
• His appointment reflects SBI’s commitment to strengthening leadership and ensuring efficient management of India's largest public sector bank.
• As MD, Amara is expected to drive the bank's strategic initiatives, enhance profitability, and focus on innovation in banking services.
• The appointment follows the guidelines set by the Government of India and the Bank Boards Bureau to ensure merit-based leadership in public sector banks.

Additional Information

• State Bank of India (SBI):
• SBI is India's largest public sector bank and financial institution, established in 1955.
• It operates globally, with a network of 22,000+ branches and 58,000+ ATMs.
• The bank plays a significant role in implementing various government schemes like PMJDY, Mudra Yojana, and Atal Pension Yojana.
• Role of Managing Director:
• The MD is responsible for overseeing the bank's operations, strategy, and financial performance.
• Key responsibilities include driving growth, innovation, and digital transformation within the organization.
• The MD also plays a crucial role in implementing government policies through the bank's services and products.
• Bank Boards Bureau:
• The Bank Boards Bureau was established in 2016 to recommend appointments to leadership positions in public sector banks and financial institutions.
• It ensures transparency and merit-based selection for key management roles.
• Recent Initiatives by SBI:
• SBI has been focusing on digital banking and enhancing customer experiences through platforms like YONO.
• The bank is actively involved in promoting financial inclusion and supporting MSMEs through loan schemes.
• SBI has introduced green banking practices, including investments in renewable energy projects.
• Important Leadership Appointments in SBI:
• Key appointments at SBI include Chairman, Managing Directors, and Chief Financial Officers, selected based on expertise and experience.
• Recent leadership appointments are geared toward fostering growth, innovation, and global competitiveness.

The correct answer is Parvathaneni Harish.

Key Points

• Parvathaneni Harish was appointed as India's Permanent Representative to the United Nations in August 2024, succeeding his predecessor.
• The Permanent Representative of India to the United Nations is a critical diplomatic position that represents India in all UN forums, including the United Nations General Assembly (UNGA) and the United Nations Security Council (UNSC).
• Parvathaneni Harish is a seasoned diplomat and a senior officer of the Indian Foreign Service (IFS), known for his extensive experience in global diplomacy, including holding key positions in India's missions abroad.
• His appointment is seen as part of India's strategy to strengthen its global diplomatic footprint and effectively articulate India's stance on key international issues, including sustainable development, peacekeeping, and global security.
• India's role at the UN has been pivotal, especially with its recent tenure as a non-permanent member of the UNSC for 2021-2022, and Harish's leadership is expected to bolster India's contributions further.

Additional Information

• United Nations and India:
• India is a founding member of the United Nations (UN), having signed the UN Charter in 1945.
• India has been a strong advocate for multilateralism, sustainable development, and international peace and security within the UN framework.
• India has contributed significantly to UN Peacekeeping Missions, being one of the largest troop-contributing nations.
• Role of Permanent Representatives:
• The Permanent Representative acts as the chief diplomat for a country at the UN, representing its interests in all UN forums and negotiations.
• Responsibilities include participating in debates, contributing to resolutions, and fostering multilateral collaborations.
• The position requires strong leadership and diplomatic skills to navigate complex global issues like climate change, conflict resolution, and human rights.
• India's Recent Achievements at the UN:
• India served as a non-permanent member of the UN Security Council (UNSC) for the 2021-2022 term, highlighting its role in global decision-making.
• During this tenure, India chaired key committees, including the Counter-Terrorism Committee and the Libya Sanctions Committee.
• India has also been actively advocating for UN reforms, including a permanent seat in the UNSC, under the G4 coalition.
• Parvathaneni Harish's Background:
• He is a senior officer of the Indian Foreign Service (IFS), having joined in 1990.
• Harish has served in various capacities, including as India's Ambassador to Vietnam and other key diplomatic postings.
• His expertise spans critical areas like trade negotiations, bilateral relations, and multilateral diplomacy.
• India's Vision at the UN:
• India emphasizes equitable global governance, counter-terrorism, climate change action, and sustainable development.
• It also champions the Global South by advocating for fair representation and addressing developmental challenges faced by developing nations.
• India's initiatives, such as the International Solar Alliance (ISA) and Coalition for Disaster Resilient Infrastructure (CDRI), highlight its global leadership in addressing climate change.

The correct answer is 2.

Key Points

• Subhadra Yojana was introduced by the Odisha government in September 2024 to provide financial assistance to beneficiaries.
• Under the scheme, beneficiaries receive a total of Rs. 50,000 over a period of 5 years. Hence, the correct answer is 5 years.
• This financial support aims to empower vulnerable sections of society, particularly women and economically weaker groups.
• The funds are disbursed systematically in installments to achieve specific goals, such as enhancing livelihood opportunities and ensuring social security.
• The scheme is monitored by the Department of Women and Child Development, Odisha, ensuring transparency and proper implementation.

Additional Information

• Key Objectives of Subhadra Yojana:
• The scheme is designed to provide financial aid to marginalized sections of society, with a focus on women-led households.
• It promotes inclusive development by addressing poverty and improving access to education, healthcare, and basic needs.
• Implementation Process:
• Funds are disbursed through Direct Benefit Transfer (DBT) to ensure transparency and prevent leakages.
• The scheme is overseen by the Department of Women and Child Development, Odisha, ensuring that all targeted beneficiaries receive their entitlements.
• Comparison with Similar Initiatives:
• Mission Shakti, another scheme by the Odisha government, focuses on women empowerment.
• Other states in India have launched similar initiatives to support vulnerable groups, such as the KALIA Scheme for farmers.
• Statistical Overview:
• The scheme aims to cover a significant portion of the population below the poverty line in Odisha.
• This initiative is expected to contribute positively to the state's Human Development Index (HDI) rankings.

Important Points

• Eligibility Criteria:
• Beneficiaries must belong to economically weaker sections or marginalized communities.
• Preference is given to women-led households and families with limited access to resources.
• Financial Inclusion:
• The scheme encourages beneficiaries to open and operate bank accounts.
• Funds are credited directly to beneficiaries’ accounts to ensure transparency.
• Examples of Similar Initiatives:
• The KALIA Scheme in Odisha provides financial assistance to farmers and landless agricultural laborers.
• The Pradhan Mantri Jan Dhan Yojana (PMJDY) focuses on financial inclusion by offering banking facilities to underprivileged groups.

The correct answer is Swachhata Hi Seva Campaign.

Key Points

• The Swachhata Hi Seva Campaign is a flagship initiative of the Department of Health Research, aligned with the Swachh Bharat Mission, to promote cleanliness and hygiene across India.
• The campaign is scheduled from 17th September 2024 to 2nd October 2024, coinciding with the birth anniversary of Mahatma Gandhi, a staunch advocate of cleanliness and sanitation.
• It emphasizes community participation to drive activities such as cleanliness drives, waste removal, and awareness programs aimed at achieving a cleaner and healthier environment.
• The campaign focuses on ensuring the active involvement of citizens, schools, businesses, NGOs, and local bodies to promote sustainable hygiene practices, particularly in urban and rural areas.
• This initiative is part of the larger Swachh Bharat Mission, which was launched on 2nd October 2014 by Prime Minister Narendra Modi to achieve universal sanitation coverage and eliminate open defecation in India.

Additional Information

• Swachh Bharat Mission:
• The Swachh Bharat Mission was launched on 2nd October 2014 to honor Mahatma Gandhi’s vision of cleanliness and sanitation.
• The mission comprises two components: Swachh Bharat Mission (Urban) and Swachh Bharat Mission (Rural).
• As of today, the mission has led to the construction of over 100 million toilets across India, significantly reducing open defecation.
• It also emphasizes waste management through methods like solid waste management and door-to-door waste collection.
• Mahatma Gandhi's Role in Cleanliness Advocacy:
• Mahatma Gandhi consistently advocated for the importance of cleanliness, considering it equally important as independence.
• He often emphasized that a clean environment is essential for building a healthy and progressive society.
• His teachings continue to inspire modern initiatives like the Swachh Bharat Mission and the Swachhata Hi Seva Campaign.
• Plastic-Free India Campaign:
• The Plastic-Free India Campaign aims to eliminate the use of single-use plastics to combat environmental pollution.
• It promotes the adoption of sustainable and eco-friendly alternatives to reduce the environmental impact of plastic waste.
• Namami Gange Program:
• The Namami Gange Program is a flagship initiative by the Government of India to clean and rejuvenate the Ganga River.
• It integrates efforts to address issues such as water pollution, waste management, and biodiversity conservation.
• Impact of the Swachhata Hi Seva Campaign:
• Contributes to reducing the prevalence of diseases such as diarrhea and cholera caused by unhygienic conditions.
• Improves the quality of life, especially for women and children.
• Promotes sustainable waste management practices like recycling and composting.

Important Points

• Government Support:
• The government provides financial assistance to urban and rural areas for constructing toilets and waste management systems.
• Educational campaigns are organized to spread awareness about the importance of cleanliness and hygiene.
• Digital platforms monitor and report the progress of cleanliness initiatives under this campaign.
• Community Involvement:
• Local bodies, schools, and NGOs are encouraged to actively participate in cleanliness drives.
• Competitions, workshops, and rallies are organized to engage citizens in promoting hygiene practices.

The correct answer is Square.

Key Points

• The standard competition platform used in Judo is a square-shaped mat, commonly referred to as the tatami.
• The contest area is typically 10 meters x 10 meters, with an additional 3-meter safety area surrounding it to ensure the safety of participants.
• The square layout ensures equal opportunities for both players, providing enough space for techniques like throws, grappling, and groundwork.
• The mats are made of shock-absorbing materials to minimize injuries during high-impact throws and falls.
• The International Judo Federation (IJF) regulations mandate the use of a square contest area to standardize competitions globally, including major events like the Olympics and World Championships.

Additional Information

• Judo History:
• Judo was founded in 1882 by Jigoro Kano in Japan.
• It emphasizes leverage, technique, and balance rather than brute strength.
• Judo became an Olympic sport in 1964 during the Tokyo Games.
• Tatami Mats:
• The mats used in Judo are known as tatami.
• Traditionally, they were made from rice straw, but modern versions use materials like foam.
• The tatami provides a non-slip surface and cushions falls to prevent injuries.
• Other Shapes in Combat Sports:
• Rectangular: Used in sports like wrestling and boxing, suitable for movement patterns in those sports.
• Hexagonal: Seen in mixed martial arts (MMA) to enhance visibility and mobility.
• Circular: Common in traditional martial arts or sumo wrestling to emphasize boundaries.
• Safety Regulations:
• The International Judo Federation (IJF) mandates a 3-meter safety area around the contest area to prevent injuries during high-intensity matches.
• The shock-absorbing mats are maintained to ensure safe competition conditions.

Important Points

• Judo Belt System:
• Judokas progress through a belt ranking system (kyu and dan grades) based on their skill levels.
• The belt colors range from white (beginner) to black (expert).
• Scoring in Judo:
• Points are awarded for techniques like throws (ippon), pins (osaekomi), and submissions.
• An ippon signifies a perfect throw or submission, instantly ending the match.

The correct answer is 1928.

Key Points

• India won its first Olympic gold medal in hockey in the year 1928 during the Amsterdam Olympics.
• The Indian hockey team defeated the Netherlands (host nation) in the final with a score of 3-0 to secure the gold medal.
• The victory marked the beginning of India's dominance in field hockey, as the team went on to win six consecutive Olympic gold medals from 1928 to 1956.
• Dhyan Chand, one of the greatest hockey players in history, played a pivotal role in this victory by scoring two goals in the final match.
• This was the first time India participated as an independent hockey team, symbolizing its emergence as a global powerhouse in the sport.

Additional Information

• Dhyan Chand's Legacy:
• Dhyan Chand, widely known as the "Wizard of Hockey," scored a total of 14 goals in five matches during the 1928 Olympics.
• His birthday, 29th August, is celebrated as National Sports Day in India to honor his contributions to Indian hockey.
• India's Dominance in Hockey:
• India won six consecutive Olympic gold medals in hockey from 1928 to 1956, remaining unbeaten during this period.
• During these years, India scored a total of 178 goals while conceding only seven, showcasing its unparalleled dominance in the sport.
• Other Olympic Gold Medals:
• India has won a total of eight Olympic gold medals in hockey. These victories came in 1928, 1932, 1936, 1948, 1952, 1956, 1964, and 1980.
• The last Olympic gold medal in hockey was achieved during the 1980 Moscow Olympics.
• Field Hockey in the Olympics:
• Field hockey was introduced in the Olympics in 1908, but India participated for the first time in 1928.
• India's early success in hockey helped popularize the sport across the country.
• In recent decades, nations like Netherlands, Germany, and Australia have emerged as strong competitors in the sport.
• Important Points:
• The 1928 victory was India's first major international achievement, instilling a sense of pride and unity during the colonial period.
• Post-independence, players like Balbir Singh Sr. and Leslie Claudius contributed to India's continued success in hockey.
• Efforts to revive Indian hockey include initiatives like the Hockey India League and grassroots development programs.
• India's bronze medal win in men's hockey at the 2021 Tokyo Olympics marked a significant step in the sport's revival.

The correct answer is Cricket.

Key Points

• Cricket is often referred to as the "Gentleman's Game" due to its long-standing association with fairness, respect, and sportsmanship.
• The term originated during the early days of cricket in England, where the sport was played predominantly by aristocrats and upper-class individuals, emphasizing gentlemanly conduct.
• Etiquette plays a key role in cricket, including respecting the umpire’s decisions, applauding opponents’ achievements, and maintaining discipline on the field.
• The International Cricket Council (ICC) actively promotes values such as fair play and mutual respect among players, aligning with the principles of the "Gentleman's Game."
• Although the phrase is traditional, modern cricket has evolved to include players from diverse social backgrounds, but the emphasis on sportsmanship remains central to the game.