SSC CHSL Tier-1 2024: Official Paper (Held On: 03 Jul, 2024 Shift 4) (Previous Year Paper)

The correct answer is Option 3.

 

Key Points

• The verb "ran" is the simple past tense of "run."
• The other options ("running," "runned," "run") are not correct in this context.
• "Running" is a gerund or present participle, "runned" is not a correct form, and "run" is the base form or past participle.
• Therefore, the correct answer is Option 3.

Correct Sentence: "He ran a long distance."

 

Additional Information

• Option 1: "running" – This is the gerund or present participle form and does not fit the past tense context.
• Option 2: "runned" – This is an incorrect form of the verb "run."
• Option 4: "run" – This is the base form or past participle, not the simple past tense.

The correct answer is Option 2.

 

Key Points

• The sentence provided is: "Mr. Narayanan is a rather lazy man."
• There is no adverbial usage error in any segment of the sentence.
• The sentence is grammatically correct as it stands.
• Thus, the correct answer is "No error".

Therefore, the correct answer is Option 2.

 

Additional Information

• Mr. Narayanan – This part of the sentence is grammatically correct and does not require any changes.
• is a rather – This part of the sentence is grammatically correct and does not require any changes.
• lazy man – This part of the sentence is grammatically correct and does not require any changes.
• No error – This is the correct option as there are no errors in the sentence.

The correct answer is Option 4.

 

Key Points

• The primary issue in the sentence is the use of the word "yearn" instead of "yearns."
• The subject "Chotu" is singular and requires the verb "yearns" to match in number.
• Therefore, the correct form should be "yearns."
• Thus, the error is located in the verb form used in the sentence.
• Therefore, the correct answer is Option 4.

Correct Sentence: "Chotu is a bright young child, who yearns to go to school but works in his uncle’s dhaba."

 

Additional Information

• Subject-Verb Agreement: Ensuring that the verb matches the subject in number is crucial for grammatical correctness.
• Context: The context of the sentence indicates Chotu's desire to attend school, which is expressed through the correct verb form "yearns."
• Other Options: The other options (yearned, working, worked) do not fit the context or correct the grammatical error in the sentence.

The correct answer is Option 4.

 

Key Points

• The primary issue in the sentence is the incorrect use of the past perfect tense "had seen" with the specific time reference "yesterday".
• The past perfect tense is used to describe an action that was completed before another action in the past, and it is not typically used with specific time expressions like "yesterday".
• The correct phrase should be "I saw her with her mother in the cinema hall yesterday," ensuring grammatical correctness and clarity.
• Thus, the error is located in part 4 of the sentence.
• Therefore, the correct answer is Option 4.

Correct Sentence: "I saw her with her mother in the cinema hall yesterday."

 

Additional Information

• 1) yesterday – This part of the sentence is grammatically correct and does not require any changes.
• 2) in the cinema hall – This part of the sentence is grammatically correct and does not require any changes.
• 3) her with her mother – This part of the sentence is grammatically correct and does not require any changes,

The correct answer is Option 3)

Key Points

• The superlative form "best" directly follows the definite article "the," which is typical in English to indicate that something is the most outstanding example among all options.
• In this context, "the best gift of nature" implies that among all possible gifts of nature, trees are considered the most exemplary.
• "The" precedes superlative adjectives like "best," "most," "least," etc., when there is a clear comparison.
• The use of "the best gift" introduces definiteness, emphasizing the uniqueness of trees as nature's gift.
• Using "an" or "a" would be grammatically incorrect as these articles would not correctly set up the superlative degree.
• Omitting the article would make the phrase grammatically incomplete and unclear in meaning.

Therefore, the correct answer is 'Option 3'.

Additional Information

• Option 1 (No article): Incorrect because it leaves the phrase incomplete and grammatically incorrect.
• Option 2 (an): Incorrect because "an best gift" does not follow grammatical norms.
• Option 4 (a): Incorrect because "a best gift" does not correctly set up the superlative form.

The correct answer is Option 4)

Key Points

• The phrase "Houses, chairs, and toys..." lists multiple items, so the plural form "are" is the correct conjugation of the verb to agree with the plural subject.
• The verb "made" is in the past participle form, which is appropriate following a form of "to be" in passive voice constructions.
• The passive voice ("are made") correctly indicates that houses, chairs, and toys are created using wood without specifying who makes them.
• "From wood" correctly describes the material used in the construction of houses, chairs, and toys.
• Using "are made" fits the present simple tense, which is commonly used for general facts and truths.
• The entire phrase "are made from wood we receive from trees" clearly communicates the relationship between the objects and their source material.

Therefore, the correct answer is 'Option 4'.

Additional Information

• Option 1 (was make): Incorrect because "was make" is grammatically incorrect; "was" should be followed by the past participle "made."
• Option 2 (had make): Incorrect because "had make" is not a recognized conjugation; it should be "had made."
• Option 3 (will made): Incorrect because "will made" is incorrect tense-wise; it should be "will be made."

The correct answer is Option 1)

Key Points

• The preposition "on" is commonly used to indicate something that is physically resting or growing on a surface or object.
• "Grown on trees" specifies that leaves, vegetables, and fruits are physically situated on the trees as they grow.
• This usage is consistent with how we describe the location of parts of plants, such as leaves growing on branches or fruits hanging on trees.
• The phrase "grown on trees" accurately conveys the natural process where these items develop on the branches and structure of the tree.
• Using "on" fits the context of explaining where certain foods that animals consume come from.
• The preposition "on" effectively indicates the source or origin of the vegetation that animals eat.

Therefore, the correct answer is 'Option 1'.

Additional Information

• Option 2 (of): Incorrect because "grown of trees" does not convey the correct relationship of physical growth on the tree.
• Option 3 (out): Incorrect because "grown out trees" does not fit grammatically or contextually; the phrase should be "grown out of," which is not suitable here.
• Option 4 (for): Incorrect because "grown for trees" suggests that the leaves, vegetables, and fruits are intended for the trees, which is not the intended meaning.

The correct answer is Option 2)

Key Points

• The context of the passage focuses on ecological conservation and the relationship between humans, trees, and the environment, making "nature" the most fitting word.
• The phrase "stop causing harm to nature" is a common and clear expression of the idea that humans should protect the natural world.
• "Nature" is a noun that encompasses the entire environment, including plants, animals, and ecosystems, which is what the passage is talking about.
• The passage discusses saving nature and planting trees, both of which are directly related to protecting and preserving natural ecosystems.
• Using "nature" maintains the thematic consistency of the passage, which is centered on natural conservation and the benefits trees provide to the natural world.
• The phrase effectively communicates the call to action for environmental protection and stewardship.

Therefore, the correct answer is 'Option 3'.

Additional Information

• Option 1 (natural): Incorrect because "natural" is an adjective and does not fit the grammatical structure of the sentence.
• Option 2 (nurture): Incorrect because "nurture" refers to the act of caring and nurturing, which does not fit contextually here.
• Option 4 (nurturing): Incorrect because "nurturing" is a present participle or gerund form, and does not fit grammatically in the sentence.v

The correct answer is Option 3)

Key Points

• "Nature" is a noun that encompasses the entire natural world, including plants, animals, and ecosystems, which aligns with the passage’s thematic focus.
• The phrase "harm to nature" is a common expression and accurately conveys the importance of protecting the environment.
• Using "nature" maintains the thematic consistency of the passage, which emphasizes ecological conservation and the benefits trees provide.
• The context of the passage is about preserving the environment and preventing damage, making "nature" the most contextually appropriate option.
• Adding "nature" fits grammatically within the sentence, ensuring the passage flows smoothly and maintains clear meaning.
• The overall theme is about the human relationship with the environment, and "nature" directly refers to all elements of the natural world that we must protect.

Therefore, the correct answer is 'Option 3.'

Additional Information

• Option 1 (natural): Incorrect because "natural" is an adjective and the sentence requires a noun.
• Option 2 (nurture): Incorrect because "nurture" is a noun or verb related to care and upbringing, which doesn't fit the context of environmental conservation.
• Option 4 (nurturing): Incorrect because "nurturing" is a gerund or adjective, and does not fit grammatically as the required noun in the sentence.

The correct answer is Option 3.

Key Points

• The word "chaste" means morally pure or abstaining from extramarital, or from all, sexual intercourse. (शुद्ध)
• Example: She lived a chaste life, dedicated to her spiritual beliefs.
• "Pure" refers to something that is not mixed or adulterated with any other substance or material; it also means morally clean. (शुद्ध)
• Example: The water from the mountain spring is pure and refreshing.
• Hence, we can infer that the synonym of 'chaste' is 'pure'.

Additional Information

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

• Flashy (चमकीला): Ostentatiously attractive or impressive.
• Example: He wore a flashy suit that caught everyone's attention.
• Sullied (मैला): Made dirty or impure.
• Example: Her reputation was sullied by false accusations.
• Corrupt (भ्रष्ट): Dishonestly exploiting one's power for personal gain.
• Example: The corrupt official was finally arrested for accepting bribes.

The correct answer is Option 3.

 

Key Points

• The correct substitution should ensure that the sentence is grammatically correct and conveys the intended meaning.
• Options 1, 2, and 4 contain grammatical errors or do not make sense in the context.
• Option 3, "people are likely to remember you," is grammatically correct and fits well within the sentence.
• Therefore, the correct choice is Option 3.

Correct Sentence: "If you behave well and exhibit good manners, then people are likely to remember you in a positive way."

 

Additional Information

• Option 1: "people likely you remember" – This option has incorrect word order and is grammatically incorrect.
• Option 2: "people will like in remember" – This option is not coherent and does not make sense in the context.
• Option 4: "people are like remember you" – This option is also grammatically incorrect and does not convey the intended meaning.
• Option 5: – Not provided, thus irrelevant in this context.

The correct answer is Option 3.

 

Key Points

• The term "tirade" typically refers to a long and angry speech, especially one that criticizes someone or something.
• In the context of Greta Thunberg's speech, "long and angry speech" accurately captures the essence of her message against environmental degeneration.
• The other options do not fit the context as precisely as "long and angry speech" does.
• Therefore, the correct answer is Option 3.

Correct Sentence: "Greta Thunberg’s long and angry speech against environmental degeneration shocked the world leaders."

 

Additional Information

• Option 1: "debatable account" – This does not convey the intensity and length of Greta Thunberg's speech.
• Option 2: "minute observation" – This implies a detailed, careful look at something, which is not the case here.
• Option 4: "innate liberal opinion" – This does not capture the nature of the speech.

The correct answer is Option 1.

 

Key Points

• The correct preposition to use with "filled" in this context is "with." Therefore**, "filled with horror"** is the correct phrase.
• Option 2 (filled of) is incorrect because "of" is not the appropriate preposition to use with "filled" in this context.
• Option 3 (filled on) is incorrect because "on" does not convey the correct meaning in this context.
• Option 4 (filled off) is grammatically incorrect and does not make sense in this context.

Therefore, the correct option is filled with.

The correct answer is Option 2.

 

Key Points

• The primary issue in the sentence is the use of the incorrect pronoun "her" in the subject position.
• The correct pronoun to use in the subject position is "she".
• Therefore, the sentence should read "It was she who first saw the criminal."
• Therefore, the correct answer is Option 2.

Correct Sentence: "It was she who first saw the criminal."

 

Additional Information

• Pronoun Usage: Pronouns must be used correctly to maintain the grammatical integrity of a sentence. In this case, "she" is the correct subject pronoun.
• Subject-Verb Agreement: Always ensure that the subject and verb in a sentence agree in number and person.
• Clarity: Using the correct pronoun helps in maintaining the clarity of the sentence.

The correct answer is Option 4.

 

Key Points

• The primary issue in the sentence is the use of the term "a disarray," which is incorrect.
• "Disarray" is an uncountable noun and does not require an article ("a" or "an").
• The correct phrase should be "led to disarray," ensuring grammatical correctness and clarity.
• Thus, the error is located in the use of the term "a disarray."
• Therefore, the correct answer is**: disorderly situation**.

Correct Sentence: "The sudden declaration of war between two countries led to a disorderly situation."

Additional Information

• Option 1: "elusive situation" – This option does not fit the context as it suggests something hard to grasp or define, which does not match the scenario of war leading to chaos.
• Option 2: "peaceful treaty" – This option is incorrect as it contradicts the context of war.
• Option 3: "refined argument" – This option is incorrect as it does not fit the context of war leading to chaos.
• Option 4: "disorderly situation" – This option correctly captures the chaos and confusion resulting from the declaration of war.

The correct answer is Option 1.

Key Points

• The word "contemplate" means to think deeply or carefully about something. (विचार करना)
• Example: She likes to contemplate the meaning of life during her morning walks.
• "Overlook" refers to fail to notice or consider something or someone. (नज़रअंदाज़ करना)
• Example: It is easy to overlook small details when you are in a hurry.

Hence, we can infer that the opposite of 'contemplate' is 'overlook'.

Additional Information

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

• Deviate (विचलित होना): To depart from an established course or norm.
• Example: He tends to deviate from the main topic during discussions.
• Follow up (अनुसरण करना): To pursue or investigate something further.
• Example: The doctor asked her to follow up with him in a week.
• Understate (कम करके आंकना): To describe something as being smaller or less important than it actually is.
• Example: He tends to understate his achievements.

The correct answer is Option 4)

Key Points

• The word "Cheerful" means noticeably happy and optimistic. (प्रसन्न)
• Example: She always has a cheerful smile on her face, no matter the situation.
• "Gloomy" refers to a state of being dark, depressing, or pessimistic. (उदास)
• Example: The room felt gloomy after the lights went out and the rain started pouring.

Hence, we can infer that the opposite of 'Cheerful' is 'Gloomy'.

Additional Information

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

• Joyful (आनंदित): Feeling, expressing, or causing great pleasure and happiness.
• Example: The joyful children ran around the playground with big smiles on their faces.
• Sunny (धूपदार): Bright with sunlight; cheerful and optimistic.
• Example: She has a sunny disposition that brightens up everyone's day.
• Hilarious (प्रफुल्लित करने वाला): Extremely amusing or funny.
• Example: The comedian's hilarious jokes had everyone in stitches.

The correct answer is Option 2.

 

Key Points

• The word "right" is the correct choice in this context, as it refers to the direction or side, fitting with the context of the punch.
• The other options "write", "rite", and "wright" have entirely different meanings and do not fit the context of a punch.
• The term "right punch" is commonly used in boxing to describe a punch thrown with the right hand.
• Therefore, the correct answer is Option 2.

Correct Sentence: "The boxer was knocked out cold by a powerful right punch to the jaw."

Additional Information

• Write – To form letters or words on a surface with a pen, pencil, or other instrument.
• Rite – A religious or other solemn ceremony or act.
• Wright – A maker or builder, such as a playwright or shipwright.
• Right – Correct or appropriate, or a direction (opposite of left). In this context, it refers to the direction/side.

The correct answer is Option 1.

Key Points

• The given word segment "incredibly foolish and next to impossible" means something that is extremely unwise and almost impossible to achieve. (अत्यंत मूर्खतापूर्ण और लगभग असंभव)
• Example: Climbing Mount Everest without any training is incredibly foolish and next to impossible.
• "like nailing jelly to the tree" is an idiom that means trying to do something that is very difficult or impossible. (ऐसा कार्य करने की कोशिश करना जो बहुत कठिन या असंभव हो)
• Example: Trying to get the kids to sit still during the long lecture was like nailing jelly to the tree.

Therefore, the correct answer is: like nailing jelly to the tree.

Additional Information

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

• like a tree known by its fruits (पेड़ को उसके फलों से पहचाना जाता है): This idiom means that you can judge the quality of something by its results or outcomes.
• Example: A teacher's effectiveness can be seen in the success of their students, like a tree known by its fruits.
• as tight as the bark of the tree (पेड़ की छाल की तरह कसा हुआ): This idiom means something that is very close or tight.
• Example: The friends were as tight as the bark of the tree, never seen apart.
• like going between the bark and the tree (छाल और पेड़ के बीच जाना): This idiom means to interfere in a close relationship.
• Example: Trying to mediate between the two lifelong friends was like going between the bark and the tree.

The correct answer is: Option 4.

Key Points

• The word "Conscientous" is incorrectly spelt and should be "Conscientious". It means wishing to do one's work or duty well and thoroughly. (ईमानदार)
• Example: She is a conscientious worker who pays attention to details.
• "Conscientious" refers to a person who is diligent and careful in their work. (ईमानदार)
• Example: He was a conscientious student, always completing his assignments on time.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Apparent (स्पष्ट): Clearly visible or understood; obvious.
• Example: The error was apparent to everyone who looked at the report.
• Acknowledgement (स्वीकृति): Acceptance of the truth or existence of something.
• Example: He gave an acknowledgment of her contribution to the project.
• Fulfil (पूरा करना): Achieve or realize something desired, promised, or predicted.
• Example: She hopes to fulfil her dreams of becoming a doctor.

The correct answer is: Option 3.

Key Points

• The word "frustrasion" is a misspelling of the correct word "frustration". "Frustration" means the feeling of being upset or annoyed as a result of being unable to change or achieve something. (निराशा)
• Example: She couldn't hide her frustration when the project was delayed again.
• The correct word is "frustration". (निराशा)
• Example: His frustration was evident when the computer crashed just before he saved his work.

Therefore, the correct answer is:  'In all instances of frustration'.

Additional Information

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

• you will always find (आप हमेशा पाएंगे): This segment is correct and means that something will be consistently discovered or observed.
• Example: You will always find her reading a book in her free time.
• the anger directed towards (गुस्सा निर्देशित होता है): This segment is correct and means that anger is aimed at or focused on someone or something.
• Example: The anger directed towards him was understandable given his actions.
• a single person only (केवल एक व्यक्ति): This segment is correct and means that something is limited to one individual.
• Example: The blame was placed on a single person only, even though it was a team effort.

The correct answer is 'Option 1'.

 

Key Points

• The word "reverberated" means to echo or resound, especially over a large area, which fits the context of the thunderous applause echoing through the stadium.
• The sentence describes the sound of applause filling the stadium, and "reverberated" perfectly captures the idea of the sound being reflected and carried throughout the space.
• The other options: "pulsed," "bounced," and "recoiled" do not fit as well. "Pulsed" refers to a rhythmic movement or vibration, "bounced" implies a physical rebound, and "recoiled" means to spring back, which does not align with the context of sound echoing.

​Therefore, the correct answer is 'Option 1'.

Complete Sentence: The thunderous applause reverberated through the stadium.

Additional Information

• Pulsed (धड़कना): Refers to a rhythmic or periodic beating or vibration, not suitable for describing the spread of sound.
• Bounced (उछलना): Refers to something rebounding off a surface, not related to the propagation of sound in the context given.
• Recoiled (पीछे हटना): Refers to a backward movement, usually due to shock or recoil, which does not apply to the echoing sound of applause.

The correct answer is Option 1.

Key Points

• The word "improve" means to make something better or enhance its quality. (सुधारना)
• Example: She enrolled in a course to improve her English skills.
• "Spoil" means to damage or ruin something, making it worse or less enjoyable. (बिगाड़ना)
• Example: The rain could spoil our picnic plans.

Hence, we can infer that the opposite of 'improve' is 'spoil'.

Additional Information

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

• Spatter (छींटें देना): To scatter or splash liquid or small particles.
• Example: The paint spattered all over the floor as she knocked over the can.
• Sprinkle (छिड़कना): To scatter small drops or particles of a substance over a surface.
• Example: She sprinkled some sugar on top of the cake.
• Specify (निर्दिष्ट करना): To state or identify clearly and definitely.
• Example: Please specify the time and place for the meeting.

The correct answer is Option 2.

 

Key Points

• "Request" means to ask for something politely or formally.
• "Petition" means to make a formal or polite request to a person or authority, making it the closest synonym in the given context.
• In the sentence, the speaker is politely asking everyone to stand up, which matches the meaning of "petition".
• Hence, Option 2 is the most appropriate synonym.

Therefore, the correct answer is Petition.

 

Additional Information

• Option 1: "Claim" – Means to assert ownership, state something as true, or demand something as a right. It does not mean to ask politely.
• Option 3: "Plead" – Means to make an emotional or urgent appeal. It implies desperation rather than a polite request.
• Option 4: "Require" – Means to need or demand something as necessary. It does not convey the polite nature of a request.

The correct answer is Option 4.

 

Key Points

• The idiom "kept at arm’s length" means to avoid intimacy or close contact with someone or something.
• In the context of the sentence, it suggests that the gun should be handled carefully and kept at a safe distance to avoid accidents.
• Other options do not fit the context of handling a gun with care.
• Therefore, the correct answer is Option 4.

Correct Sentence: "This gun should be handled with care and kept at arm’s length."

Additional Information

• Option 1: "shot for safety" – This phrase is incorrect and does not make sense in the context of handling a gun with care.
• Option 2: "mince the matters" – This idiom means to speak indirectly or to soften the impact of something, which is not relevant to the context.
• Option 3: "nip in the bud" – This idiom means to stop something at an early stage, which does not fit the context of handling a gun.

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 2".

The logic followed here is:​

ADFI is related to CFHK

​ 

​And,

EHJM is related to GJLO

​ 

​Similarly,

ILNQ is related to

​ 

Hence, "Option 3" is the correct answer.

The logic followed here is:​

'BABE' is coded as '20'

​ 

​And,

'EACH' is coded as '34'

​ 

​Similarly,

'FACT' is coded as

​ 

Hence, "Option 4" is the correct answer.

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

Here, as marked there are a total of 10 triangles.

Hence, "Option 1" is the correct answer.

Given : 59 + 39 - 63 × 21 ÷ 26 = ?

According to the question, after replacing the signs :

‘+’ and ‘-’ are interchanged 

‘×’ and ‘÷’ are interchanged

So,​​

59 - 39 + 63 ÷ 21 × 26 = ?

59 - 39 + 3 × 26 = ?

59 + 78 - 39 = ?

137 - 39 = ?

98 = ?

Hence, "98" is the correct answer.

Given Equation: 32 G 15 R 15 D 17 K 18 = ?

BODMAS Rule:

Decoding the given information:

 

Now replacing the sign from left to right using BODMAS Rule, we get:

⇒ 32 + 15 ÷ 15 - 17 × 18 = ?

⇒ 32 + 1 - 17 × 18 = ?

⇒ 32 + 1 - 306 = ?

⇒ 33 - 306 = -273.

Hence, the correct option is "Option 4".

Decoding the Symbols:

 

 

 

 

Given: A @ B & C @ D + K ÷ F

A @ B → A is the father of B.

B & C → B is the wife of C.

C @ D → C is the father of D.

D + K → D is the sister of K.​

K ÷ F → K is the mother of F.

Here, C is the father of K.

Hence, the correct answer is "Option 1".

Given: 19 July 2000 was Wednesday.

Now,

2000 to 2015 = 15 Years (12 Ordinary Years and 3 Leap Years).

So, 3 Leap Years have 6 odd days,

And, 12 Ordinary Years have 12 odd days.

Total odd days = 6 + 12 = 18.

18 odd days → 18/7 = 2 weeks and 4 odd days.

then, 19 July 2015 will be Wednesday + 4 = Sunday.

Now, the number of days between 17 March 2015 to 19 July 2015

= 14(March) + 30(Apr) + 31(May) + 30(June) + 19(July) = 124 days.

= 124 days → 124/7 = 17 weeks and 5 odd days.

So, 17 March 2015 will be Sunday - 5 = Tuesday.

Hence, the correct answer is "Option 2".

Given : 105 ÷ 2 + 4 - 120 × 6 = ? 

According to the question, after replacing the signs :

‘+’ and ‘-’ are interchanged 

‘×’ and ‘÷’ are interchanged

So,​​

105 × 2 - 4 + 120 ÷ 6 = ?

105 × 2 - 4 + 20 = ?

210 + 20 - 4 = ?

230 - 4 = ?

226 = ?

Hence, "226" is the correct answer.

The logic followed here is: No specific pattern is followed here, random digits are assigned to each letter of the word.

'RISK' is coded as '3921'

And,

'KIRT' is coded as '1693'

Therefore it can be concluded that :

S is coded as → 2

Hence, "Option 1" is the correct answer.

The logic followed here is:​

Hence, "Option 1" is the correct answer.

The logic followed here is:

Hence, "184.5" is the correct answer.

The logic followed here is:

Hence, "113" is the correct answer.

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 2".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: (1^st number × 3) = 2^nd number.

Now,

For, 129 : 387

⇒ 129 × 3 = 387.

For, 164 : 492

⇒ 164 × 3 = 492.

Similarly, for 148 : ?

⇒ 148 × 3 = 444.

Hence, the correct answer is "Option 1".

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some carrots are radish → Follow (As some carrots are onions, all onions are potatoes and all potatoes are radish. As some part of carrots is common with onions which whole comes in potatoes which whole comes in radish, therefore some carrots are radish is true.)

II. All onions are radish → Follow (As all onions are potatoes and all potatoes are radish. As some part of carrots is common with onions which whole comes in potatoes which whole comes in radish, therefore all onions are radish is true.)

III. No carrot is a potato → Does not follow (As some carrots are onions and all onions are potatoes. As no direct relation is given between carrot and potato, therefore no carrot is potato is false.)

∴ Here, Both conclusions I and II follow.​

Hence, the correct answer is "Both conclusions I and II follow"

The image embedded in the given figure is as shown below :

∴ Here, the given figure is embedded in option Figure - 3.

Hence, the correct answer is "Option 3".

According to the given figure:

The figure will appear when it is opened as follows:

Hence, "Option 2" is the correct answer.

The logic followed here is :

1. The first box series → Corner elements shift in the clockwise direction and the rest elements interchange positions.

2) The second box series → Bottom elements shift in the clockwise direction and the rest elements interchange positions. 

Thus, the final series is :

Hence, "Option 3" is the correct answer.

The logic followed here is:

Hence, "Option 4" is the correct answer.

Given: 10 October 2003 was Friday.

Now,

2003 to 2015 = 12 Years (9 Ordinary Years and 3 Leap Years).

And, In 12 Years = 3 Leap years and 9 Ordinary Years.

So, 3 Leap Years have 6 odd days,

And, 9 Ordinary Years have 9 odd days.

Total odd days = 6 + 9 = 15.

15 odd days → 15/7 = 2 weeks and 1 odd day.

Then, 10 October 2015 will be Friday + 1 = Saturday.

Now, the number of days between 10 October 2015 to 8 October 2015

= 2 days.

So, 8 October 2015 will be Saturday - 2 = Thursday.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: Opposites.

Here,

Allure : Repulse → Allure is the opposite of Repulse.

Similarly,

Creation : Destruction → Creation is the opposite of Destruction.

Fluctuate : Stabilize → Fluctuate is the opposite of Stabilize.

Notion : Reality → Notion is the opposite of Reality.

However,

Immense : Huge → Immense is not the opposite of Huge; they are synonyms.

Hence, the correct answer is "Option 2".

Decoding the Symbols:

 

 

 

 

Given: K = R ÷ M

K = R → K is the sister of R.

R ÷ M → R is the mother of M.

Here, K is the maternal aunt or mother’s sister of M.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: (1^st number)² = 2^nd number; 2^nd number × 2 = 3^rd number.

Now,

For, (4, 16, 32)

⇒ 4² = 16;

⇒ 16 × 2 = 32.

For, (7, 49, 98)

⇒ 7² = 49;

⇒ 49 × 2 = 98.

Similarly, for (12, 144, 288) 

⇒ 122 = 144;

⇒ 144 × 2 = 288.

Hence, the correct answer is "Option 2".

Calculation :-

( 9/4 × 16/5)  + (31/6 × 66/31 × 3/11) + (29/7 × 35/29)

36/5 + 3 + 5

76/5 = 15(1/5)

Shortcut Trick

When two people move in opposite directions, their relative speed is the sum of their individual speeds.

Relative Speed = 5.25 + 3 = 8.25 km/hr.

Time = Distance ÷ Relative Speed = 44 ÷ 8.25 = 16/3 hours.

16/3 hours = 5 hours + (1/3 × 60) minutes = 5 hours 20 minutes.

∴ The correct answer is 5 hr 20 min.

Alternate Method

Given:

Speed of Shyam = 5¹/₄ km/hr = 21/4 km/hr

Speed of Ram = 3 km/hr

Total Distance apart = 44 km

Formula Used:

Relative Speed (Opposite Direction) = Speed₁ + Speed₂

Time = Distance ÷ Relative Speed

Calculations:

⇒ Relative Speed = 21/4 + 3

⇒ Relative Speed = (21 + 12) / 4 = 33/4 km/hr

⇒ Time = 44 ÷ (33/4)

⇒ Time = (44 × 4) ÷ 33

⇒ Time = (4 × 4) ÷ 3 = 16/3 hours

⇒ Time = 5¹/₃ hours

⇒ Time = 5 hours + (1/3 × 60) minutes

⇒ Time = 5 hours 20 minutes

∴ The correct answer is 5 hr 20 min.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, the relative speed is the difference of their speeds: |S₁ − S₂|.

Speed Unit Conversion

To convert speed from km/hr to m/s, multiply by 5/18. To convert from m/s to km/hr, multiply by 18/5.

Average Speed for Constant Distance

If a person covers a distance at speed x and returns the same distance at speed y, average speed = (2xy) ÷ (x + y).

Given:

Original length of the field = L

Original breadth of the field = B

New length of the field = 70% of L = 0.7L

New breadth of the field = 90% of B = 0.9B

Formula Used:

Percentage Decrease in Area = ((Original Area - New Area) / Original Area) × 100

Calculation:

Original Area = L × B

New Area = 0.7L × 0.9B

New Area = 0.63LB

Percentage Decrease in Area = ((L × B - 0.63LB) / L × B) × 100

⇒ Percentage Decrease in Area = ((LB - 0.63LB) / LB) × 100

⇒ Percentage Decrease in Area = (0.37LB / LB) × 100

⇒ Percentage Decrease in Area = 0.37 × 100

⇒ Percentage Decrease in Area = 37%

The percentage decrease in the area of Rakesh's field is 37%.

Given:

The bar graph shows the production (in lakh units) of kitchen appliances for Company C over the years:

2012: 70 lakh

2013: 90 lakh

2014: 120 lakh

2015: 80 lakh

2016: 110 lakh

2017: 140 lakh

Formula used:

Percentage change = $\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100$

Calculations:

From 2012 to 2013:

⇒ $\frac{90 - 70}{70} \times 100 = 28.57\%$

From 2013 to 2014:

⇒ $\frac{120 - 90}{90} \times 100 = 33.33\%$

From 2014 to 2015:

⇒ $\frac{80 - 120}{120} \times 100 = -33.33\%$

From 2015 to 2016:

⇒ $\frac{110 - 80}{80} \times 100 = 37.5\%$

From 2016 to 2017:

⇒ $\frac{140 - 110}{110} \times 100 = 27.27\%$

∴ The maximum percentage change in production for Company C occurred from 2015 to 2016, with a 37.5% fall.

Shortcut Trick

If all questions were answered correctly, the total score would be 160 × 4 = 640 marks.

The total marks lost from the maximum possible score = 640 − 400 = 240 marks.

Marks lost per incorrect or un-attempted question = 4 (for correct) + 1 (penalty) = 5 marks.

Number of incorrect or un-attempted questions = 240 ÷ 5 = 48.

Number of correctly answered questions = 160 − 48 = 112.

∴ The correct answer is 112 questions.

Alternate Method

Given:

Total questions = 160

Marks for a correct answer = +4

Marks for a wrong or un-attempted answer = −1

Total score obtained = 400 marks

Method Used: Alligation

⇒ If all 160 questions are correct, total score = 160 × 4 = +640

⇒ If all 160 questions are wrong or un-attempted, total score = 160 × (−1) = −160

⇒ The ratio of Correct to Wrong questions = 560 : 240 = 7 : 3

⇒ Total ratio parts = 7 + 3 = 10 parts

⇒ 10 parts = 160 questions

⇒ 1 part = 160 ÷ 10 = 16 questions

⇒ Correct questions = 7 parts = 7 × 16 = 112 questions

∴ The correct answer is 112 questions.

Additional Information

Linear Equation Approach

Let the number of correct answers be x. Then the incorrect or un-attempted answers will be (160 − x). The equation is formulated as 4x − 1(160 − x) = 400.

Rule of Alligation

It is a quick cross-multiplication visual method used to find the ratio in which two components of different values are combined to produce a specific average overall value.

Penalty Mark Evaluation

In negative marking exams, each mistake causes a total loss equal to the correct mark plus the penalty mark. For example, in this case, the total loss per error is 4 + 1 = 5 marks.

Given:

Initial selling price = ₹5,000

Decreased selling price = ₹4,680

Loss percentage increased by 4%

Desired profit percentage = 4%

Formula Used:

Loss% = (Cost Price - Selling Price) / Cost Price × 100

Selling Price for desired profit = Cost Price × (1 + Profit%)

Calculation:

Let Cost Price be CP.

Initial Loss% = (CP - 5000) / CP × 100

New Loss% = (CP - 4680) / CP × 100

New Loss% = Initial Loss% + 4%

⇒ (CP - 4680) / CP × 100 = (CP - 5000) / CP × 100 + 4

⇒ 100(CP - 4680) = 100(CP - 5000) + 4CP

⇒ 100CP - 468000 = 100CP - 500000 + 4CP

⇒ -468000 = -500000 + 4CP

⇒ 4CP = 32000

⇒ CP = 8000

To get 4% profit:

Selling Price = CP × (1 + 4/100)

⇒ Selling Price = 8000 × 1.04

⇒ Selling Price = 8320

The selling price of the item should be ₹8,320 to get a 4% profit.

Given:

Radius of the first circle = 6 cm

Radius of the second circle = 3 cm

Solution:

1. Distance Between the Centers:

Distance between centers = 6 + 3 = 9 cm

2. Length of the Common Tangent:

Length of the common tangent = √[(6 + 3)² - (6 - 3)²]

Substitute the values:

Length of the common tangent = √[9² - 3²]

= √[81 - 9]

= √72

= 6√2

Answer:

The length of the common tangent is 6√2 cm.

Given:

The exports (in Rs. crore) from Companies A and B for the years are as follows:

1995: Company A = 60, Company B = 125

1996: Company A = 72, Company B = 138

1997: Company A = 80, Company B = 145

1998: Company A = 95, Company B = 152

1999: Company A = 102, Company B = 172

Formula used:

Difference between exports = |A - B|

Calculations:

For 1995: |60 - 125| = 65

For 1996: |72 - 138| = 66

For 1997: |80 - 145| = 65

For 1998: |95 - 152| = 57

For 1999: |102 - 172| = 70

∴ The minimum difference between exports from Companies A and B occurred in 1998, with a difference of 57 crore.

Given:

Price of laptop = Rs. 48,000

Discount on first Rs. 28,000 = 12%

Discount on next Rs. 12,000 = 8%

Total discount to match = 9.5%

Remaining amount to discount = Rs. 8,000

Formula Used:

Total discount = (Discount on first part) + (Discount on second part) + (Discount on remaining part)

Calculation:

Discount on first Rs. 28,000 = 28,000 × 12/100

⇒ Rs. 3,360

Discount on next Rs. 12,000 = 12,000 × 8/100

⇒ Rs. 960

Total discount on Rs. 48,000 at 9.5% = 48,000 × 9.5/100

⇒ Rs. 4,560

Remaining discount to offer = Total discount - (Discount on first part + Discount on second part)

Remaining discount to offer = 4,560 - (3,360 + 960)

⇒ Rs. 240

Rohan should offer a discount of Rs. 240 on the remaining Rs. 8,000 to match the total discount of 9.5%.

Given:

Two parallel chords, each of length 8 units, are 6 units apart in a circle.

Formula used:

For a chord of length 2a at a distance d from the center of a circle with radius r:

We use the formula for the distance from the center to the chord:

r² = d² + a²

Where a is half the length of the chord.

Calculations:

Let the distance from the center of the circle to one chord be d₁, and to the other chord be d₂.

Since the chords are 6 units apart, we assume one chord is 3 units above the center, and the other is 3 units below.

Half the length of each chord is a = 8/2 = 4 units.

For the first chord, the distance from the center is 3 units:

⇒  r² = 3² + 4² = 9 + 16 = 25 

⇒  r = √25 = 5 units

∴ The radius of the circle is 5 units.

Shortcut Trick

Ratio of Volume of Cylinder to Volume of Sphere gives the number of balls.

Number of balls (n) = (π × r² × 12r) ÷ [4/3 × π × (r/3)³]

n = 12 ÷ (4 / (3 × 27)) = 12 ÷ (4 / 81)

n = 12 × 81 ÷ 4 = 3 × 81 = 243

∴ The correct answer is 243.

Alternate Method

Given:

Radius of the cylinder = r

Height of the cylinder (h) = 12r

Radius of each spherical ball (r_s) = r/3

Formula Used:

Volume of Cylinder = πr²h

Volume of Sphere = 4/3 πr³

Calculations:

⇒ Total Volume of iron = Volume of the cylindrical rod

⇒ Volume of cylinder = π × r² × 12r = 12πr³

⇒ Volume of one spherical ball = 4/3 × π × (r/3)³

⇒ Volume of one ball = 4/3 × π × (r³ / 27) = 4πr³ / 81

⇒ Let 'n' be the number of spherical balls

⇒ n × (4πr³ / 81) = 12πr³

⇒ n = (12πr³ × 81) / (4πr³)

⇒ n = 3 × 81

⇒ n = 243

∴ The correct answer is 243.

Additional Information

Conservation of Volume

When a 3D solid is melted and recast into another shape, the total volume remains constant, assuming no wastage.

Cylinder Surface Area

The Curved Surface Area (CSA) of a cylinder is 2πrh, and the Total Surface Area (TSA) is 2πr(h + r).

Sphere Surface Area

The surface area of a sphere is given by the formula 4πr².

Volume Ratios

If dimensions are scaled by a factor k, the volume changes by a factor of k³.

Given:

Perimeter ratio of two similar triangles = 4 ∶ 7

Sum of the areas of two triangles = 195 cm²

Formula Used:

If the perimeters of two similar triangles are in the ratio a ∶ b, then their areas are in the ratio a² ∶ b².

Calculation:

Perimeter ratio = 4 ∶ 7

Area ratio = 4² ∶ 7² = 16 ∶ 49

Let the areas of the two triangles be 16x and 49x.

⇒ 16x + 49x = 195

⇒ 65x = 195

⇒ x = 195 / 65

⇒ x = 3

Area of the first triangle = 16x = 16 × 3 = 48 cm²

Area of the second triangle = 49x = 49 × 3 = 147 cm²

Difference between the areas = 147 - 48 = 99 cm²

(1/3) of the difference between the areas = 99 / 3 = 33 cm²

The correct answer is option 2.

Shortcut Trick

Side of each cube = √[3]{216} = 6 cm.

Area of one face = 6 × 6 = 36 sq cm.

Total faces in 4 cubes = 4 × 6 = 24 faces.

When 4 cubes are joined, 3 junctions are formed, hiding 3 × 2 = 6 faces.

Remaining visible faces = 24 − 6 = 18 faces.

Total surface area = 18 × 36 = 648 sq cm.

∴ The correct answer is 648 sq cm.

Alternate Method

Given:

Volume of each cube = 216 cm³

Number of cubes = 4

Formula:

Side of cube (a) = (Volume)^1/3

Surface area of cuboid = 2(lb + bh + hl)

⇒ Side of each cube (a) = √[3]{216} = 6 cm

⇒ When joined end-to-end, only the length changes.

⇒ Length (l) = 4 × 6 = 24 cm

⇒ Breadth (b) = 6 cm

⇒ Height (h) = 6 cm

⇒ Surface Area = 2 × (24×6 + 6×6 + 6×24)

⇒ Surface Area = 2 × (144 + 36 + 144)

⇒ Surface Area = 2 × 324 = 648 sq cm

∴ The correct answer is 648 sq cm.

Additional Information

Surface Area of a Cube

The total surface area of a single cube with side 'a' is 6a².

Volume of a Cuboid

The amount of space occupied by a cuboid is given by Length × Breadth × Height (l × b × h).

Lateral Surface Area

For a cuboid, the area of the four side walls is 2h(l + b).

Diagonal of a Cuboid

The longest rod that can be placed in a cuboid has length √(l² + b² + h²).

Shortcut Trick

Ratio of Areas of similar triangles = Square of the ratio of Corresponding Sides.

Area(ΔABC) : Area(ΔEDF) = 9 : 4 ⇒ Ratio of sides = √9 : √4 = 3 : 2.

Since ΔABC ∼ ΔEDF, side BC corresponds to side DF.

3 units = BC = 8 cm ⇒ 1 unit = 8/3 cm.

2 units = DF = 2 × (8/3) = 16/3 = 5 1/3 cm.

∴ The correct answer is 5 1/3 cm.

Alternate Method

Given: ΔABC ∼ ΔEDF, AB = 5 cm, BC = 8 cm, AC = 10 cm, Area(ΔABC) : Area(ΔEDF) = 9 : 4.

Formula: If Δ1 ∼ Δ2, then Area(Δ1)/Area(Δ2) = (Side1/Side2)².

For similar triangles ΔABC and ΔEDF, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

⇒ Area(ΔABC) / Area(ΔEDF) = (BC / DF)²

⇒ 9 / 4 = (8 / DF)²

Taking square root on both sides:

⇒ √(9 / 4) = 8 / DF

⇒ 3 / 2 = 8 / DF

⇒ 3 × DF = 8 × 2

⇒ 3 × DF = 16

⇒ DF = 16 / 3

⇒ DF = 5 1/3 cm

∴ The correct answer is 5 1/3 cm.

Additional Information

Area and Side Ratio Theorem

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of any two corresponding sides, altitudes, medians, or angle bisectors.

Similarity Criteria

Triangles are similar if they satisfy AA (Angle-Angle), SAS (Side-Angle-Side), or SSS (Side-Side-Side) conditions.

Perimeter Ratio

The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides: P1/P2 = s1/s2.

Given:

α + β = 45º

(tanα + 1)(tan β + 1) = 2x

Formula Used:

Using the identity: tan(α + β) = (tanα + tanβ) / (1 - tanαtanβ)

Since α + β = 45º, tan 45º = 1

So, 1 = (tanα + tanβ) / (1 - tanαtanβ)

Calculation:

1 = (tanα + tanβ) / (1 - tanαtanβ)

⇒ 1 - tanαtanβ = tanα + tanβ

⇒ tanα + tanβ + tanαtanβ = 1

Let tanα = a and tanβ = b

⇒ a + b + ab = 1

Given: (a + 1)(b + 1) = 2x

⇒ ab + a + b + 1 = 2x

We know a + b + ab = 1

⇒ 1 + 1 = 2x

⇒ 2 = 2x

⇒ x = 1

The correct answer is option 4.

Given:

Area of the triangle = 18 cm²

Base of the triangle = 6 cm

Formula Used:

Area of a triangle = 1/2 × Base × Height

Calculation:

Using the formula:

Area = 1/2 × Base × Height

⇒ 18 = 1/2 × 6 × Height

⇒ 18 = 3 × Height

⇒ Height = 18 / 3

⇒ Height = 6 cm

The height of the triangle is 6 cm.

Given:

Ratio of students in CS, EC, CE, and ME branches = 11 ∶ 5 ∶ 6 ∶ 7

Formula Used:

Percentage of students in a branch = (Number of students in the branch / Total number of students) × 100

Calculation:

Let the number of students in CS be 11x, in EC be 5x, in CE be 6x, and in ME be 7x.

Total number of students = 11x + 5x + 6x + 7x

Total number of students = 29x

Number of students in CS and ME = 11x + 7x = 18x

Percentage of students in CS and ME branches = (18x / 29x) × 100

⇒ Percentage of students in CS and ME branches = (18 / 29) × 100

⇒ Percentage of students in CS and ME branches = 0.6207 × 100

⇒ Percentage of students in CS and ME branches = 62.07%

The percentage of students belonging to CS and ME branches in the college is 62.07%.

Shortcut Trick

Valid votes = 100% − 15% = 85% of total votes.

Other candidate's share of valid votes = 100% − 60% = 40%.

Number of votes for other candidate = 8400 × 85% × 40%.

Calculation: 8400 × (85/100) × (40/100) = 84 × 85 × 0.4 = 2856.

∴ The correct answer is 2856.

Alternate Method

Given: Total votes = 8400, Invalid votes = 15%, Winner's share = 60% of valid votes.

⇒ Total votes = 8400

⇒ Valid votes = 8400 × (100 − 15)/100 = 8400 × 85/100

⇒ Valid votes = 84 × 85 = 7140

⇒ Other candidate's percentage = 100% − 60% = 40%

⇒ Votes for other candidate = 7140 × (40/100) = 714 × 4

⇒ Votes for other candidate = 2856

∴ The correct answer is 2856.

Additional Information

Percentage of a Quantity

To find x% of a value y, use the formula: Value = (x/100) × y.

Valid and Invalid Votes

In election problems, Total Votes = Valid Votes + Invalid Votes. Candidate shares are usually calculated based on Valid Votes unless stated otherwise.

Successive Percentage Reduction

If a value is reduced by a% and then the remaining is distributed as b% and (100−b)%, the final part is: Total × [(100−a)/100] × [(100−b)/100].

Shortcut Trick

Total interest in percentage = (4 ÷ 5) × 100 = 80%.

This total interest is for a duration of 8 years.

Annual Rate of Interest = Total Interest % ÷ Time = 80% ÷ 8 = 10%.

∴ The correct answer is 10%.

Alternate Method

Given:

Time (T) = 8 years

Simple Interest (SI) = 4/5 of Principal (P)

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ Let the Principal (P) be 5 units.

⇒ Simple Interest (SI) = 4/5 × 5 = 4 units.

⇒ Using the formula: 4 = (5 × R × 8) ÷ 100

⇒ 4 = (40 × R) ÷ 100

⇒ 4 = 0.4 × R

⇒ R = 4 ÷ 0.4

⇒ R = 10%

∴ The correct answer is 10%.

Additional Information

Simple Interest Components

Simple interest is calculated only on the initial Principal amount throughout the entire Time period at a constant Rate.

Amount Formula

The total Amount (A) at the end of the term is the sum of Principal and Interest: A = P + SI = P(1 + RT/100).

Rule of SI Variation

If the Principal and Time are constant, the Simple Interest is directly proportional to the Rate of Interest.

Given:

Chocolate ice creams sold = 400

Chocolate percentage = 40%

Vanilla percentage = 35%

Formula used:

Total ice creams sold = $\frac{\text{Chocolate ice creams}}{\text{Chocolate percentage}} \times 100$

Vanilla ice creams sold = $\frac{\text{Vanilla percentage}}{100} \times \text{Total ice creams}$

Calculation:

Total ice creams sold = $\frac{400}{40} \times 100 = 1000$

Vanilla ice creams sold = $\frac{35}{100} \times 1000 = 350$

∴ The number of vanilla ice creams sold is 350.

Calculations:

Total students = 1500

Cricket percentage = 35%

Tennis percentage = 20%

Students selected for cricket = 35% of 1500 = 0.35 × 1500 = 525

Students selected for tennis = 20% of 1500 = 0.20 × 1500 = 300

Total students selected for cricket and tennis = 525 + 300 = 825

Given:

Number of students with an average score of 80 = 15

Average score of these 15 students = 80

Number of students with an average score of 60 = 25 - 15 = 10

Average score of these 10 students = 60

Formula Used:

Average score of the whole class = Total score of all students / Total number of students

Calculation:

Total score of 15 students = 15 × 80

⇒ Total score of 15 students = 1200

Total score of 10 students = 10 × 60

⇒ Total score of 10 students = 600

Total score of the whole class = 1200 + 600

⇒ Total score of the whole class = 1800

Total number of students = 25

Average score of the whole class = 1800 / 25

⇒ Average score of the whole class = 72

The average score of the whole class is 72.

Calculations:

The numbers after adding x to 7, 11, 18, and 23 will be: 7 + x, 11 + x, 18 + x, and 23 + x.

Since they are in proportion:

7 + x / 11 + x = 18 + x / 23 + x

Cross multiplying, we get:

(7 + x)(23 + x) = (11 + x)(18 + x)

Expanding both sides:

161 + 30x + x² = 198 + 29x + x²

Canceling x² from both sides:

161 + 30x = 198 + 29x

Simplifying:

30x - 29x = 198 - 161

x = 37

Now, we need to find the mean proportional between x - 1 and 2x - 10.

x - 1 = 37 - 1 = 36

2x - 10 = 2(37) - 10 = 74 - 10 = 64

The mean proportional between 36 and 64 is:

√(36 × 64) = √(2304) = 48

∴ The mean proportional between x - 1 and 2x - 10 is 48.

Shortcut Trick Express n in terms of both quotients and remainders. n = 18x + 6 and n = 25y + 15. Equating both: 18x + 6 = 25y + 15. Rearranging: 18x − 25y = 15 − 6 = 9. ∴ The correct answer is 18x − 25y = 9.

Alternate Method Given: n divided by 18 gives quotient x and remainder 6. n divided by 25 gives quotient y and remainder 15. Formula Used: Dividend = (Divisor × Quotient) + Remainder

Calculations: ⇒ Case 1: n = 18 × x + 6 ⇒ Case 2: n = 25 × y + 15 ⇒ Equating n: 18x + 6 = 25y + 15 ⇒ 18x − 25y = 15 − 6 ⇒ 18x − 25y = 9 ∴ The correct answer is 18x − 25y = 9.

Additional Information Euclid's Division Lemma For any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. Linear Diophantine Equation Equations of the form ax + by = c are solvable if the greatest common divisor (GCD) of a and b divides c. Verification Rule Always ensure the remainder is smaller than the divisor. If n = dq + r, then r must be in the range [0, d−1].

Shortcut Trick

Efficiency ratio of Riya and Sangeeta = 4 : 3 (Total work = 24).

Riya works alone for 3 days: 3 × 4 = 12 units done.

Remaining work (24 − 12 = 12 units) done by both: 12 ÷ (4 + 3) = 1 5/7 days.

Total time = 3 + 1 5/7 = 4 5/7 days.

∴ The correct answer is 4 5/7 days.

Alternate Method

Given:

Time taken by Riya = 6 days

Time taken by Sangeeta = 8 days

Calculations:

⇒ Total Work = LCM of 6 and 8 = 24 units.

⇒ Work completed by Riya in first 3 days = Efficiency × Time = 4 × 3 = 12 units.

⇒ Remaining work = 24 − 12 = 12 units.

⇒ Combined efficiency of Riya and Sangeeta = 4 + 3 = 7 units/day.

⇒ Time taken to finish remaining work = 12 ÷ 7 = 1 5/7 days.

⇒ Total duration of work = 3 days + 1 5/7 days = 4 5/7 days.

Therefore, the total time the work lasted is 4 5/7 days, which corresponds to Option (4).

∴ The correct answer is 4 5/7 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. Efficiency = Total Work ÷ Time.

Combined Work Formula

If A does work in 'x' days and B in 'y' days, together they take (x × y) ÷ (x + y) days to complete the entire work.

Partial Work Remaining

When a person leaves or joins, always subtract the work already done from the total work to find the remaining task.

The Correct is Answer Nobel Peace Prize.

Key Points

• Borlaug's work in developing high-yielding varieties of wheat and other grains significantly increased agricultural production, helping to alleviate hunger and poverty in many countries.
• His contributions to global food security were recognized with the Nobel Peace Prize in 1970.
• Borlaug is often referred to as the "Father of the Green Revolution" due to his pioneering efforts in agricultural research and development.
• His work has had a lasting impact on the world's food supply and has saved countless lives.

Important Points

• M.S. Swaminathan: An Indian agricultural scientist who played a crucial role in the Green Revolution in India.
• Indira Gandhi: The Prime Minister of India during the Green Revolution, who provided political and financial support for agricultural development.
• Robert McNamara: The President of the World Bank during the Green Revolution, who helped to finance agricultural development projects in developing countries.

The Correct is Answer Makemake.

Key Points

 

• Makemake is a distant dwarf planet located in the Kuiper Belt, a region beyond Neptune's orbit.  

1. Makemake - NASA Science

science.nasa.gov

• It has an orbital period of approximately 310 years and an average distance from the Sun of about 45.5 astronomical units (AU).

Additional Information

• Makemake was discovered in 2005 and is named after the Polynesian creation deity.  

1. Makemake - NASA Science

science.nasa.gov

• It is one of the largest known dwarf planets in the Solar System, with a diameter estimated to be around 1,430 kilometres.
• Makemake is believed to have a cold, icy surface and is thought to be a potentially habitable world due to the possibility of subsurface oceans.

The correct answer is André-Marie Ampère.

Key Points

• Ampère's Law describes the relationship between electric current and the magnetic field it produces.

1. Magnetic Fields Produced by Currents: Ampere's Law | Physics

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• He discovered that parallel wires carrying currents in the same direction attract each other, while wires carrying currents in opposite directions repel each other.
• Ampère was a French physicist and mathematician who made significant contributions to the understanding of electromagnetism.
• His work laid the foundation for the development of electric motors, generators, and other electromagnetic devices.

Additional Information 

• Ampère's Law is a fundamental equation in electromagnetism that relates the magnetic field to the electric current producing it. It states that the line integral of the magnetic field around a closed loop is equal to the product of the permeability of free space (μ₀) and the total current passing through the loop.

Mathematical Expression: ∮ B · dl = μ₀I_enc  ​ 

1. www.numerade.com

www.numerade.com

1. www.numerade.com

www.numerade.com

• B: Magnetic field vector
• dl: Line element along the closed loop
• μ₀: Permeability of free space (4π × 10⁻⁷ T·m/A)
• I_enc: Net current enclosed by the loop

The correct answer is average fixed cost.

 Key Points

• AFC is the average fixed cost per unit of output, calculated by dividing total fixed costs by the quantity of output produced.
• ​Behavior: AFC decreases as output increases since fixed costs remain constant, but they are spread over more units of output.
• Graph Shape: The AFC curve is downward sloping and never touches the axes, indicating that as output rises, AFC approaches but never reaches zero.

 Additional Information

• Rectangular Hyperbola
• Geometerically, it is a curve where (x,y) co-ordinates of the production at any point on the curve becomes constant.
• The graph indicates inverse relationship.
• Some other important Cost curves:
• Total Cost Curve: It is the sum of Total fixed costs and Total Variable Costs.
• Average Cost Curve (Average Total Cost): it is the ratio of Total cost to the quantity of output produced.
• Marginal cost: It is additional cost of producing one more unit of output.

Solution: The correct answer is Federalism.

Key Points

• The establishment of UPSC, SPSC's, and JPSC's falls under "Federal" feature of Indian Constitution.
• The role and creation of all these Commissions  are enshrined in Part-XIV (14) of Constitution of India.
• Article 315 to 323, deals with the establishment appointments role and participations of these commissions.
• These commission are formed to maintain and regulate public services for general and essential purposes in country.

Additional Information Fundamental Rights

• Fundamental rights are enshrined part-III of Indian constitution form article 12 to 35.
• They are known as Magna Carta.
• They are provided protection against the rights which sometimes violated by the state/country.

Parliamentary government

• A Parliamentary form of Government is defined as a setup in which the Executive is directly answerable to legislature.
• Parliament is formed by the elected members through voting.
• The elected members are directly answerable to the people of land.
• INDIA is an example of Parliamentary form of Government.

Directive Principles of State Policy (DPSP's)

• DPSP's are instructions given to government while framing any policy or law for the peoples of india.
• These are enshrined in Part-IV of Indian Constitution from articles 36 to 51.
• These are non-justiciable in Court of law.
• Some important DPSP's are:
• Article 38: state to secure a social order for the promotion of the welfare of the people.
• Article 39: certain principles of policy to be followed by the state, such as the right to adequate means of livelihood, equal pay for equal work, and protection of children.
• Article 40: organization of village panchayats.
• Article 41: right to work, education, and public assistance in certain cases.
• Article 44: uniform civil code for the citizens.
• Article 45: provision for early childhood care and education to children below the age of six years.
• Article 48: organization of agriculture and animal husbandry.
• Article 50: separation of judiciary from the executive.

The Correct answer is Sakshi Malik.

Key Points

• Sakshi Malik was the first Indian Women Wrestler to win Medal in Olympics.
• She won this medal in 2016 Olympics held in Rio de Janeiro.
• She won the Bronze medal in 56 kg weight freestyle wrestling category.
• She had honoured with Rajiv Gandhi Khel Ratna Award **(**presently known as Major Dhyan Chand Khel Ratna Award) and Padma Shri in 2017.

 Additional InformationGeeta Phogat

• Geeta Phogat is an Indian freestyle wrestler.
• She won the gold medal in the 55 kg freestyle category at the 2010 Commonwealth Games held in Delhi.
• She was the the first Indian woman wrestler to win a gold medal at the Commonwealth Games.

​Babita Phogat

• Babita Phaogat is also a renounced wrestling player of India
• She won Silver medal in Commonwealth Games 2010.
• She won Gold medal in Commonwealth Games 2014.
• She won Silver medal in Commonwealth Games 2018.

Alka Tomar

• Alka Tomar is also Prominent Wrestler of India.
• She won Gold medal at Commonwealth Wrestling Championship.

Important Points

• Olympics
• Anciently, it was originated in Greece in 776BC. Modern Olympics were started in 1896. It held after every four years.
• There are two forms of Olympics: Summer Olympics and Winter Olympics.
• it is organized by  International Olympic Committee.
• its symbol have 5 rings where each ring represents one continent..

The correct answer is Uruguay.

Key Points

• The first FIFA World Cup was hosted by Uruguay.
• The choice of Uruguay as the host country was influenced by its recent success in football, having won gold in the 1924 and 1928 Olympic Games.
• FIFA (Fédération Internationale de Football Association), founded in 1904, sought to organize a world football championship independent of the Olympics.
• The inaugural FIFA World Cup took place from July 13 to July 30, 1930.
• Uruguay became the first-ever FIFA World Cup champion by defeating Argentina by 4-2 in the final.

Additional Information

• The 1930 World Cup was organized to celebrate the 100^th anniversary of Uruguay's independence.
• 13 teams participated:
• 7 from South America: Argentina, Brazil, Chile, Bolivia, Paraguay, Peru, Uruguay.
• 4 from Europe: Belgium, France, Romania, Yugoslavia.
• 2 from North America: Mexico and the United States.

The correct answer is Eid-Ul-Fitr.

Key Points

• Eid al-Fitr, also known as the "Festival of Breaking the Fast," is celebrated by Muslims worldwide.
• It is celebrated to mark the end of Ramadan, a month of fasting, prayer, and reflection.
• It is a day of joy and thanksgiving to Allah for the strength and patience shown during the month of fasting.
• The festival is also a time for community prayers, and giving charity (known as Zakat al-Fitr).

Additional Information

The correct answer is Thawarchand Gehlot.

Key Points

• Thawarchand Gehlot is an Indian politician from the Bharatiya Janata Party (BJP).
• He was appointed as the Governor of Karnataka in July 2021.
• He is currently serving as Governor of Karnataka.
• Prior to that, he was the Minister of Social Justice and Empowerment in the Government of India.

Additional Information

• In July 2021, Hari Babu Kambhampati was serving as the Governor of Mizoram. He is currently serving as Governor of Mizoram.
• In July 2021, Rajendra Vishwanathan was the Governor of the Indian state of Sikkim. Rajendra Vishwanath is currently serving as the governor of the state of Arunachal Pradesh.
• In July 2021, Arjun Munda was serving as the Minister of Tribal Affairs in the Government of India. Currently, the Minister of Tribal Affairs is Shri Jual Oram.