SSC CHSL Tier-1 2024: Official Paper (Held On: 02 Jul, 2024 Shift 3) (Previous Year Paper)

The correct answer is: A.

 

Key Points

• The primary issue in the sentence is the omission of the preposition "to" after the verb "live."
• The correct phrase should be "live up to" to indicate meeting expectations or standards.
• Thus, the error is located in part A of the sentence.

Therefore, the correct answer is A.

 

Correct Sentence: "It is difficult to live up to the societal expectations when one has fewer resources.

The correct answer is Option 3.

 

Key Points

• The primary issue in the sentence is the use of "too intelligent" in part D.
• Using "too intelligent" implies more intelligence than is acceptable or needed, which is not the intended meaning. The correct wording should be "very intelligent."
• Thus, the error is located in part D of the sentence.

Therefore, the correct answer is Option 3)

 

Correct Sentence: "Since the little girl answers a few simple questions, her parents say that she is very intelligent."

 

Additional Information

• Since the little girl answers – This part of the sentence is grammatically correct and does not require any changes.
• her parents say that – This part of the sentence is grammatically correct and does not require any changes.
• she is too intelligent – The word "too" is incorrect here, and "very" should be used instead.
• a few simple questions – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is Option 4.

 

Key Points

• The primary issue in the sentence is the incorrect usage of the indefinite article "an" with "ice" in part D.
• The word "ice" is an uncountable noun and does not require an indefinite article. The correct phrase should be "some ice" or simply "ice."
• Thus, the error is located in part D of the sentence.

Therefore, the correct answer is D.

 

Correct Sentence: "We took some ice and applied it on the wound."

 

Additional Information

• We took – This part of the sentence is grammatically correct and does not require any changes.
• and applied it on – This part of the sentence is grammatically correct and does not require any changes.
• the wound. – This part of the sentence is grammatically correct and does not require any changes.
• an ice – The indefinite article "an" is incorrectly used here. Replace it with "some ice" or simply "ice."

The correct answer is Option 2.

 

Key Points

• The phrase "looking around" is incorrect in the context of the sentence. The correct preposition here is "for" to indicate searching.
• Therefore, the correct form of the sentence should be "What are you looking for?"
• Thus, the correct option is Option 2.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "What are you looking for?"

 

Additional Information

• What are you looking across? – This is not the correct preposition for this context.
• What are you looking for? – This is the correct option as it indicates searching for something.
• What are you looking through? – This implies examining or searching something within a container or medium, which is not appropriate here.
• What are you looking among? – This implies searching within a group or collection, which is not suitable here.

The correct answer is 'large'.

 

Key Points

• The passage emphasizes the importance of a sufficient population to support cultural and social amenities in cities.
• A "large" population is necessary for maintaining museums, concert halls, sports teams, and nightlife districts.
• "Large" fits well within the context of a vibrant city life dependent on a substantial number of residents.
• Other options (dumb, lazy, small) do not accurately describe the type of population needed to sustain these institutions.

Therefore, the correct answer is 'Option 3'.

 

Complete Passage: Cities are the great havens for knowledge, culture, and social life. Vibrant cultures are found in cities because it takes a 1. large population to support museums, concert halls, sports teams, and night-life districts. Cities also offer rich social opportunities. People in rural areas enjoy only limited social opportunities because 2. of the small local population. City dwellers can choose their friends and mates from among a large number of people of 3. diverse interests and inclinations. We are not likely to abandon the city as a 4. vital institution, but we need to make sure that our transport arrangements do not 5. undermine the 'city’s' other functions.

 

Additional Information

• Dumb (मूर्ख): "Dumb" means a lack of intelligence, which does not describe the population needed for vibrant cultural and social life.
• Lazy (आलसी): "Lazy" means unwilling to work or use energy, which does not fit the context of a population contributing to city life.
• Small (छोटा): "Small" means of limited size, which contradicts the need for a substantial population to support city institutions.

The correct answer is 'of'.

 

Key Points

• The passage explains why people in rural areas have limited social opportunities.
• The phrase "because of" is commonly used to indicate the reason or cause of something.
• "Of" fits perfectly in the context of explaining the limited social opportunities due to the small local population.
• Other options (for, off, with) do not accurately convey the intended meaning in this context.

Therefore, the correct answer is 'Option 4'.

 

Complete Passage: Cities are the great havens for knowledge, culture, and social life. Vibrant cultures are found in cities because it takes a 1. large population to support museums, concert halls, sports teams, and night-life districts. Cities also offer rich social opportunities. People in rural areas enjoy only limited social opportunities because 2. of the small local population. City dwellers can choose their friends and mates from among a large number of people of 3. diverse interests and inclinations. We are not likely to abandon the city as a 4. vital institution, but we need to make sure that our transport arrangements do not 5. undermine the 'city’s' other functions.

 

Additional Information

• For (के लिए): "For" typically indicates purpose or benefit and does not fit the context of explaining a cause.
• Off (बंद): "Off" indicates separation or disconnection, which does not convey the cause of limited social opportunities.
• With (साथ): "With" indicates accompaniment, which does not accurately explain the cause in this context.

The correct answer is 'similar'.

 

Key Points

• The passage highlights the advantage of city dwellers in choosing friends and mates from a large number of people.
• The word "similar" aligns well with the idea of people having common interests and inclinations.
• "Similar" fits perfectly in this context as it implies a shared or common thread among city inhabitants' interests and inclinations.
• Other options (feigning, wasteful, declining) do not fit the context of describing the nature of interests and inclinations.

Therefore, the correct answer is 'Option 2'.

 

Complete Passage: Cities are the great havens for knowledge, culture, and social life. Vibrant cultures are found in cities because it takes a 1. large population to support museums, concert halls, sports teams, and night-life districts. Cities also offer rich social opportunities. People in rural areas enjoy only limited social opportunities because 2. of the small local population. City dwellers can choose their friends and mates from among a large number of people of 3. similar interests and inclinations. We are not likely to abandon the city as a 4. vital institution, but we need to make sure that our transport arrangements do not 5. undermine the 'city’s' other functions.

 

Additional Information

• Feigning (दिखावा): "Feigning" means pretending, which is not related to the shared interests and inclinations among city dwellers.
• Wasteful (अपव्ययी): "Wasteful" means using resources carelessly, which does not fit the context of interests and inclinations.
• Declining (गिरावट): "Declining" means becoming smaller or less, which does not appropriately describe the nature of people’s interests and inclinations.

The correct answer is 'cultural'.

 

Key Points

• The passage speaks about the various attributes that make cities centers for knowledge, culture, and social life.
• The term "cultural institution" aligns with the context of supporting museums, concert halls, sports teams, and night-life districts.
• "Cultural" substantially fits within the context as it denotes the hub for artistic and social activities often found in cities.
• Other options (educational, psychological, religious) do not comprehensively describe the nature of institutions that contribute to the vibrant life in a city according to the passage.

Therefore, the correct answer is 'Option 3'.

 

Complete Passage: Cities are the great havens for knowledge, culture, and social life. Vibrant cultures are found in cities because it takes a 1. large population to support museums, concert halls, sports teams, and night-life districts. Cities also offer rich social opportunities. People in rural areas enjoy only limited social opportunities because 2. of the small local population. City dwellers can choose their friends and mates from among a large number of people of 3. similar interests and inclinations. We are not likely to abandon the city as a 4. cultural institution, but we need to make sure that our transport arrangements do not 5. undermine the 'city’s' other functions.

 

Additional Information

• Educational (शैक्षणिक): While education is important, the passage is focused more broadly on cultural and social aspects.
• Psychological (मनोवैज्ञानिक): "Psychological" pertains to the mind and behavior and does not describe the broad cultural role mentioned.
• Religious (धार्मिक): Although cities can be religious centers, the passage does not specifically focus on religion in the context being discussed.

The correct answer is 'damage'.

 

Key Points

• The passage discusses making sure that transport arrangements do not negatively impact or harm the city's functions.
• The word "damage" accurately conveys the idea of transport arrangements potentially harming other city functions.
• "Damage" is well-suited in this context as it indicates the need to avoid negative consequences for the city’s multifaceted roles.
• Other options (support, boost, help) do not convey the potential negative impact that the passage aims to avoid.

Therefore, the correct answer is 'Option 3'.

 

Complete Passage: Cities are the great havens for knowledge, culture, and social life. Vibrant cultures are found in cities because it takes a 1. large population to support museums, concert halls, sports teams, and night-life districts. Cities also offer rich social opportunities. People in rural areas enjoy only limited social opportunities because 2. of the small local population. City dwellers can choose their friends and mates from among a large number of people of 3. similar interests and inclinations. We are not likely to abandon the city as a 4. cultural institution, but we need to make sure that our transport arrangements do not 5. damage the 'city’s' other functions.

 

Additional Information

• Support (सहयोग देना): "Support" means to uphold or maintain, which does not imply prevention of negative consequences.
• Boost (बढ़ावा देना): "Boost" means to increase or improve, which does not imply prevention of negative consequences and doesn’t fit the context.
• Help (सहायता करना): "Help" means to aid or assist, which does not imply preventing harm and doesn’t fit the intended meaning of the passage.

The correct answer is: Option 4.

Key Points

• The word "refined" means something that is elegant, cultured, or polite. (शिष्ट)
• Example: Her refined taste in art was evident from her collection.
• "Crude" refers to something that is raw, unrefined, or lacking in culture and manners. (अशिष्ट)
• Example: His crude behavior at the dinner party was embarrassing for everyone.
• Hence, we can infer that the opposite of 'refined' is 'crude'.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Elegant (शानदार): Tastefully fine or luxurious in dress, style, design, etc.
• Example: She wore an elegant gown to the ball.
• Brood (गहन चिंतन): To think deeply about something that makes one unhappy.
• Example: He would often brood over his past mistakes.
• Shrewd (चतुर): Having or showing sharp powers of judgment; astute.
• Example: Her shrewd business tactics earned her a fortune.

The correct answer is: Sanctify.

Key Points

• The word "desecrate" means to treat (a sacred place or thing) with violent disrespect; violate. (अपवित्र करना)
• Example: Vandals desecrated the cemetery last night.
• "Sanctify" refers to making something holy or setting it apart as sacred. (पवित्र करना)
• Example: The priest sanctified the water before the baptism.
• Hence, we can infer that the opposite of 'desecrate' is 'sanctify'.

Therefore, the correct answer is: Sanctify.

Additional Information

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

• Integrate (एकीकृत करना): To combine one thing with another so that they become a whole.
• Example: The new policy will integrate immigrants into the workforce more effectively.
• Damage (क्षति): Physical harm caused to something in such a way as to impair its value, usefulness, or normal function.
• Example: The storm caused significant damage to the buildings.
• Violate (उल्लंघन करना): To break or fail to comply with (a rule or formal agreement).
• Example: The company violated environmental regulations.

The correct answer is: Option 4 i.e. Betrey.

Key Points

• The word "Betrey" is incorrectly spelt. The correct spelling is "Betray" which means to be disloyal to someone or something. (धोखा देना)
• Example: He felt that she would never betray his trust.
• "Betray" refers to the act of being disloyal or treacherous to someone or something. (धोखा देना)
• Example: She betrayed her best friend by revealing her secret.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Destroy (नष्ट करना): To ruin or put an end to something.
• Example: The tornado destroyed several homes in the village.
• Develop (विकसित करना): To grow or cause to grow and become more mature, advanced, or elaborate.
• Example: She plans to develop her skills in digital marketing.
• Demolish (ध्वस्त करना): To completely destroy a building or other structure.
• Example: The old factory was demolished to make way for new apartments.

The correct answer is: exhaustive.

Key Points

• The word "unrestrained" means something that is not controlled or limited; it can refer to actions or descriptions that are free and unrestricted. (अप्रतिबंधित)
• Example: His unrestrained laughter filled the room with joy.
• "Exhaustive" refers to something that is thorough and complete, covering all possible aspects or elements. (व्यापक)
• Example: The report provided an exhaustive analysis of the market trends over the last decade.
• Hence, using the word 'exhaustive' in place of 'unrestrained' makes the sentence more accurate in context.

Therefore, the correct answer is: exhaustive.

Additional Information

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

• Limited (सीमित): Something that is restricted in size, amount, or extent.
• Example: The resources available for the project were quite limited.
• Excessive (अत्यधिक): More than necessary, normal, or desirable; immoderate.
• Example: The excessive use of plastic is harming the environment.
• Exhausting (थकाऊ): Making one feel very tired; very tiring.
• Example: The exhausting hike left everyone feeling drained.

The correct answer is: Option 4 i.e. 'fell out'.

Key Points

• The word "fell out" means to have a disagreement or argument and stop being friendly with someone. (झगड़ना)
• Example: They fell out over a trivial matter and didn’t speak for years.
• "fell down" refers to the act of losing balance and collapsing to the ground. (गिर जाना)
• Example: He fell down while running and scraped his knee.
• Hence, we can infer that the correct idiom to fill in the blank is 'fell out'.

Therefore, the correct answer is: Option 4 i.e. 'fell out'.

Additional Information

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

• fell down (गिर जाना): The act of losing balance and collapsing to the ground.
• Example: He fell down while running and scraped his knee.
• look down upon (नजरअंदाज करना): To regard someone with a feeling of superiority.
• Example: She tends to look down upon people who don’t share her opinions.
• got the sack (नौकरी से निकाल दिया जाना): To be dismissed from one’s job.
• Example: He got the sack for consistently arriving late to work.

The correct answer is: Option 1.

Key Points

• The word "Abandon" means to give up completely or to leave behind. (त्याग देना)
• Example: The sailors were forced to abandon the ship during the storm.
• "Forsake" means to renounce or turn away from entirely. (त्याग देना)
• Example: He decided to forsake his bad habits for a healthier lifestyle.
• Hence, we can infer that the synonym of 'Abandon' is 'Forsake'.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Improved (सुधार): To make something better or to enhance its quality.
• Example: She improved her cooking skills by taking a culinary class.
• Participation (भागीदारी): The action of taking part in something.
• Example: Her participation in the event was highly appreciated.
• Decided (निर्णय लिया): To make a choice or come to a conclusion.
• Example: He decided to pursue higher education abroad.

The correct answer is: Option 3 i.e. Concealed.

Key Points

• The word "revealed" means to make known something that was previously hidden or unknown. (प्रकट किया)
• Example: The magician revealed the secret behind his trick.
• "Concealed" refers to something that is hidden or kept secret. (छिपाया हुआ)
• Example: The treasure was concealed under the old oak tree.
• Hence, we can infer that the opposite of 'revealed' is 'concealed'.

Therefore, the correct answer is: Option 3 i.e. Concealed.

Additional Information

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

• Evident (स्पष्ट): Something that is clear and obvious.
• Example: The joy on her face was evident to everyone in the room.
• Found (पाया गया): Something that is discovered or located.
• Example: They found the missing keys under the couch.
• Declared (घोषित): Something that is announced formally or officially.
• Example: The results of the election were declared last night.

The correct answer is Option 4.

 

Key Points

• The subject of the sentence "One of my best friends" requires that the verb agrees with "one", which is singular.
• Therefore, the correct verb form should be "is" instead of "are".
• Option 4 correctly changes "friends are" to "friends is".

Therefore, the correct answer is Option 4.

 

Correct Sentence: One of my best friends is here.

 

Additional Information

• One of my better friends is here – Incorrect option, because "better" doesn’t fit the context.
• One of my best friend is here – Incorrect option, singular "friend" doesn’t fit since we're referring to one among many friends.
• One of my better friends are here – Incorrect option, "better" doesn’t fit the context.

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

Key Points

• The word "discriminate" means to make an unjust or prejudicial distinction in the treatment of different categories of people or things, especially on the grounds of race, age, or sex. (भेदभाव करना)
• Example: The company was accused of discriminating against older workers.
• "Differentiate" refers to recognizing or ascertaining what makes someone or something different. (अंतर करना)
• Example: It is important to differentiate between fact and opinion.
• Hence, we can infer that the synonym for 'discriminate' is 'differentiate'.

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

Additional Information

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

• Part (भाग): A piece or segment of something.
• Example: This is just one part of a much larger project.
• Sever (काटना): To cut off or separate.
• Example: He severed all ties with his family.
• Divide (विभाजित करना): To separate into parts or groups.
• Example: The teacher divided the class into groups for the activity.

The correct answer is: Option 2.

Key Points

• The word "weird" means something that is strange or unusual. (अजीब)
• Example: She had a weird feeling that she was being watched.
• "Wired" refers to being equipped with wires or connected via wiring, often used in the context of electronic devices. (तारों से लैस)
• Example: The office is fully wired for high-speed internet.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Wired (तारों से लैस): Equipped with wires or connected via wiring.
• Example: The security system is wired to the main control room.
• Beer (बीयर): An alcoholic drink made from yeast-fermented malt flavored with hops.
• Example: They enjoyed a cold beer after the long hike.
• Bier (अर्थी): A stand on which a corpse or coffin is placed.
• Example: The bier was set in the center of the room for the viewing.

The correct answer is: Option 2 i.e. 'hit the sack'.

Key Points

• The idiom "hit the sack" means to go to bed or to go to sleep. (सोने जाना)
• Example: After finishing all my work, I decided to hit the sack early.
• "Face the music" means to confront the consequences of one's actions. (परिणामों का सामना करना)
• Example: After failing the exam, he had to face the music from his parents.
• "Get into deep water" refers to getting into trouble or a difficult situation. (मुश्किल में पड़ना)
• Example: She got into deep water when she couldn't repay her loan on time.
• "Go from rags to riches" means to rise from poverty to wealth. (गरीबी से अमीरी तक पहुंचना)
• Example: His inspiring story of going from rags to riches is well-known in the business world.

Therefore, the correct answer is: Option 2 i.e. 'hit the sack'.

Additional Information

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

• Face the music (परिणामों का सामना करना): Confront the consequences of one's actions.
• Example: After failing the exam, he had to face the music from his parents.
• Get into deep water (मुश्किल में पड़ना): Getting into trouble or a difficult situation.
• Example: She got into deep water when she couldn't repay her loan on time.
• Go from rags to riches (गरीबी से अमीरी तक पहुंचना): To rise from poverty to wealth.
• Example: His inspiring story of going from rags to riches is well-known in the business world.

The correct answer is Option 2.

 

Key Points

• The word "bald" means having no hair on the scalp, which likely fits the context of describing Ravi.
• The other options have different meanings:
• "baled" – to tie up or package material, such as hay.
• "bawled" – to cry or shout loudly.
• "balled" – to form into a ball, or slang for playing ball games.

Therefore, the correct answer is Option 2.

The correct answer is Option 1.

 

Key Points

• The word "save" means to reduce the use or consumption of something, fitting the context of conserving electricity.
• The other options have different meanings:
• "deposit" – to put or set down (something) in a specific place, or to put money in a bank account.
• "rescue" – to save someone from a dangerous or distressing situation.
• "retain" – to keep possession of something.

Therefore, the correct answer is Option 1.

The correct answer is 'instinctive'.

 

Key Points

• The word "intuitive" is closely related to "instinctive", meaning something done without conscious thought or based on instinct. (स्वाभाविक)
• In the context of the sentence, "instinctive" best describes the immediate reaction to catch the falling glass.
• The other options: "voluntary," "insightful," and "shrewd" do not fit the context as appropriately.

​Therefore, the correct answer is 'Option 2'.

Complete Sentence: In a split second, her instinctive reaction kicked in as she swiftly reached out to catch the falling glass.

Additional Information

• Voluntary (स्वैच्छिक): means done, given, or acting of one's own free will.
• Insightful (सूझ-बूझ से भरा हुआ): means having or showing an accurate and deep understanding.
• Shrewd (तेज़-तर्रार): means having or showing sharp powers of judgment; astute.

The correct answer is Option 1.

 

Key Points

• The primary issue in the sentence is the verb tense used. "Keep" should be in the past tense to match the past action described in the sentence.
• The correct verb should be "held" to indicate that the action has been completed in the past.
• The sentence should read: "Then I unfurled the Indian tri-colour and held it aloft at the roof of the world."

Therefore, the correct answer is Option 1.

The correct answer is Option 1.

 

Key Points

• The phrase "in compliance in EU law" is grammatically incorrect and unclear.
• The correct prepositional phrase should be "in compliance with EU law" to indicate that the process adheres to or follows the regulations set by EU law.
• This ensures that the sentence is grammatically correct and clearly communicated.

Therefore, the correct answer is Option 1.

 

Correct Sentence: "The Privacy Shield establishes a process to allow companies to transfer consumer data from European Union countries to the United States in compliance with EU law."

 

Additional Information

• Option 2: in compliance under the – This phrase is grammatically incorrect in this context.
• Option 3: in compliance for the – This phrase is also not appropriate for this context.

Given word: 'DICTIONARY'

After arranged in alphabetical order:

 

Now,

there is two alphabet "I and Y" that will remain unchanged if each of the letters in the word 'DICTIONARY' is arranged in English alphabetical order.

Hence, the correct answer is "Option 1".

Let's check each option,

1. CKP

2. EMS

3. TBG

4. LTY

Here, all terms followed a pattern except EMS.

Hence, the correct answer is "EMS".

Preparing the family tree using the following symbols,

Given equation: A × B – C + D ÷ E

The family tree can be drawn as per the given information,

Here, we can see that E is the daughter’s husband of A.

Hence, the correct answer is "Daughter’s husband".

Let's check each option,

Hence, the correct answer is "Option 1".

The logic followed here is:

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

Now,

For, (26, 38, 128):

⇒ (26 + 38) × 2 = 64 × 2 = 128.

For, (42, 19, 122):

⇒ (42 + 19) × 2 = 61 × 2 = 122.

Similarly, for (33, 23, 112):

⇒ (33 + 23) × 2 = 56 × 2 = 112.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: The image is rotating 90° in clockwise direction.

Hence, the correct answer is "Option 4".

The logic followed here is,

Hence, the correct answer is "QINK".

The logic followed here is,

Hence, the correct answer is "62".

Let's check each option

Hence, the correct answer is "Option 3".

When the paper is unfolded, we get:

 

Hence, the correct answer is "Option 3".

The logic followed here is,

LH3 is related to RN21,

JF5 is related to PL35,

Similarly,

ZV6 is related to,

Hence, the correct answer is "FB42".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 2".

Given equation: 90 × 2 - 43 + 7 ÷ 7 = ?

After replacing the sign, the equation we get:

→ 90 ÷ 2 + 43 - 7 × 7 = ?

→ 45 + 43 - 7 × 7 = ?

→ 45 + 43 - 49 = ?

→ 88 - 49 = ?

→ 39 = ?

Hence, the correct answer is "39".

According to the given information,

Here, we can see that the code for 'heavy' is 'ct'.

Hence, the correct answer is "ct".

The correct mirror image of the given figure is:

     Hence, the correct answer is "Option 2".

The least possible venn diagram is shown below,

Conclusion (I): Some glasses are bottles → True (Some bottles are pens, all pens are tables and all tables are glasses implies that some glasses are bottles).

Conclusion (II): Some pens are glasses → True (All pens are tables and all tables are glasses implies that some pens are definitely glasses).

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

Let's count the number of semi circles in the given figure,

Hence, the correct answer is "8".

The logic followed here is:

Logic: (1^st number × 2) + 10 = 2^nd number.

Now,

For, 45 : 100

⇒ (45 × 2) + 10 = 90 + 10 = 100.

For, 65 : 140

⇒ (65 × 2) + 10 = 130 + 10 = 140.

Similarly, for 105 ∶ ?

⇒ (105 × 2) + 10 = 210 + 10 = 220.

Hence, the correct answer is "Option 3".

Let's check each option,

1) 21 B 11 D 33 A 11 C 5

→ 21 × 11 – 33 ÷ 11 + 5

→ 21 × 11 – 3 + 5

→ 231 – 3 + 5

→ 236 – 3 = 233

2) 21 C 11 D 33 A 11 B 5

→ 21 + 11 – 33 ÷ 11 × 5

→ 21 + 11 – 3 × 5

→ 21 + 11 – 15

→ 32 – 15 = 17

3) 21 B 11 A 33 D 11 C 5

→ 21 × 11 ÷ 33 – 11 + 5

→ 21 × 1/3 – 11 + 5

→ 7 – 11 + 5

→ 12 – 11 = 1

4) 21 A 11 D 33 B 11 C 5 

→ 21 ÷ 11 – 33 × 11 + 5 

→ 21/11 – 33 × 11 + 5

→ 21/11 – 363 + 5

→ 6.9 – 363 = –357.9

Here, we can see that only Option gives the resultant 233.

Hence, the correct answer is "21 B 11 D 33 A 11 C 5".

The logic followed here is,

Hence, the correct answer is "OAO".

The logic followed here is,

Hence, the correct answer is "110".

Given: 24 August 1932 was Wednesday.

Now,

1932 to 1943 = 11 Years (9 Ordinary Years and 2 Leap Years).

And, In 11 Years = 2 Leap years(1936,1940) and 9 Ordinary Years.

So, 2 Leap Years have 4 odd days,

And, 9 Ordinary Years have 9 odd days.

Total odd days = 4 + 9 = 13.

13 odd days → 13/7 = 1 weeks and 6 odd days.

then, 24 August 1943 will be Wednesday + 6 = Tuesday.

Now, the number of days between 24 August 1943 to 11 September 1943

= 7 (August) + 11 (September) = 18 days.

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

So, 11 September 1943 will be Tuesday + 4 = Saturday.

Hence, the correct answer is "Option 2".

Given equation: 8 × (7 + 5 − 3) + (46 ÷ 23) × 6 − 69 = 44

Let's check each option,

1) 6 and 7

→ 8 × (6 + 5 − 3) + (46 ÷ 23) × 7 − 69 = 44

→ 8 × 8 + 2 × 7 − 69 = 44

→ 64 + 14 − 69 = 44

→ 78 − 69 = 44

→ 9 ≠ 44

→ LHS ≠ RHS

2) 3 and 5

→ 8 × (7 + 3 − 5) + (46 ÷ 23) × 6 − 69 = 44

→ 8 × 5 + 2 × 6 − 69 = 44

→ 40 + 12 − 69 = 44

→ 52 − 69 = 44

→ -17 ≠ 44

→ LHS ≠ RHS

3) 8 and 6

→ 6 × (7 + 5 − 3) + (46 ÷ 23) × 8 − 69 = 44

→ 6 × 8 + 2 × 8 − 69 = 44

→ 14 + 16 − 69 = 44

→ 30 − 69 = 44

→ -39 ≠ 44

→ LHS ≠ RHS

4) 46 and 69

→ 8 × (7 + 5 − 3) + (69 ÷ 23) × 6 − 46 = 44

→ 8 × 9 + 3 × 6 − 46 = 44

→ 72 + 18 − 46 = 44

→ 90 − 46 = 44

→ 44 = 44

→ LHS = RHS ⇒ Satisfies the equation.

Hence, the correct answer is "46 and 69".

The logic followed here is,

‘ETHICS’ is related to ‘AVDKYU’,

‘CUSTOM’ is related to ‘YWOVKO",

Similarly,

‘PRINCIPLES’ is related to,

Hence, the correct answer is "LTEPYKLNAU".

The logic followed here is:

Logic: (Number of letters in the word)² - 1 = Code.

Now,

‘INDULGE’ is coded as ‘48' 

→ (7)² - 1

→ 49 - 1 = 48.

‘PURGE' is coded as ‘24'

→ (5)2 - 1

→ 25 - 1 = 24.

Similarly, for 'PUNY':

→ (4)2 - 1

→ 16 - 1 = 15.

So, 'PUNY' will be coded as '15'.

Hence, the correct answer is "Option 3".

Shortcut Trick Total Cost Price (CP) = Rs. 115.20. Selling Price (SP) of 50 oranges = 50 × 0.70 = Rs. 35. SP of remaining oranges = Rs. 46.20. Total SP = 35 + 46.20 = Rs. 81.20. Since CP > SP, it is a Loss. Loss = 115.20 − 81.20 = Rs. 34. ∴ The correct answer is Loss, Rs. 34.

Alternate Method Given → Total Oranges = 288, Total CP = Rs. 115.20, Rate of 50 oranges = 70 paise (Rs. 0.70), SP of rest = Rs. 46.20. Formulas: Loss = CP − SP | Loss% = (Loss ÷ CP) × 100

⇒ Calculate SP of first part: 50 × 0.70 = Rs. 35. ⇒ Total SP = SP1 + SP2 = 35 + 46.20 = Rs. 81.20. ⇒ Loss = CP − SP = 115.20 − 81.20 = Rs. 34. ∴ The correct answer is Loss, Rs. 34.

Additional Information Profit and Loss Basics When Selling Price is greater than Cost Price, the merchant makes a Profit. Conversely, if Cost Price is greater, it results in a Loss. Unit Conversion Always ensure all values are in the same unit. Here, 70 paise was converted to Rs. 0.70 (100 paise = Rs. 1).

Given:

Δ ABC ~ Δ QRP

Area of Δ ABC : Area of Δ PQR = 9 : 4

AB = 18 cm

BC = 15 cm

Formula Used:

Ratio of the areas of two similar triangles = (Ratio of the corresponding sides)²

Calculation:

Let the ratio of the corresponding sides of Δ ABC and Δ QRP be k.

Then, $k^2 = \frac{9}{4}$

⇒ $k = \sqrt{\frac{9}{4}}$

⇒ $k = \frac{3}{2}$

Since Δ ABC ~ Δ QRP, the corresponding sides are proportional.

We need to find the length of PR which corresponds to BC.

Let PR = x cm.

Then, $\frac{BC}{PR}$ = $\frac{3}{2}$

⇒ $\frac{15}{x} = \frac{3}{2}$

⇒ 15 × 2 = 3 × x

⇒ 30 = 3x

⇒ x = $\frac{30}{3}$

⇒ x = 10 cm

The length of PR is 10 cm.

Given:

Simplify the following expression:

[40 - 48 ÷ 4 of 3] ÷ {(6 + 4) - 4 of 4 + 4 + (6 - 4) + (4 × 4) ÷ 4} × 3.

Formula Used:

Order of operations (BODMAS/BIDMAS):

Brackets, Orders (i.e., powers and square roots, etc.), Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right).

Calculation:

First, simplify the expression inside the brackets:

⇒ 40 - 48 ÷ 4 of 3

Order of operations dictates we handle division and multiplication first:

⇒ 40 - 48 ÷ (4 × 3)

⇒ 40 - 48 ÷ 12

⇒ 40 - 4

⇒ 36

Next, simplify the expression inside the curly braces:

⇒ (6 + 4) - 4 of 4 + 4 + (6 - 4) + (4 × 4) ÷ 4

Handle multiplication and division first:

⇒ (6 + 4) - 4 × 4 + 4 + (6 - 4) + (16) ÷ 4

⇒ 10 - 16 + 4 + 2 + 4

Perform addition and subtraction from left to right:

⇒ 10 - 16 + 4 + 2 + 4

⇒ -6 + 4 + 2 + 4

⇒ -2 + 2 + 4

⇒ 0 + 4

⇒ 4

Now, substitute these simplified values back into the main expression:

⇒ 36 ÷ 4 × 3

Perform division and multiplication from left to right:

⇒ 9 × 3

⇒ 27

The correct answer is option 3.

Shortcut Trick

Let the annual instalment be 100%.

Total Debt is the sum of future values of all instalments at simple interest.

Total Debt = 100% + 105% + 110% + 115% + 120% = 550% of the instalment.

Given, 100% = ₹200.

Total Debt = 550% of ₹200 = 5.5 × 200 = ₹1100.

∴ The correct answer is ₹1100.

Alternate Method

Given:

Instalment (I) = ₹200

Rate of Interest (R) = 5% p.a.

Time (T) = 5 years

Year 1 ₹200

• 4 yrs @ 5% ₹240

Year 2 ₹200

• 3 yrs @ 5% ₹230

Year 3 ₹200

• 2 yrs @ 5% ₹220

Year 4 ₹200

• 1 yr @ 5% ₹210

Year 5 ₹200

Final Payment ₹200

Total Debt Discharged = ₹1100

Calculations:

⇒ 1^st instalment future value = 200 + (200 × 5 × 4) ÷ 100 = ₹240

⇒ 2^nd instalment future value = 200 + (200 × 5 × 3) ÷ 100 = ₹230

⇒ 3^rd instalment future value = 200 + (200 × 5 × 2) ÷ 100 = ₹220

⇒ 4^th instalment future value = 200 + (200 × 5 × 1) ÷ 100 = ₹210

⇒ 5^th instalment future value = ₹200 (Paid at maturity, no interest)

⇒ Total Debt = 240 + 230 + 220 + 210 + 200 = ₹1100

∴ The correct answer is ₹1100.

Additional Information

Simple Interest Instalment Formula

Total Debt = I × T + [I × R × T(T − 1)] ÷ 200, where I is the instalment amount, R is rate %, and T is time in years.

Understanding Debt vs Principal

The "Debt" mentioned in simple interest instalment questions represents the total future amount due at maturity (Principal + total accrued Interest), not the initially borrowed sum.

Compound Interest Instalments

For Compound Interest, the relationship calculates the present value of instalments: Principal = I ÷ (1 + R/100) + I ÷ (1 + R/100)² + ... + I ÷ (1 + R/100)^T.

Given:

A and B together complete the work in 15 days.

A alone completes the work in 18 days.

Formula Used:

Work rate of A = 1/Time taken by A

Work rate of B = 1/Time taken by B

Combined work rate of A and B = Work rate of A + Work rate of B

Calculation:

Work rate of A = 1/18

Work rate of A and B together = 1/15

Let the time taken by B alone to complete the work be B days.

Work rate of B = 1/B

Combined work rate of A and B:

1/18 + 1/B = 1/15

Solving for B:

⇒ 1/18 + 1/B = 1/15

⇒ 1/B = 1/15 - 1/18

⇒ 1/B = (18 - 15) / (15 × 18)

⇒ 1/B = 3 / 270

⇒ 1/B = 1 / 90

⇒ B = 90

B alone would take 90 days to complete the same work.

Shortcut Trick

Put y = 0 to find the x-intercept: 6x = 48 ⇒ x = 8.

Put x = 0 to find the y-intercept: 8y = 48 ⇒ y = 6.

The shortest length of the intercept between the axes is the hypotenuse of the right triangle formed.

Length = √(8² + 6²) = √(64 + 36) = √100 = 10 units.

∴ The correct answer is 10 units.

Alternate Method

Given:

Equation of the line: 6x + 8y − 48 = 0

Formula Used:

Intercept form of a line: x/a + y/b = 1

Length of intercept between axes = √(a² + b²)

O(0,0)

A(8,0)

B(0,6) 8 units 6 units 10 units

Calculations:

⇒ 6x + 8y = 48

Divide the entire equation by 48 to convert it into the intercept form:

⇒ 6x/48 + 8y/48 = 48/48

⇒ x/8 + y/6 = 1

Comparing with the intercept form x/a + y/b = 1, we get:

⇒ x-intercept (a) = 8 units

⇒ y-intercept (b) = 6 units

The coordinates of the intercepts on the axes are A(8, 0) and B(0, 6).

The shortest distance between these axes intercepts is the straight line segment AB.

⇒ Length AB = √(a² + b²)

⇒ Length AB = √(8² + 6²)

⇒ Length AB = √(64 + 36)

⇒ Length AB = √100 = 10 units.

∴ The correct answer is 10 units.

Additional Information

Intercept Form of a Line

The equation of a straight line making intercepts a and b on the x and y axes respectively is x/a + y/b = 1.

Distance Formula

The distance between two points (x₁, y₁) and (x₂, y₂) is given by D = √((x₂ − x₁)² + (y₂ − y₁)²).

Area of Triangle Formed by Line and Axes

The area of the right-angled triangle formed by the straight line x/a + y/b = 1 and the coordinate axes is 1/2 × |a| × |b|.

Given:

Marked Price (MP) = ₹150

Discount = 25% of ₹150 = ₹37.50

Gift worth = ₹2.50

Profit = 10%

Formula used:

Selling Price (SP) = MP - Discount - Gift worth

Profit = SP - Cost Price (CP)

Profit% = $\frac{(SP - CP)}{CP} × 100$

SP = CP + Profit

Calculation:

⇒ SP = ₹150 - ₹37.50 - ₹2.50

⇒ SP = ₹110

⇒ Profit% = $\frac{(SP - CP)}{CP} × 100$

⇒ 10% = $\frac{(110 - CP)}{CP} × 100$

⇒ $\frac{1}{10}$ = $\frac{(110 - CP)}{CP}$

⇒ CP = 1100 - 10 CP

⇒ 11CP = 1100

⇒ CP = ₹100

∴ The cost price of the article is ₹100.

Given:

We need to find the number which, when added to 20% of 460, equals 70% of 920.

Formula Used:

Let the number be x .

20% of 460 + x = 70% of 920

Calculation:

20% of 460 = 460 × 0.20 = 92

70% of 920 = 920 × 0.70 = 644

92 + x = 644

⇒ = 644 - 92

⇒ x = 552

The correct answer is option 4.

Given:

Centre of the circle, O

External point, P

PQ and PR are tangents to the circle at Q and R respectively

∠ROQ = 110°

Formula Used:

∠PQR = 90° and ∠PRQ = 90° (radius of a circle and a tangent line are always perpendicular to each other)

Sum of all angles of Quadrilateral = 360°

Calculation:

∠ROQ = 110°

Using the formula:

∠ROQ + ∠PQR + ∠PRQ + ∠RPQ = 360°

⇒ 110° + 90° + 90° +∠RPQ = 360°

⇒ ∠RPQ = 360° - 290°

⇒ ∠RPQ = 70°

The correct answer is option 3: 70°

Shortcut Trick

External Volume = 60 × 40 × 20 = 48,000 cm³

Internal dimensions (subtracting 2 cm from each): 58, 38, 18

Internal Volume = 58 × 38 × 18 = 39,672 cm³

Volume of Iron = 48,000 − 39,672 = 8,328 cm³

Weight = 8,328 × 50 gm = 416,400 gm = 416.40 kg

∴ The correct answer is 416.40 kg.

Alternate Method

Given: External Length (L) = 60 cm, Breadth (B) = 40 cm, Height (H) = 20 cm. Thickness (t) = 1 cm. Density = 50 gm/cm³.

Formula: Volume of material = External Volume − Internal Volume

⇒ External Volume = 60 × 40 × 20 = 48,000 cm³

⇒ Internal Length (l) = 60 − (2 × 1) = 58 cm

⇒ Internal Breadth (b) = 40 − (2 × 1) = 38 cm

⇒ Internal Height (h) = 20 − (2 × 1) = 18 cm

⇒ Internal Volume = 58 × 38 × 18 = 39,672 cm³

⇒ Volume of Iron = 48,000 − 39,672 = 8,328 cm³

⇒ Weight in gm = 8,328 × 50 = 416,400 gm

⇒ Weight in kg = 416,400 ÷ 1,000 = 416.40 kg

∴ The correct answer is 416.40 kg.

Additional Information

Volume of Cuboid

The volume of a cuboid is calculated as Length × Breadth × Height.

Hollow Cuboid Dimensions

For a hollow box with thickness 't', the internal dimension is (External Dimension − 2t).

Weight and Density

Weight = Volume × Density. Always ensure units are consistent (1 kg = 1000 gm).

Given:

The bar graph shows the distribution of marks obtained by students.

Formula Used:

1. Average marks = Total marks / Total number of students
2. Number of students who obtained more than the average marks.

Calculation:

Step 1: Calculate total marks and total number of students

Total students = 1 + 3 + 2 + 8 + 5 + 4 + 1 = 24

Total marks = (1 × 125) + (3 × 130) + (2 × 135) + (8 × 140) + (5 × 145) + (4 × 150) + (1 × 160) = 125 + 390 + 270 + 1120 + 725 + 600 + 160 = 3390

Step 2: Calculate the average marks

Average marks ⇒ 3390 / 24 ≈ 141.25

Step 3: Find the number of students who obtained more than the average marks

Students who scored above 141.25 are those who scored 145, 150, and 160 marks.

Number of students in these categories: 5 (145 marks) + 4 (150 marks) + 1 (160 marks) = 10

Therefore, 10 students obtained more than the average marks of the class.

Given:

Initial increase = 40%

Subsequent decrease = 45%

Formula used:

Net Percentage Change = ($\text{Initial Increase \%}$ + $\text{Subsequent Decrease \%}$ + $\frac{\text{Initial Increase \% × Subsequent Decrease \%}}{100}$)

Calculation:

⇒ Net Percentage Change = 40 - 45 + $\frac{40 × ( -45)}{100}$

⇒ Net Percentage Change = -5 - 18

⇒ Net Percentage Change = -23%

∴ The net percentage change in the final price of the article is a 23% decrease.

Given:

Perimeter of the triangle = 36 units

Formula used:

Area of a triangle with maximum possible area is of equilateral triangle.

Maximum area of an equilateral triangle = (side²) × $\frac{√3}{4}$

For an equilateral triangle, side = $\frac{Perimeter}{3}$

Calculation:

⇒ Side = 36 / 3 = 12 units

⇒ Area = (12)² × $\frac{√3}{4}$

⇒ Area = 144 × $\frac{√3}{4}$

⇒ Area = 36√3 square units

∴ The maximum area is 36√3 square units, so the correct answer is Option 2.

Given:

The table shows the number of 5 types of cars (Swift, Sx4, Ertiga, Zen, Echo) manufactured (in thousand) by Maruti over the years 2007 to 2012.

Formula Used:

Total number of cars manufactured (for each type) = Sum of cars manufactured each year from 2007 to 2012

Calculation:

Total number of Swift cars manufactured (2007 to 2012) = 250 + 200 + 230 + 245 + 260 + 275

Total number of Swift cars manufactured = 250 + 200 + 230 + 245 + 260 + 275

Total number of Swift cars manufactured = 1460

Total number of Sx4 cars manufactured (2007 to 2012) = 200 + 230 + 225 + 210 + 135 + 155

Total number of Sx4 cars manufactured = 200 + 230 + 225 + 210 + 135 + 155

Total number of Sx4 cars manufactured = 1155

Total number of Ertiga cars manufactured (2007 to 2012) = 128 + 150 + 142 + 170 + 180 + 230

Total number of Ertiga cars manufactured = 128 + 150 + 142 + 170 + 180 + 230

Total number of Ertiga cars manufactured = 1000

Total number of Zen cars manufactured (2007 to 2012) = 140 + 155 + 160 + 175 + 185 + 220

Total number of Zen cars manufactured = 140 + 155 + 160 + 175 + 185 + 220

Total number of Zen cars manufactured = 1035

Total number of Echo cars manufactured (2007 to 2012) = 115 + 120 + 135 + 125 + 130 + 120

Total number of Echo cars manufactured = 115 + 120 + 135 + 125 + 130 + 120

Total number of Echo cars manufactured = 745

Minimum number of cars manufactured by Maruti during 2007 to 2012 is Echo with 745 thousand units.

Given:

First increase = 15%

Second increase = 10%

Formula used:

Net Percentage Change = ($\text{Initial Increase \%}$ + $\text{Other increase \%}$ + $\frac{\text{Initial Increase \% × other increase \%}}{100}$)

Calculation:

⇒ Equivalent Percentage Increase = 15 + 10 + ​​$\frac{15 × 10}{100}$

⇒ Equivalent Percentage Increase = 25 + 1.5

⇒ Equivalent Percentage Increase = 26.5%

∴ The equivalent single percentage increase is 26.5%.

Given:

Distance between policeman and thief = 1.5 km

Speed of the thief = 90 km/h

Speed of the policeman = 120 km/h

Formula Used:

Relative speed = Speed of policeman - Speed of thief

Distance = Relative speed × Time

Calculation:

Relative speed = 120 km/h - 90 km/h

Relative speed = 30 km/h

Let the time taken to catch the thief be t hours.

Distance covered by the policeman in time t = Distance covered by the thief in time t + Initial distance

120t = 90t + 1.5

⇒ 120t - 90t = 1.5

⇒ 30t = 1.5

⇒ t = 1.5 / 30

⇒ t = 0.05 hours

Distance at which the policeman catches the thief = Speed of policeman × Time

Distance = 120 km/h × 0.05 hours

Distance = 6 km

The police will catch the thief at a distance of 6 km.

Given:

Length (height) of the cylinder, h = 68 cm

Base diameter of the cylinder, d = 28 cm

Radius of the cylinder, r = d/2 = 14 cm

Formula used:

Curved Surface Area (CSA) of a cylinder = 2 * π * r * h

Total Surface Area (TSA) of a cylinder = 2 * π * r * (h + r)

Calculation:

⇒ CSA = 2 * π * 14 * 68

⇒ CSA = 2 * 22/7 * 14 * 68

⇒ CSA = 5984 cm²

⇒ TSA = 2 * π * 14 * (68 + 14)

⇒ TSA = 2 * 22/7 * 14 * 82

⇒ TSA = 7216 cm²

Difference between TSA and CSA:

⇒ Difference = 7216 - 5984

⇒ Difference = 1232 cm²

∴ The difference between the curved surface area and total surface area of the cylinder is 1232 cm².

Given:

Turnover of A = ₹30 lakh

Turnover of E = ₹60 lakh

Profitability percentage of A = 25%

Profitability percentage of E = 25%

Turnover of B = ₹40 lakh

Turnover of C = ₹20 lakh

Turnover of D = ₹50 lakh

Profitability percentage of B = 7.5%

Profitability percentage of C = 20%

Profitability percentage of D = 7.5%

Formula used:

Profit = Turnover × Profitability Percentage

Share of A and E = (Profit of A + Profit of E) / Total Profit × 100%

Calculation:

Profit of A = 30 × (25/100)

⇒ Profit of A = ₹7.5 lakh

Profit of E = 60 × (25/100)

⇒ Profit of E = ₹15 lakh

Profit of B = 40 × (7.5/100)

⇒ Profit of B = ₹3 lakh

Profit of C = 20 × (20/100)

⇒ Profit of C = ₹4 lakh

Profit of D = 50 × (7.5/100)

⇒ Profit of D = ₹3.75 lakh

Total Profit of Company X = 7.5 + 3 + 4 + 3.75 + 15

⇒ Total Profit of Company X = ₹33.25 lakh

Share of A and E = (7.5 + 15) / 33.25 × 100%

⇒ Share of A and E ≈ 67.67%

∴ The correct answer is approximately 70%.

Shortcut Trick

If tan θ + cot θ = 2, this condition is only satisfied when tan θ = 1 and cot θ = 1 (since θ = 45°).

Substitute tan θ = 1 and cot θ = 1 in the required expression:

Expression = 1³ + 1³ + 6 × 1³ × 1²

Expression = 1 + 1 + 6 = 8

∴ The correct answer is 8.

Alternate Method

Given: tan θ + cot θ = 2

Formula Used: cot θ = 1/tan θ and (a + b)³ = a³ + b³ + 3ab(a + b)

⇒ tan θ + 1/tan θ = 2

⇒ tan² θ + 1 = 2 tan θ

⇒ tan² θ − 2 tan θ + 1 = 0

⇒ (tan θ − 1)² = 0

⇒ tan θ = 1

⇒ cot θ = 1/1 = 1

Now, calculate: tan³ θ + cot³ θ + 6tan³ θ cot² θ

⇒ (1)³ + (1)³ + 6(1)³(1)²

⇒ 1 + 1 + 6 = 8

∴ The correct answer is 8.

Additional Information

Reciprocal Trig Identities

tan θ × cot θ = 1. Similarly, sin θ × cosec θ = 1 and cos θ × sec θ = 1.

Special Case for x + 1/x

If x + 1/x = 2, then xⁿ + 1/xⁿ is always 2 for any positive integer n.

Standard Trig Values

For θ = 45°, tan 45° = 1 and cot 45° = 1. This is the only acute angle satisfying tan θ + cot θ = 2.

Shortcut Trick

Total Distance = 50 + 30 = 80 km

Total Time (including rest) = 90 + 15 + 35 = 140 minutes

Total Time in hours = 140 ÷ 60 = 7/3 hours

Average Speed = 80 ÷ (7/3) = 240/7 = 34(2/7) km/h

∴ The correct answer is 34(2/7) km/h.

Alternate Method

Given:

Distance₁ = 50 km, Time₁ = 90 min

Rest Time = 15 min

Distance₂ = 30 km, Time₂ = 35 min

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = 50 km + 30 km = 80 km

⇒ Total Time = 90 + 15 + 35 = 140 minutes

⇒ Conversion to hours: 140/60 hours = 7/3 hours

⇒ Average Speed = 80 ÷ (7/3)

⇒ Average Speed = (80 × 3) ÷ 7 = 240/7

⇒ Average Speed = 34(2/7) km/h

∴ The correct answer is 34(2/7) km/h.

Additional Information

Average Speed with Rest

When rest time is included in the journey, it must be added to the total time taken to find the overall average speed for the whole journey.

Unit Conversion

To convert speed from km/h to m/s, multiply by 5/18. To convert time from minutes to hours, divide by 60.

Special Case: Equal Distances

If a person covers two equal distances at speeds V₁ and V₂, the average speed = (2 × V₁ × V₂) ÷ (V₁ + V₂).

Given:

Ratio of quantities = 3 : 5

First quantity = 155 kg

Formula used:

Let the second quantity be x.

Ratio = First quantity / Second quantity

Calculation:

⇒ $\frac{3}{5}$ = $\frac{155}{x}$

⇒ x = 155 × $\frac{5}{3}$

⇒ x ≈ 258.3 kg

∴ The other quantity is approximately 258.3 kg.

Given:

Diameter of the hemisphere = 42 cm

Radius (r) = Diameter / 2 = 42 / 2 = 21 cm

Formula Used:

Volume of a hemisphere = $(2/3)πr^3$

Calculation:

Volume of the hemisphere = (2/3) × (22/7) × 21³

⇒ Volume = (2/3) × (22/7) × 21 × 21 × 21

⇒ Volume = (2/3) × (22/7) × 9261

⇒ Volume = (2 × 22 × 9261) / (3 × 7)

⇒ Volume = (44 × 9261) / 21

⇒ Volume = 407484 / 21

⇒ Volume = 19404 cm³

The volume of the hemisphere is 19404 cm³.

Given:

Total production of model C in 2021 = 6 lakhs

Total production of model C in 2022 = 5 lakhs

Total production of model A in 2019 = 5 lakhs

Total production of model A in 2020 = 4 lakhs

Formula used:

Percentage =  × 100

Calculations:

⇒ Total production of C in 2021 and 2022 = 6 + 5 = 11 lakhs

⇒ Total production of A in 2019 and 2020 = 5 + 4 = 9 lakhs

⇒ Percentage = $\frac{11}{9} × 100$

⇒ Percentage = 122.22%

∴ The total production of model C in 2021 and 2022 is approximately 122.22% of the total production of model A in 2019 and 2020.

Given:

Diameter of the first circle (D1) = 16 cm

Diameter of the second circle (D2) = 20 cm

Distance between the centers of the circles (d) = 13 cm

Formula used:

Length of the common tangent (L) = $\sqrt{(d² - (r1 - r2)²)}$

Where:

r1 = Radius of the first circle = $\frac{D1}{2}$

r2 = Radius of the second circle = $\frac{D2}{2}$

Calculations:

r1 = 16/2 = 8 cm

r2 = 20/2 = 10 cm

⇒ L = $\sqrt{(13² - (10 - 8)²)}$

⇒ L = $\sqrt{(169 - 4)}$

⇒ L = $\sqrt{165}$

Therefore, the length of the common tangent is √165 cm.

Given:

Expression: ${(3^3 + 2^3) × 22/7} × {(6^2 + 3^2 - 4^2) ÷ (14 1/2)}$

Formula Used:

1. Cube of a number: $n^3$
2. Square of a number: $n^2$
3. Mixed fraction: Convert mixed fraction to improper fraction

Calculation:

Step 1: Simplify inside the brackets

Calculate $3^3: ⇒ 3^3 = 27$

Calculate $2^3: ⇒ 2^3 = 8$

Add them together: ⇒ 27 + 8 = 35

Step 2: Multiply by 22/7

Calculate: ⇒ 35 × 22/7 = 5 × 22 = 110

Step 3: Simplify the second part

Calculate $6^2: ⇒ 6^2$ = 36

Calculate $3^2: ⇒ 3^2$ = 9

Calculate $4^2: ⇒ 4^2$ = 16

Subtract and add: ⇒ 36 + 9 - 16 = 29

Convert mixed fraction $14\frac{1}{2}$ to improper fraction: ⇒ $14\frac{1}{2}$ = 29/2

Divide: ⇒ 29 ÷ 29/2 = 29 × 2/29 = 2

Step 4: Multiply the results from Step 2 and Step 3

Final calculation: ⇒ 110 × 2 = 220

Therefore, the simplified value of the given expression is 220.

The correct answer is The document is saved in a disk file.

Key Points

• The document is saved in a disk file. This action ensures that all the changes made to the document are stored on the disk.
• When you click the Save button or press Ctrl + S, Microsoft Word writes the current state of the document to the storage medium, preventing data loss.
• This operation can be performed multiple times during a session to ensure that the most recent changes are preserved.
• Saving a document frequently is a good practice to avoid losing data in case of unexpected software or hardware failures.

Additional Information

• Microsoft Word provides different save options, such as Save As, which allows you to save the document with a different name or in a different location.
• Using Ctrl + S is a quick way to save the document without interrupting the workflow.
• It is advisable to regularly save your work, especially when working on lengthy documents, to ensure that all modifications are not lost.
• Microsoft Word also offers an AutoSave feature in Office 365, which automatically saves the document at regular intervals.

The correct answer is 1-a, 2-b, 3-c

Key Points

• Tidal energy is primarily produced in the Gulf of Khambhat, which is known for its high tidal range.
• Wind energy is significantly harnessed in Nagercoil, Tamil Nadu, due to the region's consistent and strong wind patterns.
• Geo Thermal energy is found in the Puga valley in Ladakh, which has geothermal springs indicating the presence of geothermal energy.
• The correct matching of the renewable sources of energy with their producing regions is:
• 1. Tidal energy - a. Gulf of Khambhat
• 2. Wind energy - b. Nagercoil
• 3. Geo Thermal energy - c. Puga valley
• Therefore, the correct answer is option 1.

Additional Information

• India is actively investing in renewable energy sources to reduce its carbon footprint and ensure sustainable development.
• The country has set ambitious targets for increasing the share of renewable energy in its energy mix, with significant investments in solar, wind, and other renewable sources.
• Government policies and incentives play a crucial role in promoting the adoption and expansion of renewable energy projects across various states.

The correct answer is Kerala

Key Points

• Kerala was ranked as the best-governed state in the large states category according to the Public Affairs Index, 2020.
• The index was released by the Public Affairs Centre, which is a non-profit organization.
• The ranking is based on various parameters of governance and public administration.
• Kerala has consistently performed well in areas such as health, education, and social welfare.
• The Public Affairs Index is a comprehensive framework that assesses the quality of governance in Indian states.

Additional Information

• The Public Affairs Centre was established in 1994 by Dr. Samuel Paul.
• The organization aims to improve governance in India through research, public policy, and advocacy.
• Other states that performed well in the large states category include Tamil Nadu and Andhra Pradesh.
• The index helps in identifying best practices and encourages healthy competition among states to improve governance.
• In the small states category, Goa was ranked as the best-governed state.