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

The correct answer is '4' i.e. "All the workers have called off the strike."

Key Points

• The original sentence uses "called of" instead of the correct phrasal verb "called off."
• The phrasal verb "call off" means to cancel or stop something that was planned, like a strike.
• Option 4, "called off the strike," is grammatically correct and fits well in the sentence.

Hence, the correct answer is option 4.

Correct sentence: All the workers have called off the strike.

Additional Information

• Option 1, "called at the strike," and Option 2, "called through the strike," do not make sense in the context of cancelling a strike.
• Option 3, "called between the strike," is also incorrect as it does not logically convey the meaning of stopping the strike.

The segment with a grammatical error is ‘3’ i.e. and his friends comes.

Key Points

• The segment "and his friends comes" is incorrect because of subject-verb agreement.
• The word "friends" is plural, so the correct verb form should be "come" instead of "comes."
• The corrected segment should read "and his friends come."

Hence, the correct answer is option 3.

Correct sentence: He organises a children’s fair every year, and his friends come to attend it.

Additional Information

• Option 1, "He organises," is correct with the British English spelling of "organises."
• Option 2, "to attend it," is grammatically correct and contextually appropriate.
• Option 4, "a children’s fair every year," is also correct and does not contain any grammatical errors.
• Proper subject-verb agreement is essential for maintaining grammatical accuracy in sentences.

The correct answer is ‘1’ i.e. asked for.

Key Points

• The phrase "asked out" is incorrect in the context of requesting a favor.
• The correct phrase should be "asked for," as it properly conveys the act of requesting something.
• The corrected sentence should read “Samita asked for a favour of going early today.”

Hence, the correct answer is option 1.

Correct sentence: Samita asked for a favour of going early today.

Additional Information

• Option 2, "asked around," means to inquire among several people, which does not fit the context.
• Option 3, "asked after," means to inquire about someone’s well-being, which is also not suitable for this context.
• Option 4, "asked over," means to invite someone to one’s home, which is not appropriate here either.
• Choosing the correct phrasal verb is crucial for conveying the intended meaning accurately.

The segment that contains an error is ‘4’ i.e. to wind out.

Key Points

• The phrase "to wind out" is incorrect.
• The correct phrase should be "to wind up," which means to bring an activity or business to an end.
• The corrected sentence should read “They have decided to wind up their business without delay.”

Hence, the correct answer is option 4.

Correct sentence: They have decided to wind up their business without delay.

Additional Information

• Option 1, "They have decided," is grammatically correct.
• Option 2, "their business," is grammatically correct and contextually appropriate.
• Option 3, "without delay," is also correct.
• Using the correct phrasal verbs ensures clarity and precision in communication.

The correct answer is 'Numerous'.

 

Key Points

• The passage discusses multiple health benefits associated with antioxidants.
• The appropriate adjective should indicate a large quantity to match the context of varied health benefits.
• "Numerous" fits well as it means many or a large number, which aligns with the context of the sentence describing multiple health benefits.
• Other options ("Few", "Countable", "Limited") do not convey the sense of a large quantity of benefits.

Therefore, the correct answer is 'Option 4'.

 

Complete Passage: (1)Numerous health benefits, including protection from cardiovascular disease and cancer, have been (2)_______ to antioxidants; however, according to dietitian Vinson, these benefits depend on how well antioxidants are absorbed and (3)______ by the body. According to the study, coffee has more antioxidant power than other well-known foods and drinks, like tea, milk, chocolate, and cranberries. Dates had the highest antioxidants per serving out of all the foods and drinks (4), but because dates are not consumed to the same extent as coffee, the latter comes out on (5), according to Vinson.

 

Additional Information

• Few: Indicates a small number, which does not align with the context of the passage describing a large number of health benefits.
• Countable: Refers to something that can be counted, which is not suitable for describing the numerous health benefits.
• Limited: Suggests a restricted quantity, which is not appropriate for the context of the passage discussing a wide range of benefits.

The correct answer is 'attributed'.

 

Key Points

• The passage is explaining that health benefits are associated with or due to antioxidants.
• The word "attributed" means to regard something as being caused by or linked to a particular source, which fits the context of the sentence.
• "Negative" would imply an adverse effect, which is not suitable here.
• "Parallel" and "similar" do not convey the idea of causation or linking health benefits to antioxidants.

Therefore, the correct answer is 'Option 4'.

 

Complete Passage: (1) Numerous health benefits, including protection from cardiovascular disease and cancer, have been (2) attributed to antioxidants; however, according to dietitian Vinson, these benefits depend on how well antioxidants are absorbed and (3) ______ by the body. According to the study, coffee has more antioxidant power than other well-known foods and drinks, like tea, milk, chocolate, and cranberries. Dates had the highest antioxidants per serving out of all the foods and drinks (4) ______, but because dates are not consumed to the same extent as coffee, the latter comes out on (5) ______, according to Vinson.

 

Additional Information

• Negative: Suggests an adverse effect, which is not suitable in the context of health benefits.
• Parallel: Means running alongside, which does not fit the context of attributing benefits to a cause.
• Similar: Indicates likeness, which does not convey the idea of causation or linking benefits to antioxidants.

The correct answer is 'utilised'.

 

Key Points

• The passage discusses how health benefits from antioxidants depend on their absorption and use in the body.
• "Utilised" means to make effective use of, which fits the context of the sentence describing the effective absorption and use of antioxidants by the body.
• "Rejected," "hinder," and "impede" all imply negative actions and do not fit the positive context of absorption and utilization of antioxidants.

Therefore, the correct answer is 'Option 1'.

 

Complete Passage: (1) Numerous health benefits, including protection from cardiovascular disease and cancer, have been (2) attributed to antioxidants; however, according to dietitian Vinson, these benefits depend on how well antioxidants are absorbed and (3) utilised by the body. According to the study, coffee has more antioxidant power than other well-known foods and drinks, like tea, milk, chocolate, and cranberries. Dates had the highest antioxidants per serving out of all the foods and drinks (4) ______, but because dates are not consumed to the same extent as coffee, the latter comes out on (5) ______, according to Vinson.

 

Additional Information

• Rejected: Means not accepted or discarded, which does not align with the context of the passage discussing how antioxidants are beneficial when absorbed and used by the body.
• Hinder: Means to create difficulties resulting in delay or obstruction, which is not suitable as it has a negative connotation.
• Impede: Means to delay or prevent, which also has a negative connotation and does not fit the positive context of the passage.

The correct answer is 'analysed'.

 

Key Points

• The passage is discussing a study that compares the antioxidant power of various foods and drinks.
• The phrase "out of all the foods and drinks ______" implies that an analysis or comparison was made in the study.
• "Synthesised" means produced, which does not fit this context.
• "Consumed" means eaten or drunk, which would not fit the structure of the sentence here.
• "Assimilated" means absorbed, which is different from the action being described.

Therefore, the correct answer is 'Option 4'.

 

Complete Passage: (1) Numerous health benefits, including protection from cardiovascular disease and cancer, have been (2) attributed to antioxidants; however, according to dietitian Vinson, these benefits depend on how well antioxidants are absorbed and (3) utilised by the body. According to the study, coffee has more antioxidant power than other well-known foods and drinks, like tea, milk, chocolate, and cranberries. Dates had the highest antioxidants per serving out of all the foods and drinks (4) analysed, but because dates are not consumed to the same extent as coffee, the latter comes out on (5) ______, according to Vinson.

 

Additional Information

• Synthesised: Means to produce something by chemical or biological synthesis, not suitable here.
• Consumed: Means eaten or drunk, which does not fit the context.
• Assimilated: Means absorbed, but the context here is about analytical comparison.

The correct answer is 'top'.

 

Key Points

• The passage is determining which food or drink has the highest antioxidant power, leading to a ranking where the "top" refers to the highest position.
• The word "top" is fitting as it denotes the highest rank or position in the comparison.
• "Below," "bottom," and "lowest" would incorrectly suggest a lower ranking.

Therefore, the correct answer is 'Option 4'.

 

Complete Passage: (1) Numerous health benefits, including protection from cardiovascular disease and cancer, have been (2) attributed to antioxidants; however, according to dietitian Vinson, these benefits depend on how well antioxidants are absorbed and (3) utilised by the body. According to the study, coffee has more antioxidant power than other well-known foods and drinks, like tea, milk, chocolate, and cranberries. Dates had the highest antioxidants per serving out of all the foods and drinks (4) analysed, but because dates are not consumed to the same extent as coffee, the latter comes out on (5) top, according to Vinson.

 

Additional Information

• Below: Indicates a lower position, which is incorrect in this context.
• Bottom: Refers to the lowest position, not applicable here.
• Lowest: Again suggests the least in rank, which does not fit.

The correct answer is ‘2’ i.e. is covered in.

Key Points

• The phrase "is cover in" is grammatically incorrect because "cover" is not in the correct form.
• The correct phrase should be "is covered in," which is the past participle form of "cover" used in passive voice structures.
• The corrected sentence should read "The plum tree in our garden is covered in blossoms, as are the trees outside my office window."

Hence, the correct answer is option 2.

Correct sentence: The plum tree in our garden is covered in blossoms, as are the trees outside my office window.

Additional Information

• Option 1, "are cover at," is incorrect as it uses the wrong verb form and preposition.
• Option 3, "No substitution required," is incorrect because the original phrase "is cover in" is grammatically incorrect.
• Option 4, "is covering at," is incorrect because it uses the wrong verb form and preposition.
• Using the correct verb and preposition ensures the sentence is grammatically and contextually accurate.

The correct answer is ‘3’ i.e. warmly about.

Key Points

• The phrase "feel warm on" is incorrect idiomatically and contextually.
• The correct phrase should be "feel warmly about," which properly conveys positive feelings regarding the subject.
• The correct sentence should read "We feel warmly about the subject."

Hence, the correct answer is option 3.

Correct sentence: We feel warmly about the subject.

Additional Information

• Option 1, "warming about," is incorrect because "warming" is not appropriate in this context.
• Option 2, "warmed on," is incorrect because "warmed on" does not accurately convey the intended meaning.
• Option 4, "warmer on," is also incorrect as it does not fit the idiomatic expression correctly.
• Choosing the correct phrase is crucial for proper and clear communication.

The correct answer is: Abundance.

Key Points

• The word "dearth" means a scarcity or lack of something. (कमी)
• Example: The dearth of resources in the region made survival difficult for the inhabitants.
• "Abundance" refers to a very large quantity of something. (प्रचुरता)
• Example: The garden was filled with an abundance of flowers in the spring.
• Hence, we can infer that the opposite of 'dearth' is 'abundance'.

Therefore, the correct answer is: Abundance.

Additional Information

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

• Lacunae (अभाव): An unfilled space or gap.
• Example: There were several lacunae in the manuscript that needed to be filled.
• Paucity (अल्पता): The presence of something in only small or insufficient quantities or amounts.
• Example: The paucity of water in the region has led to severe drought conditions.
• Brevity (संक्षिप्तता): Concise and exact use of words in writing or speech.
• Example: The brevity of his speech was appreciated by the audience.

The correct answer is: Option 1.

Key Points

• The word "Enemy" means a person who is actively opposed or hostile to someone or something. (दुश्मन)
• Example: In the story, the hero had to face his greatest enemy in the final battle.
• "Friend" refers to a person with whom one has a bond of mutual affection, typically one exclusive of sexual or family relations. (मित्र)
• Example: She has been my best friend since we were children.
• Hence, we can infer that the opposite of 'Enemy' is 'Friend'.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Attacker (आक्रमणकारी): A person who attacks someone or something.
• Example: The attacker was quickly apprehended by the police.
• Combatant (योद्धा): A person or nation engaged in fighting during a war.
• Example: The combatants fought bravely on the battlefield.
• Colleague (सहकर्मी): A person with whom one works, especially in a profession or business.
• Example: She always collaborates well with her colleagues.

The correct answer is: Option 2.

Key Points

• The idiom "Put in mind" means to remind someone of something. (याद दिलाना)
• Example: Before you leave, let me put in mind that you need to lock the door.
• "Remind" means to make someone remember something that they have forgotten or need to do. (याद दिलाना)
• Example: Can you remind me to call my mom later?

Therefore, the correct answer is: Option 2.

Additional Information

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

• To calculate (गणना करना): To determine the amount or number of something mathematically.
• Example: I need to calculate the total cost of our trip.
• To forget (भूल जाना): To fail to remember something.
• Example: I always forget where I put my keys.
• To understand (समझना): To grasp the meaning, significance, or nature of something.
• Example: She tried to understand the complex math problem.

The correct answer is ‘4’ i.e. the ship touched the shore.

Key Points

• The phrase "the ship touches the shore" is incorrect because the sentence is describing a past action.
• The correct phrase is "the ship touched the shore" to match the past tense "leaped."
• The correct sentence should read "A soldier of the tenth legion leaped into the water as soon as the ship touched the shore."

Hence, the correct answer is option 4.

Correct sentence: A soldier of the tenth legion leaped into the water as soon as the ship touched the shore.

Additional Information

• Option 1, "No substitution required," is incorrect because the original sentence does not match the tense.
• Option 2, "the ship was touch the shore," is incorrect as it is grammatically incorrect.
• Option 3, "the ship touch the shore," is incorrect as it is not in the past tense.
• Using the correct verb tense ensures that the sentence is grammatically correct and clear.

The correct answer is: Option 4.

Key Points

• The word "barren" means unable to produce or sustain life; not productive or fruitful. (बंजर)
• Example: The farmers struggled to grow crops on the barren land.
• "Fertile" refers to land or soil that is rich in nutrients and capable of producing abundant vegetation or crops. (उपजाऊ)
• Example: The fertile plains of the region are ideal for growing wheat and corn.
• Hence, we can infer that the opposite of 'barren' is 'fertile'.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Fruitless (अफल): Producing no useful or desired result.
• Example: His efforts to negotiate a truce were fruitless.
• Vile (नीच): Extremely unpleasant or morally bad.
• Example: He was arrested for his vile behavior towards his neighbors.
• Sterile (बाँझ): Unable to produce offspring or fruit; free from bacteria or other living microorganisms.
• Example: The sterile environment of the laboratory ensures that experiments are not contaminated.

The correct answer is 'aroma'.

 

Key Points

• The word "aroma" is used to describe a pleasant smell, often associated with food, which fits the context of enjoying the smell of one's mother's cooking.
• "Stench" has a negative connotation, referring to a strong and unpleasant smell, which is inappropriate here.
• "Scent" can refer to any smell, but it is more neutral and does not specifically convey the pleasant nature expected in this context.
• "Perfume" is typically used to describe a pleasant smell associated with fragrances or flowers, not food.

Therefore, the correct answer is 'Option 4'.

Complete Sentence: I always love the aroma of my mother’s cooking.

Additional Information

• Stench: Strong, unpleasant smell, negative connotation.
• Scent: Can refer to any smell, neutral connotation.
• Perfume: Pleasant smell associated with fragrances or flowers, not food.

The correct answer is: Option 2.

Key Points

• The word "marijuena" is incorrectly spelt.
• Correct spelling: marijuana (गांजा)
• English Meaning: A psychoactive drug from the Cannabis plant used primarily for medical or recreational purposes.
• Example: The use of marijuana for medicinal purposes is becoming more accepted worldwide.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Stationery (स्टेशनरी): Writing and other office materials.
• Example: She bought new stationery for her office work.
• Lascivious (कामुक): Feeling or revealing an overt sexual interest or desire.
• Example: The movie was criticized for its lascivious content.
• Dictator (तानाशाह): A ruler with total power over a country, typically one who has obtained power by force.
• Example: The dictator ruled the country with an iron fist.

The correct answer is ‘4’ i.e. to be.

Key Points

• The phrase "were jailed" is incorrect because the dictator is ordering an action to be performed in the future.
• The correct phrase should be "to be jailed," which properly conveys the order given by the dictator.
• The correct sentence should read "The dictator ordered the traitor to be jailed."

Hence, the correct answer is option 4.

Correct sentence: The dictator ordered the traitor to be jailed.

Additional Information

• Option 1, "was," is incorrect because it does not fit the structure of an order.
• Option 2, "is," is incorrect because it indicates a present action rather than a directive.
• Option 3, "might," is incorrect as it implies possibility rather than a command.
• Choosing the correct phrase ensures the sentence is grammatically correct and accurately conveys the intended meaning.

The correct answer is: Option 2.

Key Points

• The word "Illusion" means something that deceives by producing a false or misleading impression of reality. (मोह-जाल)
• Example: The magician's performance was full of clever illusions.
• "Illusion" refers to a deceptive appearance or impression. (मोह-जाल)
• Example: The desert mirage is an illusion caused by the refraction of light.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Illuzion (भ्रम): This is an incorrect spelling of the word "Illusion".
• Illuseon (भ्रम): This is another incorrect spelling of the word "Illusion".
• Ilusion (भ्रम): This is yet another incorrect spelling of the word "Illusion".

The correct answer is: Amazing.

Key Points

• The word "Wonderful" means something that is extremely good, marvelous, or inspiring delight. (अद्भुत)
• Example: The view from the top of the mountain was wonderful and breathtaking.
• "Amazing" refers to something that causes great surprise or wonder; it is often used to describe something that is extremely good or impressive. (अद्भुत)
• Example: She gave an amazing performance that captivated the entire audience.
• Hence, we can infer that the synonym of 'Wonderful' is 'Amazing'.

Therefore, the correct answer is: Amazing.

Additional Information

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

• Awful (भयानक): Very bad or unpleasant.
• Example: The weather was awful, with heavy rain and strong winds.
• Synthetic (कृत्रिम): Made by chemical synthesis, especially to imitate a natural product.
• Example: The jacket is made of synthetic materials to mimic the feel of leather.
• Upright (ईमानदार): Strictly honorable or honest.
• Example: He has always been an upright man, known for his integrity and fairness.

The correct answer is: Option 2.

Key Points

• The idiom "Dog eat dog" means ruthlessly competitive, where people are willing to harm each other to succeed. (निर्दयी प्रतिस्पर्धा)
• Example: In the corporate world, it's often a dog eat dog situation where only the strongest survive.
• "Ruthlessly competitive" refers to a scenario where individuals or groups are extremely determined to achieve their goals, even at the expense of others. (निर्दयी प्रतिस्पर्धा)
• Example: The job market has become ruthlessly competitive, with candidates going to great lengths to secure positions.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Like-minded people connect better (समान सोच वाले लोग बेहतर जुड़ते हैं): This phrase suggests that people with similar interests or opinions get along well.
• Example: Like-minded people connect better, which is why they often form strong communities.
• Tit for tat (जैसे को तैसा): A retaliatory action, where one responds to an action with a similar one.
• Example: In a tit for tat move, the company matched the competitor's price cuts.
• Being calculative (सावधानीपूर्वक योजनाबद्ध): Being very careful and strategic in one's actions or decisions.
• Example: She is very calculative in her investments, ensuring maximum returns with minimal risk.

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

Key Points

• The word "Competent" means having the necessary ability, knowledge, or skill to do something successfully. (सक्षम)
• Example: She is a very competent teacher who brings out the best in her students.
• "Qualified" refers to having the necessary skills, experience, or knowledge to do a particular job or activity. (योग्य)
• Example: He is well-qualified for the position of a manager.
• Hence, we can infer that the synonym of 'Competent' is 'Qualified'.

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

Additional Information

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

• Dumb (मूर्ख): Lacking intelligence or good judgment.
• Example: It was a dumb idea to go out in the storm.
• Chatty (बातूनी): Fond of talking in an easy, informal way.
• Example: She is very chatty and loves to share stories.
• Unskilled (अकुशल): Not having or requiring special skill or training.
• Example: The job was simple and could be done by an unskilled worker.

The correct answer is: explicit.

Key Points

• The word "equivocal" means something that is ambiguous or open to more than one interpretation; not clear or decided. (संदिग्ध)
• Example: Her answer was equivocal, leaving everyone confused about her true intentions.
• "Explicit" refers to something that is stated clearly and in detail, leaving no room for confusion or doubt. (स्पष्ट)
• Example: The instructions were explicit, so everyone knew exactly what to do.
• Hence, we can infer that the opposite of 'equivocal' is 'explicit'.

Therefore, the correct answer is: explicit.

Additional Information

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

• Conflicting (विरोधाभासी): Incompatible or at variance; contradictory.
• Example: The two reports were conflicting, making it hard to know which one to trust.
• Irresolute (अस्थिर): Showing or feeling hesitancy; uncertain.
• Example: He stood irresolute at the crossroads, unsure of which path to take.
• Iffy (अनिश्चित): Full of uncertainty; doubtful.
• Example: The weather forecast looks iffy, so the picnic might be canceled.

The correct answer is: Barren.

Key Points

• The word "fertile" means capable of producing abundant vegetation or crops; it often refers to soil that is rich in nutrients. (उपजाऊ)
• Example: The fertile land in the valley is perfect for growing a variety of crops.
• "Barren" refers to land that is too poor to produce much or any vegetation; it is the opposite of fertile. (बंजर)
• Example: The barren desert landscape stretched for miles, with hardly any signs of life.
• Hence, we can infer that the opposite of 'fertile' is 'barren'.

Therefore, the correct answer is: Barren.

Additional Information

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

• Scanty (अल्प): Small or insufficient in quantity or amount.
• Example: The rainfall this year has been scanty, affecting the crop yields.
• Potent (शक्तिशाली): Having great power, influence, or effect.
• Example: The medicine was potent enough to cure the illness in just a few days.
• Timid (डरपोक): Showing a lack of courage or confidence; easily frightened.
• Example: The timid child hesitated to speak in front of the class.

Given equation: 80 + 18 × 3 ÷ 5 - 23 = ?

After interchanging the signs, the equation we get:

→ 80 - 18 ÷ 3 × 5 + 23 = ?

→ 80 - 6 × 5 + 23 = ?

→ 80 - 30 + 23 = ?

→ 103 - 30 = 73

Hence, the correct answer is "73".

The logic followed here is,

Hence, the correct answer is "73".

The logic followed here is:

Logic: Synonyms.

Here,

Plain : Austere  → Plain is a synonym of Austere.

Similarly,

Clean : Sterile → Clean is a synonym of Sterile.

Hence, the correct answer is "Option 4".

When the paper is unfolded, we get:

Hence, the correct answer is "Option 1".

Given: 9 March 2007 was Friday.

Now,

2007 to 2012 = 5 Years (3 Ordinary Years and 2 Leap Year 2008, 2012).

So, 2 Leap Year has 4 odd days,

And, 3 Ordinary Years have 3 odd days.

Total odd days = 4 + 3 = 7 odd days.

→ 7 odd days = 7/7 = 1 week and 0 odd day.

Then, 9 March 2012 will be Friday + 0 = Friday.

Now, the number of days between 9 March 2012 to 13 March 2012

= 4 days.

So, 13 March 2012 will be Friday + 4 = Tuesday.

Hence, the correct answer is "Option 3".

Given word: 'ABDUCTS'

After arranged in alphabetical order:

 

After arranged in alphabetical order,

The positions of the letters 'A', 'B', and 'T' remain unchanged.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: Step 1 and Step 2 are being followed on alternate basis.

Hence, the correct answer is "Option 1".

Given equation: 132 - 12 × 17 + 3 ÷ 27 = ?

After interchanging the signs, the equation we get:

→ 132 ÷ 12 + 17 × 3 - 27 = ?

→ 11 + 17 × 3 - 27 = ?

→ 11 + 51 - 27 = ?

→ 62 - 27 = 35

Hence, the correct answer is "35".

The logic followed here is,

Hence, the correct answer is "2111".

Let's count the number of rectangles in the given figure, 

Hence, the correct answer is "9".

The logic followed here is:

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

Now,

For, 5 : 27

⇒ (5 × 5) + 2 = 25 + 2 = 27.

For, 7 : 51

⇒ (7 × 7) + 2 = 49 + 2 = 51.

Similarly, for 4 ∶ ?

⇒ (4 × 4) + 2 = 16 + 2 = 18.

Hence, the correct answer is "Option 2".

The logic followed here is,

Hence, the correct answer is "156".

Let's check each option,

Hence, the correct answer is "Option 3".

The logic followed here is:

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

Now,

For, (6, 12, 3)

⇒ (3 × 2) + 6 = 6 + 6 = 12.

For, (10, 20, 5)

⇒ (5 × 2) + 10 = 10 + 10 = 20.

Now, let's check the options:

1. (21, 28, 7)

⇒ (7 × 2) + 21 = 14 + 21 = 35 ≠ 28

2. (14, 21, 7)

⇒ (7 × 2) + 14 = 14 + 14 = 28 ≠ 21

3. (14, 28, 7)

⇒ (7 × 2) + 14 = 14 + 14 = 28

4. (14, 28, 9)

⇒ (9 × 2) + 14 = 18 + 14 = 32 ≠ 28

Hence, the correct answer is "Option 3".

According to the given information,

 

Here, we can see that the code for 'H' is '5'.

Hence, the correct answer is "5".

The logic followed here is,

for, PTL : NRJ

for, AEX : YCV

Let's check each option, 

1) TVN : RTL

 

⇒ Follows the logic.

2) GIF : FIG

3) BTM : DVO

4) ABC : ZTS

Hence, the correct answer is "Option 1".

Let's check each option,

1) 3 and 9

→ 45 ÷ 9 + 12 × 3 – 15 + 2 × 5 = 36

→ 5 + 12 × 3 – 15 + 2 × 5 = 36

→ 5 + 36 – 15 + 10 = 36

→ 51 – 15 = 36

→ LHS = RHS ⇒ Satisfies the equation.

2) 5 and 3

→ 45 ÷ 5 + 12 × 9 – 15 + 2 × 3 = 36

→ 9 + 12 × 9 – 15 + 2 × 3 = 36

→ 9 + 108 – 15 + 6 = 36

→ 123 – 15 ≠ 36

→ LHS ≠ RHS

3) 12 and 5

→ 45 ÷ 3 + 5 × 9 – 15 + 2 × 12 = 36

→ 15 + 5 × 9 – 15 + 2 × 12 = 36

→ 15 + 45 – 15 + 24 = 36

→ 84 – 15 = 36

→ 69 ≠ 36

→ LHS ≠ RHS

4) 2 and 9

→ 45 ÷ 3 + 12 × 2 – 15 + 9 × 5 = 36

→ 15 + 12 × 2 – 15 + 9 × 5 = 36

→ 15 + 24 – 15 + 45 = 36

→ 84 – 15 = 36

→ 69 ≠ 36

→ LHS ≠ RHS

Hence, the correct answer is "3 and 9".

The least possible venn diagram is shown below,

Conclusion (I): Some journals are wood → False (Because no definite relation given between journal and wood, so it can be possible only).

Conclusion (II): Some fans are books → True (Some books are fans implies that some fans are definitely books).

So, Only conclusion (II) follows.

Hence, the correct answer is "Option 4".

Preparing the family tree using the following symbols,

Let's check each option,

1) X × Y + Z

 ⇒ Here, X is Z's father's brother.

2) X + Y – Z

 ⇒​ Here, X is Z’s mother’s father

3) X + Y × Z

 ⇒ Here, X is Z's brother's father.

4) X – Y + Z

 ⇒ Here, X is Z's father's father.

Hence, the correct answer is "Option 2".

The logic followed here is,

Hence, the correct answer is "KML".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 4".

Opposite surface of the open dice can be found by the below methods: -

• Alternate surfaces are opposite to each other.
• No two opposite surface are touched by side or by corners.

So, by using the above rule we can find the opposite surface of open dice.

Below are the opposite surfaces: -

Here, we can see that the letter on the opposite side of 'R' is 'Q'.

Hence, the correct answer is "Option 2".

Let's check each option,

 

Hence, the correct answer is "Option 1".

Let's check each option,

1) PTV

 

⇒ Different from others.

2) LQO

3) XCA

4. EJH

Hence, the correct answer is "Option 1".

According to the given information,

Here, we can see that the code for 'art' is 'ml'.

Hence, the correct answer is "ml".

Given:

Maximum marks in Maths, Physics, and Chemistry = 140 each

Marks obtained by Rida in Maths = 70

Marks obtained by Rida in Physics = 110

Marks obtained by Rida in Chemistry = 120

Formula Used:

Percentage Marks = (Marks obtained/Maximum marks) × 100

Calculation:

Total marks obtained by Rida in PCM = 70 + 110 + 120 = 300

Total maximum marks in PCM = 140 × 3 = 420

Percentage Marks = (300/420) × 100

⇒ Percentage Marks = 71.43%

The percentage of marks obtained by Rida in PCM is 71.43%.

Given:

Area of ΔPQR = 12.96 cm²

Area of ΔXYZ = 635.04 cm²

QR = 2.9 cm

Formula used:

$\dfrac{Area of ΔPQR}{Area of ΔXYZ}$ = $\dfrac{QR^2}{YZ^2}$

Calculation:

$\dfrac{12.96}{635.04}$ = $\dfrac{(2.9)^2}{YZ^2}$

⇒ $\dfrac{12.96}{635.04}$ = $\dfrac{8.41}{YZ^2}$

⇒ YZ² = $\dfrac{8.41 \times 635.04}{12.96}$

⇒ YZ² = 412.86

⇒ YZ = √412.86

⇒ YZ ≈ 20.3 cm

∴ The correct answer is option (3).

Given:

In ΔABC, XY is drawn parallel to BC, cutting sides at X and Y.

AB = 5.4 cm

BC = 7.2 cm

BX = 3 cm

Formula Used:

By Basic Proportionality Theorem (Thales' theorem):

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

Calculation:

By Basic Proportionality Theorem,

AX / XB = AY / YC

Let AX = x and AY = y.

We know AB = AX + XB, so 5.4 = x + 3

⇒ x = 5.4 - 3

⇒ x = 2.4 cm

Now, AX / XB = AY / YC

⇒ 2.4 / 3 = y / (7.2 - y)

⇒ 2.4(7.2 - y) = 3y

⇒ 17.28 - 2.4y = 3y

⇒ 17.28 = 5.4y

⇒ y = 17.28 / 5.4

⇒ y = 3.2 cm

Therefore, the length of XY is 3.2 cm.

The correct answer is option 4.

Alternate Method By Basic Proportionality Theorem,

AX / AB = XY / BC

AX = 5.4 - 3 = 2.4

2.4 / 5.4 = XY / 7.2

XY = (2.4 × 7.2) / 5.4 = 3.2 cm

The correct answer is option 4.

Given:

Radius of the circle with center O (r₁) = 49 cm.

Radius of the circle with center A (r₂) = 16 cm.

Formula used:

Length of the common tangent = $\sqrt{d^2-(r_1 -r_2)^2}$

Where, d = distance between centre

Calculation:

Distance between centre = 49 + 16 = 65

So,

Length of the common tangent 

⇒ $\sqrt{65^2-(49 -16)^2}$

⇒ $\sqrt{65^2-33^2}$

⇒ $\sqrt{(65+33)(65-33)}$

⇒ $\sqrt{98× 32}$

⇒ $\sqrt{98× 2×16}$

⇒ 7 × 2 × 4 = 56 cm

∴ The correct answer is option (4).

Shortcut Trick

Compare the coefficients of the variables x and y in the given equations.

Ratio of x-coefficients (a₁/a₂) = 1/4

Ratio of y-coefficients (b₁/b₂) = 2/8 = 1/4

Ratio of constants (c₁/c₂) = 15/13

Since 1/4 = 1/4 ≠ 15/13, the lines are parallel.

∴ The correct answer is parallel.

Alternate Method

Given:

Equation 1: x + 2y = 15 (where a₁ = 1, b₁ = 2, c₁ = 15)

Equation 2: 4x + 8y = 13 (where a₂ = 4, b₂ = 8, c₂ = 13)

Condition for Parallel Lines:

For two linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂, the lines are parallel if:

(a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂)

Calculations:

⇒ a₁/a₂ = 1/4

⇒ b₁/b₂ = 2/8 = 1/4

⇒ c₁/c₂ = 15/13

⇒ 1/4 = 1/4 ≠ 15/13

⇒ Therefore, the system of equations has no solution and the graphs are parallel lines.

∴ The correct answer is parallel.

Additional Information

Intersecting Lines

If (a₁/a₂) ≠ (b₁/b₂), the lines intersect at exactly one point (Unique solution).

Coincident Lines

If (a₁/a₂) = (b₁/b₂) = (c₁/c₂), the lines overlap and are coincident (Infinitely many solutions).

Consistency

A system is Inconsistent if the lines are parallel (no solution) and Consistent if there is at least one solution.

Given:

Distance downstream = 60 km

Time taken downstream = 4 hours

Speed of the boat in still water = 13 km/h

Distance to cover upstream = 30 km

Formula Used:

Speed downstream = Distance downstream / Time downstream

Speed downstream = Speed of boat in still water + Speed of stream

Speed upstream = Speed of boat in still water - Speed of stream

Time upstream = Distance upstream / Speed upstream

Calculation:

Speed downstream = 60 km / 4 h

Speed downstream = 15 km/h

Speed downstream = Speed of boat in still water + Speed of stream

15 km/h = 13 km/h + Speed of stream

Speed of stream = 15 km/h - 13 km/h

Speed of stream = 2 km/h

Speed upstream = Speed of boat in still water - Speed of stream

Speed upstream = 13 km/h - 2 km/h

Speed upstream = 11 km/h

Time upstream = Distance upstream / Speed upstream

Time upstream = 30 km / 11 km/h

Time upstream = $\frac{30}{11}$ hours

Time upstream = $2 \frac{8}{11}$ hours

The correct answer is option 4.

Shortcut Trick

Net percentage change = 5 − 5 − (5 × 5) ÷ 100 = −0.25%

Net population ratio = 100% − 0.25% = 99.75%

99.75% of population = 47,880

Initial population = 47,880 ÷ 0.9975 = 48,000

∴ The correct answer is 48000.

Alternate Method

Given: Final population = 47,880, First year increase = 5%, Second year decrease = 5%.

Formula Used: Final Value = Initial Value × (1 + r₁/100) × (1 − r₂/100)

⇒ Let the population at the beginning be P.

⇒ Population after 1st year = P × (1 + 5/100) = P × (105/100) = 21P/20

⇒ Population after 2nd year = (21P/20) × (1 − 5/100) = (21P/20) × (95/100) = (21P/20) × (19/20)

⇒ (21P/20) × (19/20) = 47,880

⇒ 399P / 400 = 47,880

⇒ P = (47,880 × 400) ÷ 399

⇒ P = 120 × 400 = 48,000

∴ The correct answer is 48000.

Additional Information

Successive Percentage Change

When a value changes by x% and then y%, the net change is given by [x + y + (xy/100)]%.

Population Growth Formula

The final population after n years with constant growth rate r is P_n = P₀(1 ± r/100)ⁿ.

Ratio Method for Percentages

A 5% increase corresponds to a ratio of 21/20, while a 5% decrease corresponds to a ratio of 19/20.

Given:

The ratio of a father's age to his son's age is 7 ∶ 4.

The product of the numbers representing their ages is 1372.

Formula Used:

Let the father's age be 7x and the son's age be 4x.

The product of their ages = 7x × 4x = 1372

Calculation:

7x × 4x = 1372

⇒ 28x² = 1372

⇒ x² = 1372 / 28

⇒ x² = 49

⇒ x = 7

Father's age = 7x = 7 × 7 = 49 years

Son's age = 4x = 4 × 7 = 28 years

After 8 years:

Father's age = 49 + 8 = 57 years

Son's age = 28 + 8 = 36 years

New ratio = 57 ∶ 36

New ratio = 19 ∶ 12

The ratio of their ages after 8 years will be 19 ∶ 12.

Given:

Export in 2013 = 9.9 crores

Export in 2014 = 10.8 crores

Export in 2015 = 7.8 crores

Export in 2016 = 5.2 crores

Export in 2017 = 6.5 crores

Export in 2018 = 9.5 crores

Export in 2019 = 11.4 crores

Formula used:

Percentage Increase = $\dfrac{Current Year Export - Previous Year Export}{Previous Year Export} \times 100$

Calculation:

For 2014:

⇒ $\dfrac{10.8 - 9.9}{9.9} \times 100$ = 9.09%

For 2015:

⇒ $\dfrac{7.8 - 10.8}{10.8} \times 100$ = -27.78% (decrease)

For 2016:

⇒ $\dfrac{5.2 - 7.8}{7.8} \times 100$ = -33.33% (decrease)

For 2017:

⇒ $\dfrac{6.5 - 5.2}{5.2} \times 100$ = 25%

For 2018:

⇒ $\dfrac{9.5 - 6.5}{6.5} \times 100$ = 46.15%

For 2019:

⇒ $\dfrac{11.4 - 9.5}{9.5} \times 100$ = 20%

∴ The maximum percentage increase is in 2018 with 46.15%.

Given:

We need to find the value of cos(x + y) - sin(x - y) + tan(2z) .

Formula Used:

cos(x + y) =$cos x \cdot cos y$ - $sin x \cdot sin y$

sin(x - y) = $sin x \cdot cos y$ - $cos x \cdot sin y$

tan(2z) = $\frac{2 \tan z}{1 - \tan^2 z}$

Calculation:

Using the formulas:

cos(x + y) = $cos x \cdot cos y$ - $sin x \cdot sin y$

sin(x - y) = $sin x \cdot cos y$ - $cos x \cdot sin y$

tan(2z) =$\frac{2 \tan z}{1 - \tan^2 z}$

Combining these results:

⇒ cos(x + y) - sin(x - y) + tan(2z)

⇒ $cos x \cdot cos y$ - $sin x \cdot sin y$ - ($sin x \cdot cos y$ - $cos x \cdot sin y$) + $\frac{2 \tan z}{1 - \tan^2 z}$

⇒ $cos x \cdot cos y$ - $sin x \cdot sin y$ - $sin x \cdot cos y$ + $cos x \cdot sin y$ + $\frac{2 \tan z}{1 - \tan^2 z}$

⇒ $cos x \cdot cos y$ - $sin x \cdot sin y$ - $sin x \cdot cos y$ + $cos x \cdot sin y$ + $\frac{2 \tan z}{1 - \tan^2 z}$

The correct answer is option 2.

Given:

Radius of the circle (r) = 4 units.

Angle subtended by the minor sector (θ) = 45º.

Formula Used:

Perimeter of a sector = 2r + 2πr × θ /360 (in radians)

Calculation:

Now, use the formula to calculate the perimeter:

⇒ Perimeter = 2 × 4 + 2π × 4 × 45/360

⇒ Perimeter = 8 + π

The perimeter of the minor sector is 8 + π.

Given:

The production of cars from 2018 to 2020 for each type:

Type A: 2018 - 39, 2019 - 25, 2020 - 18

Type B: 2018 - 14, 2019 - 12, 2020 - 8

Type C: 2018 - 19, 2019 - 25, 2020 - 30

Type D: 2018 - 21, 2019 - 19, 2020 - 20

Formula Used:

Identify continuous decrease by checking if each year's production is less than the previous year's.

Calculation:

For Type A:

2018: 39, 2019: 25, 2020: 18

39 > 25 > 18

Continuous decrease

For Type B:

2018: 14, 2019: 12, 2020: 8

14 > 12 > 8

Continuous decrease

For Type C:

2018: 19, 2019: 25, 2020: 30

19 < 25 < 30

No continuous decrease

For Type D:

2018: 21, 2019: 19, 2020: 20

21 > 19 < 20

No continuous decrease

The correct answer is option 4.

Given:

12 men working 9 hours/day complete the work in 24 days.

Formula Used:

Work = Number of Men × Number of Hours/Day × Number of Days

Calculation:

Work done by 12 men in 24 days:

Work = 12 × 9 × 24

Work = 2592 man-hours

Now, let x be the number of days required for 8 men working 12 hours/day to complete the same work.

Work = 8 × 12 × x

Since the work is the same, we set the equations equal:

8 × 12 × x = 2592

⇒ x = 2592 / (8 × 12)

⇒ x = 2592 / 96

⇒ x = 27

The number of days required is 27 days.

Given:

Percentage of Skilled, Semi-skilled, and Un-skilled workers in companies A, B, C, and D:

Company A: Skilled = 30%, Semi-skilled = 40%, Un-skilled = 30%

Company B: Skilled = 25%, Semi-skilled = 30%, Un-skilled = 45%

Company C: Skilled = 40%, Semi-skilled = 40%, Un-skilled = 20%

Company D: Skilled = 40%, Semi-skilled = 25%, Un-skilled = 35%

Formula used:

To find the company with the highest and lowest percentages in specific categories, compare the given percentages.

Calculation:

Highest number of Un-skilled workers:

⇒ Company B: 45% Un-skilled (Highest)

Lowest number of Skilled workers:

⇒ Company B: 25% Skilled (Lowest)

∴ The company B has the highest number of Un-skilled workers and the lowest number of Skilled workers.

Shortcut Trick

Convert quantity per rupee to price per liter.

CP of Milk = 1 ÷ (3/2) = ₹2/3 per liter.

CP of Water = ₹0 per liter.

Mean Price = 1 ÷ (15/8) = ₹8/15 per liter.

Using Alligation: Ratio of Milk to Water = (8/15 − 0) : (2/3 − 8/15) = 8/15 : 2/15 = 4 : 1.

If 4 units = 60 liters, then 1 unit = 15 liters.

∴ The correct answer is 15 liters.

Alternate Method

Given:

Initial quantity of milk = 60 liters

Rate of milk = 1.5 liters per rupee ⇒ Price = ₹1/1.5 = ₹2/3 per liter

Rate of mixture = 1.875 liters per rupee ⇒ Price = ₹1/1.875 = ₹8/15 per liter

Calculations:

⇒ Let the quantity of water added be 'x' liters.

⇒ Total quantity of mixture = (60 + x) liters.

⇒ Cost of milk + Cost of water = Cost of mixture

⇒ 60 × (2/3) + x × 0 = (60 + x) × (8/15)

⇒ 40 = (60 + x) × 8/15

⇒ 40 × 15 = 480 + 8x

⇒ 600 = 480 + 8x

⇒ 8x = 120

⇒ x = 15 liters

∴ The correct answer is 15 liters.

Additional Information

Alligation Rule

It states that (Quantity of cheaper / Quantity of dearer) = (Price of dearer − Mean Price) / (Mean Price − Price of cheaper).

Cost of Water

In problems involving milk and water, the cost price of water is always assumed to be zero unless specified otherwise.

Unit Consistency

Always ensure all values (CP of cheaper, CP of dearer, and Mean Price) are in the same units (e.g., ₹ per liter) before applying the alligation rule.

Given:

Diameter of the hemisphere = 21 cm

Radius (r) = Diameter / 2 = 21 / 2 = 10.5 cm

Formula Used:

Curved Surface Area (CSA) of a hemisphere = 2πr²

Calculation:

Radius (r) = 10.5 cm

π = 22 / 7

Curved Surface Area (CSA) = 2 × π × r²

CSA = 2 × (22 / 7) × (10.5)²

CSA = 2 × (22 / 7) × 110.25

CSA = 2 × 22 × 15.75

CSA = 693 cm²

The correct answer is option 4: 693 cm².

Given:

A bank charges simple interest for Rs. K at the rate of $n^2$ years.

Another bank charges simple interest for Rs. L at the rate of $n^3$ years and gives the same interest.

Formula Used:

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

Calculation:

Let the interest be I.

For the first bank:

SI = K $\times r^{\frac{1}{2}} \times n^2 / 100$

⇒ I = $K \times r^{\frac{1}{2}} \times n^2 / 100$ ... (1)

For the second bank:

SI = $L \times r^{\frac{3}{2}} \times n^3 / 100$

⇒ I = $L \times r^{\frac{3}{2}} \times n^3 / 100$ ... (2)

Since the interest is the same:

From equations (1) and (2),

⇒ $K \times r^{\frac{1}{2}} \times n^2 / 100 = L \times r^{\frac{3}{2}} \times n^3 / 100$

⇒ $K \times r^{\frac{1}{2}} \times n^2 = L \times r^{\frac{3}{2}} \times n^3$

⇒ $K / L = r^{\frac{3}{2}} \times n^3 / (r^{\frac{1}{2}} \times n^2)$

⇒ $K / L = r^{\frac{3}{2} - \frac{1}{2}} \times n^{3 - 2}$

⇒ $K / L = r \times n$

⇒ $K / L = rn$

The ratio between K and L is r n : 1.

Given:

Simplify: 18 ÷ (7 × 2 - 5) × 5 × 24 ÷ 30

Formula Used:

Order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)

Calculation:

18 ÷ (7 × 2 - 5) × 5 × 24 ÷ 30

First, solve inside the parentheses:

7 × 2 = 14

14 - 5 = 9

Now the expression is:

18 ÷ 9 × 5 × 24 ÷ 30

Next, perform the divisions and multiplications from left to right:

⇒ 18 ÷ 9 = 2

⇒ 2 × 5 = 10

⇒ 10 × 24 = 240

⇒ 240 ÷ 30 = 8

The correct answer is option 1: 8

Given:

Range: 2000 to 2020

Formula Used:

Number divisible by 8: n × 8

Calculation:

Number divisible by 8 from 2000 to 2020 : 2000, 2008, and 2016

Since we have to find the numbers lie between 2000 to 2020

Then, only 2008 and 2016 will be considered.

Thus, numbers = 2

∴ The correct answer is option (1).

Additional Information

Note: If we have to find the numbers from 2000 to 2020 that are divisible by 8, then 2000 will also be considered.

Hence, the total number in this case will be 3.

Given:

Selling price of each refrigerator = Rs. 10,000

Loss on one refrigerator = 20%

Gain on the other refrigerator = 20%

Formula Used:

Loss Percentage = [(Cost Price - Selling Price)/Cost Price] × 100

Gain Percentage = [(Selling Price - Cost Price)/Cost Price] × 100

Calculation:

Let the cost price of the first refrigerator be C1.

Loss of 20% means 10,000 = C1 - 0.2C1

⇒ 10,000 = 0.8C1

⇒ C1 = 10,000/0.8

⇒ C1 = 12,500

Let the cost price of the second refrigerator be C2.

Gain of 20% means 10,000 = C2 + 0.2C2

⇒ 10,000 = 1.2C2

⇒ C2 = 10,000/1.2

⇒ C2 = 8,333.33

Total cost price = C1 + C2 = 12,500 + 8,333.33 = 20,833.33

Total selling price = 10,000 + 10,000 = 20,000

Loss = Total cost price - Total selling price

Loss = 20,833.33 - 20,000 = 833.33

Loss Percentage = (833.33/20,833.33) × 100

⇒ Loss Percentage = 4%

The merchant incurred a loss of 4% on the whole transaction.

Given:

Initial Salary = Rs. 2,00,000

New Salary = Rs. 2,40,000

Formula Used:

Percentage Increase = $\frac{(New Salary - Initial Salary)}{Initial Salary} \times 100$

Calculation:

Percentage Increase = $\frac{(2,40,000 - 2,00,000)}{2,00,000} \times 100$

Percentage Increase = $\frac{40,000}{2,00,000} \times 100$

Percentage Increase = 0.2 × 100

Percentage Increase = 20%

The percentage increase in the salary is 20%.

Given:

Capacity of the cylinder tank = 8316 cm³

Radius of the base (r) = 21 cm

Formula Used:

Volume of a cylinder = πr²h

Where, π (pi) ≈ 22/7, r = radius, h = height (or depth)

Calculation:

Volume = πr²h

8316 = (22/7) × 21² × h

⇒ 8316 = (22/7) × 441 × h

⇒ 8316 = 22 × 63 × h

⇒ 8316 = 1386h

⇒ h = 8316 / 1386

⇒ h = 6 cm

The depth of the tank is 6 cm.

Shortcut Trick

Angle subtended by major arc PQR at centre O = 240°

Angle subtended by the same arc at circumference (say ∠PSR) = 240° ÷ 2 = 120°

In a cyclic quadrilateral, the exterior angle is equal to the interior opposite angle.

Since PQ is extended to A, the exterior angle ∠AQR = interior opposite ∠PSR.

⇒ ∠AQR = 120°

∴ The correct answer is 120°.

Alternate Method

Given:

Centre of circle = O

Angle subtended by arc PQR at O = 240°

PQ is extended to point A.

Property used:

1. The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
2. The sum of opposite angles of a cyclic quadrilateral is 180°.
3. Exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

Let S be any point on the minor arc PR.

⇒ Reflex ∠POR = 240° (Angle subtended by arc PQR at centre)

⇒ ∠PSR = 1/2 × Reflex ∠POR

⇒ ∠PSR = 1/2 × 240° = 120°

Now, PQRS is a cyclic quadrilateral because all four vertices lie on the circle.

⇒ ∠PQR + ∠PSR = 180° (Opposite angles of cyclic quadrilateral)

⇒ ∠PQR = 180° − 120° = 60°

Since PQA is a straight line (extension of PQ):

⇒ ∠PQR + ∠AQR = 180° (Linear pair)

⇒ ∠AQR = 180° − 60° = 120°

∴ The correct answer is 120°.

Additional Information

Angle at Centre Theorem

The angle subtended by an arc at the center is exactly double the angle subtended by the same arc at any point on the circumference of the circle.

Cyclic Quadrilateral Exterior Angle

The exterior angle formed by extending one side of a cyclic quadrilateral is always equal to the interior opposite angle of the quadrilateral.

Opposite Angles Property

In any cyclic quadrilateral, the sum of a pair of opposite angles is always 180° (supplementary angles).

Given:

Total persons in the group = 250

Percentage of males = 40%

Percentage of females = 60%

Additional females joining the group = 30

Formula Used:

Percentage of females in the new group = (Number of females in the new group / Total number of persons in the new group) × 100

Calculation:

Number of females in the original group = 60% of 250

Number of females in the original group = 0.60 × 250

Number of females in the original group = 150

Number of females in the new group = 150 + 30

Number of females in the new group = 180

Total number of persons in the new group = 250 + 30

Total number of persons in the new group = 280

Percentage of females in the new group = (180 / 280) × 100

Percentage of females in the new group = (180 / 280) × 100

Percentage of females in the new group = 0.642857 × 100

Percentage of females in the new group = 64.29%

The percentage of females in the new group is 64.29%.

Shortcut Trick

Discounted Price of 12 pairs = 180 − (10% of 180) = 180 − 18 = 162.

Price per pair = 162 ÷ 12 = 13.5.

Number of pairs for Rs. 54 = 54 ÷ 13.5 = 4.

∴ The correct answer is 4 pairs.

Alternate Method

Given → Marked Price (MP) of 12 pairs = Rs. 180, Discount = 10%, Total Amount = Rs. 54. Formulas: SP = MP × (100 − Discount%) ÷ 100 | Quantity = Total Amount ÷ SP per unit.

⇒ Selling Price (SP) for 12 pairs = 180 × (90 ÷ 100) = Rs. 162. ⇒ Cost of 1 pair of gloves = 162 ÷ 12 = Rs. 13.5. ⇒ Pairs bought for Rs. 54 = 54 ÷ 13.5. ⇒ Pairs = 4.

∴ The correct answer is 4 pairs.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on the label. Discount is always calculated on the MP to find the Selling Price.

Unitary Method

Finding the value of a single unit first (price per pair) helps in calculating the quantity for any given total amount.