SSC CHSL Tier-1 2024: Official Paper (Held On: 05 Jul, 2024 Shift 2) (Previous Year Paper)

The correct answer is Option 2.

 

Key Points

• The primary issue in the sentence is the incorrect usage of the verb "has" instead of "have" in "We has travelled."
• The subject "We" requires the verb "have" to be grammatically correct.
• The correct phrase should be "We have travelled," ensuring grammatical correctness and clarity.
• Thus, the error is located in Option 2 of the sentence.
• Therefore, the correct answer is Option 2.

 

Correct Sentence: "We have travelled to many states of India to get an essence of its diversity."

 

Additional Information

• 1: "an essence of its diversity" – This part of the sentence is grammatically correct and does not require any changes.
• 3: "to many states" – This part of the sentence is grammatically correct and does not require any changes.
• 4: "of India to get" – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is Option 2.

 

Key Points

• The primary issue in the sentence is the use of the phrase "sold away" which is incorrect in this context.
• The correct phrase should be "sold out" which means that all tickets have been purchased.
• The phrase "sold away" is not commonly used in English and does not convey the intended meaning.
• Thus, the error is corrected by replacing "sold away" with "sold out".
• Therefore, the correct answer is Option 2.

 

Correct Sentence: "All tickets of the FIFA World Cup have been sold out."

 

Additional Information

• Option 1: "sold among" – This phrase is incorrect and does not fit the context of the sentence.
• Option 3: "sold into" – This phrase is incorrect and does not fit the context of the sentence.
• Option 4: "sold across" – This phrase is incorrect and does not fit the context of the sentence.

The correct answer is Option 2.

 

Key Points

• The sentence requires the past continuous tense to indicate an action that was ongoing at the time another action occurred.
• The past continuous tense is formed using "was/were" + the present participle (verb + -ing).
• In this case, "was celebrating" correctly indicates that the celebration was in progress when the trophy was dropped.
• Therefore, the correct answer is Option 2.

 

Correct Sentence: "The captain dropped the trophy while he was celebrating the victory with his teammates."

 

Additional Information

• Option 1: "celebrated" – This is the simple past tense, which does not convey the ongoing nature of the action.
• Option 3: "is celebrating" – This is the present continuous tense, which is not appropriate for past events.
• Option 4: "celebrates" – This is the simple present tense, which is not appropriate for past events.

The correct answer is Option 4.

 

Key Points

• The primary issue in the sentence is the incorrect use of the preposition "on" before the term "section."
• The correct preposition should be "on the basis of" to convey the intended meaning accurately.
• The correct phrase should be "on the basis of ‘gallantry of spirits’," ensuring grammatical correctness and clarity.
• Thus, the error is located in part 4 of the sentence.
• Therefore, the correct answer is Option 4.

 

Correct Sentence: "The soldiers were selected on the basis of ‘gallantry of spirits’."

 

Additional Information

• 1: "The soldiers" – This part of the sentence is grammatically correct and does not require any changes.
• 2: "were selected" – This part of the sentence is grammatically correct and does not require any changes.
• 3: "of ‘gallantry of spirits’." – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is: Option 4.

Key Points

• Explanation of the word "widely" with its English and Hindi meanings:
• Widely: By a large number of people; extensively. (व्यापक रूप से)
• Example: The author's first novel was widely acclaimed by critics.
• Explanation of the word "accepted" with its English and Hindi meanings:
• Accepted: Generally believed or recognized as valid or correct. (स्वीकार किया गया)
• Example: The theory of evolution is widely accepted in the scientific community.
• In context, "widely accepted" means something that is recognized and endorsed by a large number of people or groups.

Therefore, the correct answer is: widely.

Additional Information

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

• Vastly (बहुत अधिक): To a very great degree or extent.
• Example: The two species are vastly different in their physical characteristics.
• Largely (मुख्य रूप से): For the most part; mainly.
• Example: The success of the project was largely due to his efforts.
• Loosely (ढीले ढंग से): In a way that is not firmly or tightly fixed.
• Example: The instructions were loosely translated from another language.

The correct answer is: Option 2.

Key Points

• Explanation of the word "eventually" with its English and Hindi meanings:
• Eventually: In the end, especially after a long delay, dispute, or series of problems. (आखिर में)
• Example: After years of training, she eventually became a professional athlete.
• Explanation of the word "form" with its English and Hindi meanings:
• Form: To make or be made into a specific shape or structure; to develop or emerge into something. (रूप देना/बनाना)
• Example: These small cells can form larger structures like tissues and organs.
• In context, "eventually form" means that the matter and energy contained in the singularity will eventually develop or create the stars, galaxies, and other structures in the universe.

Therefore, the correct answer is: form.

Additional Information

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

• Destroy (नष्ट करना): To put an end to the existence of something by damaging or attacking it.
• Example: The fire destroyed several homes in the neighborhood.
• Design (डिज़ाइन करना): To create, fashion, execute, or construct according to a plan.
• Example: He spent hours designing a new logo for the company.
• Prepare (तैयार करना): To make ready for use or consideration.
• Example: She prepared a delicious meal for her guests.

The correct answer is Option 3.

 

Key Points

• Explanation of the word "wealth" with its English and Hindi meanings:
• Wealth: A large amount or number of something. (प्रचुरता/धन)
• Example: She has a wealth of experience in the tech industry.
• Explanation of the word "supported" with its English and Hindi meanings:
• Supported: To hold up or serve as a foundation for something. (समर्थित)
• Example: His claims were supported by ample evidence.
• In context, "a wealth of observational evidence" means a large amount of data and findings that back up the Big Bang theory.

Therefore, the correct answer is: wealth.

 

Additional Information

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

• Rich (समृद्ध): Having abundant possessions and material wealth.
• Example: The country is rich in natural resources.
• Store (भंडार): A place where goods are kept for future use.
• Example: We have a store of food for the winter months.
• Debt (ऋण): Something owed, usually money.
• Example: He is still paying off his student debt.

The correct answer is Option 3.

 

Key Points

• The word "abundance" means a very large quantity of something.
• In the context of the passage, "abundance of light elements" fits appropriately as it aligns with the scientific terminology used.
• The other options: "plenty," "fortune," and "success" do not fit the context as precisely.

​Therefore, the correct answer is 'Option 3'.

Complete Sentence: The Big Bang theory is supported by a abundance of observational evidence, including the cosmic microwave background radiation, the abundance of light elements in the universe and the large-scale structure of the cosmos.

Additional Information

• Plenty: means many or enough of something.
• Fortune: means chance or luck as an arbitrary force affecting human affairs.
• Success: means the accomplishment of an aim or purpose.

The correct answer is Option 3.

 

Key Points

• The word "nature" refers to the innate or essential characteristics of something. (स्वभाव)
• In context, it is about understanding the fundamental properties and behaviors of dark matter and energy.
• The other options: "brand," "environment," and "capture" do not fit the context as appropriately.
• ​Therefore, the correct answer is 'Option 3'.

Complete Sentence: For decades, humans have tried to theorise the origin and evolution of the universe. Many theories have been proposed and rejected. However, the Big Bang theory has been the most commonly accepted. According to this theory, the universe began as a single point, or singularity, around 13.8 billion years ago. This singularity contained all the matter and energy that would eventually form the stars, galaxies and other structures that make up our universe today. The Big Bang theory is supported by a wealth of observational evidence, including the cosmic microwave background radiation, the abundance of light elements in the universe and the large-scale structure of the cosmos. Despite its success, the Big Bang theory is still an active area of research, with scientists seeking to better understand the earliest moments of the universe and the nature of dark matter and energy.

Additional Information

• Brand: A type of product manufactured by a particular company under a particular name.
• Environment: The surroundings or conditions in which a person, animal, or plant lives or operates.
• Capture: The act of capturing something or someone.

The correct answer is: Option 2.

Key Points

• The idiom "Bag and baggage" means with all one's belongings or goods. (सामान समेत)
• Example: He left the town bag and baggage, never to return.
• "With all goods" refers to including everything one owns or possesses. (सामान समेत)
• Example: They moved to the new house with all their goods.

Therefore, the correct answer is: Option 2.

Additional Information

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

• By force (बलपूर्वक): Using physical power or violence to make someone do something.
• Example: The invaders took control of the city by force.
• Fair and honest (निष्पक्ष और ईमानदार): Being just, equitable, and truthful.
• Example: He is known for his fair and honest dealings in business.
• At the service (सेवा में): Available to help or assist someone.
• Example: The staff at the hotel were always at the service of the guests.

The correct answer is Option 2.

 

Key Points

• The primary issue in the sentence is the incorrect form of the verb "affected."
• The correct form should be "affecting" to properly convey the ongoing impact on their capacity to innovate.
• The revised phrase should be "affecting their capacity," ensuring grammatical correctness and clarity.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "Employers in many developing countries report that a lack of skilled workers is a major and increasing bottleneck for their operations, affecting their capacity to innovate."

 

Additional Information

• Option 1: "effect their capacity" – This option is incorrect as "effect" is a noun, not a verb. The sentence requires a verb.
• Option 3: "effecting their capacity" – This option is incorrect because "effect" as a verb means to bring about or cause, which does not fit the context.
• Option 4: "affect their capacity" – This option is incorrect because it does not fit the sentence structure that requires a present participle form.

The correct answer is Option 1.

 

Key Points

• The word "assiduously" means showing great care and perseverance.
• The word "committed" is a suitable synonym for "assiduously" in this context, as it conveys dedication and hard work.
• The other options do not convey the same level of dedication and effort required to aid pupils in achieving success.
• Therefore, the correct answer is Option 1.

 

Correct Sentence: The dedicated teacher laboured committedly to aid her pupils in achieving success.

 

Additional Information

• Option 2: "un-biased" - This word means impartial, which does not fit the context of showing dedication.
• Option 3: "uninvolved" - This word means not taking part, which is the opposite of showing dedication.
• Option 4: "apathetic" - This word means showing no interest or enthusiasm, which is contrary to the meaning of "assiduously".

The correct answer is Option 1.

 

Key Points

• The term "route" is used to describe the way or path taken to reach a destination.
• Options like "rude," "rout," and "root" are incorrect in this context.
• "Rude" refers to impoliteness, "rout" refers to a disorderly retreat or defeat, and "root" refers to the part of a plant that is usually hidden underground.
• Thus, the correct choice is "route" as it appropriately fits the context of the sentence.

Therefore, the correct answer is Option 1.

 

Correct Sentence: "Which route do you usually take to reach your office?"

 

Additional Information

• Route: A way or course taken in getting from a starting point to a destination.
• Rude: Offensively impolite or ill-mannered.
• Rout: A disorderly retreat of defeated troops.
• Root: The part of a plant that attaches it to the ground or to a support, typically underground, conveying water and nourishment to the rest of the plant.

The correct answer is: Option 2.

Key Points

• The word "superior" means of higher quality or greater value. (श्रेष्ठ)
• Example: The superior craftsmanship of the watch made it highly sought after.
• "Inferior" refers to something that is of lower quality or lesser value. (निम्न)
• Example: The inferior materials used in the construction caused the building to deteriorate quickly.

Hence, we can infer that the opposite of 'superior' is 'inferior'.

Additional Information

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

• Small (छोटा): Of limited size or extent.
• Example: The small puppy fit comfortably in her arms.
• Excellent (उत्कृष्ट): Extremely good; outstanding.
• Example: She received excellent grades in her final exams.
• Distasteful (अप्रिय): Causing dislike or aversion.
• Example: The distasteful smell made it hard to stay in the room.

The correct answer is: Option 3.

Key Points

• The word "vicious cycle" means a sequence of reciprocal cause and effect in which two or more elements intensify and aggravate each other, leading to a worsening situation. (दुष्चक्र)
• Example: The family was trapped in a vicious cycle of debt and poverty.
• "Vicious cycle" refers to a situation where one problem causes another, which then makes the original problem worse, creating a loop of negative outcomes. (दुष्चक्र)
• Example: Lack of education leads to unemployment, which leads to poverty, and poverty leads to lack of education, forming a vicious cycle.
• Hence, we can infer that the phrase 'vicious cycle' means 'one problem causes another'.

Therefore, the correct answer is: Option 3.

Additional Information

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

• Strength of something (शक्ति): The quality or state of being physically strong.
• Example: The strength of the bridge was tested by the engineers.
• Loophole of something (कानूनी खामी): An ambiguity or inadequacy in the law or a set of rules.
• Example: The company exploited a loophole in the tax law to avoid paying taxes.
• The barrier of poverty (गरीबी की बाधा): An obstacle that prevents progress or achievement, specifically related to poverty.
• Example: The barrier of poverty often prevents children from receiving a proper education.

The correct answer is: Option 3.

Key Points

• The word "concise" means giving a lot of information clearly and in a few words; brief but comprehensive. (संक्षिप्त)
• Example: His speech was concise and straight to the point.
• "Lengthy" refers to something that is long in duration or extent; extended and protracted. (लंबा)
• Example: The meeting was so lengthy that everyone felt exhausted by the end.

Hence, we can infer that the opposite of 'concise' is 'lengthy'.

Additional Information

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

• Total (कुल): Comprising the whole number or amount.
• Example: The total cost of the project was higher than expected.
• Precise (सटीक): Marked by exactness and accuracy of expression or detail.
• Example: Her instructions were clear and precise.
• Excise (उत्पाद शुल्क): A tax levied on certain goods and commodities produced or sold within a country.
• Example: The government decided to increase the excise on tobacco products.

The correct answer is: Option 1.

Key Points

• The word "clamour" means a loud and confused noise, especially that of people shouting. (कोलाहल)
• Example: The clamour of the crowd drowned out the speaker's voice.
• "loud and confused noise" refers to a sound that is both high in volume and disorganized, making it hard to concentrate or hear anything else. (तेज़ और भ्रमित करने वाली आवाज़)
• Example: The loud and confused noise from the construction site made it hard to focus on my work.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Introduction of new things (नए चीजों का परिचय): The act of bringing something new into use or practice.
• Example: The introduction of new things in the curriculum has made learning more interesting.
• Humorous deception (हास्यपूर्ण धोखा): The act of deceiving someone in a funny or amusing manner.
• Example: His humorous deception during the magic show left the audience in splits.
• Narrow-mindedness (संकीर्ण मानसिकता): The quality of having a limited or closed perspective; not willing to consider different ideas.
• Example: His narrow-mindedness prevents him from accepting new and innovative ideas.

The correct answer is Option 1.

 

Key Points

• The primary issue in the sentence is the use of the word "which" instead of "who."
• When referring to people, "who" is the correct relative pronoun.
• The correct phrase should be "who is wearing a blue shirt," ensuring grammatical correctness and clarity.

Therefore, the correct answer is Option 1.

 

Correct Sentence: "The girl who is wearing a blue shirt is my sister."

 

Additional Information

• Option 2: "which wear a blue shirt" – This option is incorrect because "which" should not be used for people, and the verb form "wear" is incorrect.
• Option 3: "who wear a blue shirt" – This option is incorrect because the verb form "wear" does not agree with the singular subject "girl."
• Option 4: "which is wearing the blue shirt" – This option is incorrect because "which" should not be used for people.

The correct answer is 'Option 3'

Key Points

• The word "incadescent" is incorrectly spelled and should be "incandescent" which means emitting light as a result of being heated. (दीप्तिमान)
• Example: The incandescent bulb lit up the entire room.
• "Incandescent" refers to something that emits light as a result of being heated. (दीप्तिमान)
• Example: The incandescent lamps in the make-up room were very bright.

Therefore, the correct answer is: with incandescent lights.

Additional Information

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

• of those subjected to make-up (मेकअप के अधीन लोगों का): Refers to people who are undergoing the process of make-up.
• Example: The actors were among those subjected to make-up before the shoot.
• The make-up room was filled (मेकअप रूम भरा हुआ था): Indicates that the make-up room had many items or people in it.
• Example: The make-up room was filled with artists and their tools.
• which added to the misery (जिससे दुःख और बढ़ गया): Refers to something that increased the suffering or discomfort.
• Example: The heat in the room added to the misery of the actors.

The correct answer is: Option 1.

Key Points

• The word "explicit" means something that is clear and fully expressed, leaving no room for confusion or doubt. (स्पष्ट)
• Example: The instructions were explicit, so everyone knew exactly what to do.
• "Ambiguous" refers to something that is unclear or open to more than one interpretation. (अस्पष्ट)
• Example: The terms of the contract were ambiguous, leading to a lot of confusion.

Hence, we can infer that the opposite of 'explicit' is 'ambiguous'.

Additional Information

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

• Exact (सटीक): Something that is precise and accurate.
• Example: He gave the exact measurements needed for the project.
• Precise (सटीक): Marked by exactness and accuracy of expression or detail.
• Example: Her instructions were precise, leaving no room for error.
• Distant (दूर): Far away in space or time.
• Example: The distant mountains looked beautiful at sunset.

The correct answer is: Option 2.

Key Points

• Explanation of the word "use" with its English and Hindi meanings:
• Use: The act of putting something into action or service. (इस्तेमाल)
• Example: He made good use of his free time by learning a new skill.
• Explanation of the word "full" with its English and Hindi meanings:
• Full: Entire or complete in extent or degree. (पूर्ण)
• Example: She made full use of the resources available to her.
• In context, "full use" means to make the most comprehensive or effective use of something.

Therefore, the correct answer is: full.

Additional Information

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

• Entire (सम्पूर्ण): Referring to the whole of something without exception or reservation.
• Example: He ate the entire pizza by himself.
• Whole (सम्पूर्ण): Also means complete, but often refers to something undivided or unbroken.
• Example: She spent the whole day at the beach.
• Total (कुल): Refers to the sum or entire amount of something.
• Example: The total cost of the project was very high.

The correct answer is: Option 2.

Key Points

• The word "tedious" means something that is too long, slow, or dull; tiresome or monotonous. (उबाऊ)
• Example: The lecture was so tedious that many students started to fall asleep.
• "Boring" refers to something that is not interesting or exciting. (नीरस)
• Example: The movie was so boring that I couldn't watch it till the end.

Hence, we can infer that the synonym of 'tedious' is 'boring'.

Additional Information

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

• Working (काम कर रहा): Engaged in a task or activity.
• Example: She is currently working on a new project.
• Exciting (रोमांचक): Causing great enthusiasm and eagerness.
• Example: The match was so exciting that the audience couldn't sit still.
• Happening (घटित): An event or occurrence.
• Example: There is a lot happening in the city this weekend.

The correct answer is: Option 3.

Key Points

• "Sauce" refers to a liquid or semi-liquid substance served with food to add moistness and flavor. (चटनी)
• Example: He added a spicy sauce to his pasta to enhance its flavor.

Hence, we can infer that the correct homophone to fill in the blank is 'sauce'.

Additional Information

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

• Source (स्रोत): The origin or starting point of something.
• Example: The source of the information was highly reliable.
• Saws (आरी ): Tools used for cutting wood or other materials.
• Example: He used saws to cut the wooden planks for the project.
• Sause (गलत वर्तनी): Incorrect spelling, not a valid word.
• Example: There is no valid example as this is a misspelling of 'sauce'.

The correct answer is: Option 3.

Key Points

• The word "Permit" means to give authorization or consent to someone to do something. (अनुमति देना)
• Example: The city council will permit the construction of the new park.
• "Approve" means to officially agree to or accept as satisfactory. (मंजूरी देना)
• Example: The manager will approve the budget proposal by the end of the day.

Therefore, the correct answer is: Approve.

Additional Information

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

• Flout (उल्लंघन करना): To openly disregard a rule, law, or convention.
• Example: He decided to flout the traffic rules and drove through the red light.
• Abandon (त्यागना): To give up completely or leave behind.
• Example: They had to abandon the project due to lack of funds.
• Disgrace (अपमान): Loss of reputation or respect as the result of a dishonorable action.
• Example: His unethical behavior brought disgrace to the entire family.

The correct answer is: Option 4.

Key Points

• The word "Innoculate" is an incorrect spelling. The correct spelling is "Inoculate," which means to introduce a vaccine or antigenic substance into the body to produce immunity to a specific disease. (टीका लगाना)
• Example: The doctor will inoculate the children against measles.
• "Inoculate" is the correct spelling of the word, referring to the act of introducing a vaccine into the body to prevent disease. (टीका लगाना)
• Example: Health workers inoculate people to protect them from infectious diseases.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Immaculate (निर्मल): Perfectly clean, neat, or tidy.
• Example: Her house was immaculate, with not a speck of dust to be found.
• Immense (विशाल): Extremely large or great.
• Example: The immense size of the universe is beyond human comprehension.
• Irreverent (असम्मानजनक): Showing a lack of respect for people or things that are generally taken seriously.
• Example: The comedian's irreverent jokes often offended the audience.

The logic followed here is:​

RTVX is related to SUWY

And,

KMOQ is related to LNPR

Similarly,

FHJL is related to

Hence, "Option 4" is the correct answer.

The logic followed here is:​

TMBF is related to ATIM

And,

CLGP is related to JSNW

Similarly,

QEAD is related to

Hence, "Option 2" is the correct answer.

According to the given figure:

The figure will appear when it is opened as follows:

Hence, "Option 2" is the correct answer.

The logic followed here is: (1^st number × 3^rd number × 2) = 2^nd number

(13, 234, 9)

13 × 9 × 2 = 234

234 = 234 (LHS = RHS)

And,

(15, 180, 6)

15 × 6 × 2 = 180

180 = 180 (LHS = RHS)

So, checking each option one by one

Option 1) (14, 196, 7)

14 × 7 × 2 = 196

196 = 196 (LHS = RHS)

Option 2) (12, 108, 9)

12 × 9 × 2 = 108

216 ≠ 108 (LHS ≠ RHS)

Option 3) (16, 240, 5)

16 × 5 × 2 = 240

160 ≠ 240 (LHS ≠ RHS)

Option 4) (17, 340, 5)

17 × 5 × 2 = 340

170 ≠ 340 (LHS ≠ RHS)

Thus, out of all the options '(14, 196, 7)' follows the same logic as given.

Hence, "Option 1" is the correct answer.

Decoding the Symbols:

Given: P + Q × R - S ÷ T

P + Q → P is the daughter of Q.

Q × R → Q is the brother of R. 

 

R - S → R is the wife of S.

 

S ÷ T → S is the father of T.

Thus, according to the final family tree:

Option 1) P is the daughter of T's Mother's Brother → Correct

Option 2) T is S's Son → Incorrect as T can be either the son or daughter of S, therefore cannot be determined.

Option 3) Q is the brother of S → Incorrect as Q is the brother-in-law of S.

Option 4) P is the sister of T → Incorrect as P is the cousin of T.

Hence, "Option 1" is the correct answer.

The correct mirror image of the given combination when mirror is placed at MN is as shown below:

Detailed Explanation:

The line MN is the mirror

Option 1) The word "Wph4y" the second letter is "p". So, the mirror image should be  

⇒ Option 1 is eliminated.

Option 2) The word "Wph4y", so, the mirror image should be

⇒ Correct

Option 3) The word "Wph4y" the third letter is "h". So, the mirror image should be

 ⇒ Option 3 is eliminated.

Option 4) The word "Wph4y" the fifth letter is "Y". So, the mirror image should be " 

⇒ Option 4 is eliminated.

Hence, the correct answer is "Option 2".

The logic followed here is:

Hence, "Option 1" is the correct answer.

Given word: DIALECT

According to the question, all the letters in the word are arranged in alphabetical order:

Thus, according to the final arrangement only position of 'T' remains unchanged.

Hence, "Option 1" is the correct answer.

The correct mirror image of the given combination when mirror is placed at MN is as shown below:

Detailed Explanation:

The line MN is the mirror

Option 1) The word "Pam@43k" the first letter is "P". So, the mirror image should be  

⇒ Option 1 is eliminated.

Option 2) The word "Pam@43k", so, the mirror image should be

⇒ Correct 

Option 3) The word "Pam@43k" the fifth letter is "4". So, the mirror image should be

 ⇒ Option 3 is eliminated.

Option 4) The word "Pam@43k" the second letter is "a". So, the mirror image should be

⇒ Option 4 is eliminated.

Hence, the correct answer is "Option 2".

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

Here, as marked there are a total of 14 triangles.

Hence, "14" is the correct answer.

The logic followed here is:

1. For the first box series: Corner elements including the center element shift in the clockwise direction and rest of the elements interchange positions.

2. For the second box series:

The top elements shift in the anticlockwise direction.

The bottom center element is replaced by new elements and the rest of elements shift in the anticlockwise direction.

Thus, the final series is :

Hence, "Option 4" is the correct answer.

According to the given information,

Thus, according to the given codes 'bj' is the code for the word 'meet'.

Hence, the correct answer is "bj".

The logic followed here is:​

Hence, "Option 2" is the correct answer.

Given : 15 + 2 - 13 × 13 ÷ 3 = ?

After '+' and ‘-' are interchanged and '×' and ‘÷' are interchanged then,

15 + 2 - 13 × 13 ÷ 3 = ? ⇒ 15 - 2 + 13 ÷ 13 × 3 = ? 

⇒ 15 - 2 + 13 ÷ 13 × 3 = ?

⇒ 15 - 2 + 1 × 3 = ?

⇒ 15 + 3 - 2 = ?

⇒ 18 - 2 = ?

⇒ 16 = ?

Hence, "Option 4" is the correct answer.

Given: 19 July 2012 is Thursday

The number of odd days from 19 July 2012 to 11 January 2018 :

∴ The number of odd days from 19 July 2012 to 11 January 2018 ⇒ 0

⇒So, Zero odd days will be added to Thursday because the day is asked in future.

∴ Thursday was the day of the week on 11 January 2018.

Hence, "Option 4" is the correct answer.

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

Conclusions:

I. Some ink is butter → Does not follow (As some nibs are ink and some nibs are butter. So, it is possible but not definitely true.)

II. All jams are nibs → Does not follow (As all jams are butter and some nibs are butter. So, it is possible but not definitely true.)

∴ Here, Neither conclusion (I) nor (II) follows.​

Hence, the correct answer is "Option 4"

The faces opposite to each other are shown below:

⇒ As the alternate positions become opposite to each other, the remaining two faces become opposite to each other.

So, opposite pairs are:

6 → 5

8 → 7

9 → 10

Therefore, '7' is the opposite of '8'.

Hence, "7" is the correct answer.

Given series: GH_ST_HO_RGHOSPG_OS_

The logic followed here is:

Hence, "Option 1" is the correct answer.

Decoding letters:

Given: 17 C 69 A 3 D 22 B 1 = ?

After interchanging the letters,

17 C 69 A 3 D 22 B 1 = ? ⇒ 17 + 69 ÷ 3 - 22 × 1 = ?

⇒ 17 + 69 ÷ 3 - 22 × 1 = ?

⇒ 17 + 23 - 22 × 1 = ?

⇒ 17 + 23 - 22 = ?

⇒ 40 - 22 = ?

⇒ 18 = ?

Hence, "Option 2" is the correct answer.

Given : 21 – 7 × 26 + 46 ÷ 36 = ?

After ‘+’ and ‘×’ are interchanged and ‘–’ and ‘÷’ are interchanged then,

21 – 7 × 26 + 46 ÷ 36 = ? ⇒ 21 ÷ 7 + 26 × 46 - 36 = ?

⇒ 21 ÷ 7 + 26 × 46 - 36 = ?

⇒ 3 + 26 × 46 - 36 = ?

⇒ 3 + 1196 - 36 = ?

⇒ 1199 - 36 = ?

⇒ 1163 = ?

Hence, "Option 2" is the correct answer.

The logic followed here is:​

'SOAP' is coded as '4629'

And,

'SPOT' is coded as '9824'

As, S, O, and P are common, therefore A is coded as:

A → 6

Hence, "Option 3" is the correct answer.

The logic followed here is: (1^st number × 6) = 2^nd number

12 is related to 72

12 × 6 = 72

72 = 72 (LHS = RHS)

And,

19 is related to 114

19 × 6 = 114

114 = 114 (LHS = RHS)

Similarly,

29 is related to

29 × 6 = ?

174 = ?

Hence, "Option 1" is the correct answer.

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

∴ Here, Option Figure 2 is embedded in the given figure.

Hence, the correct answer is "Option 2".

The logic followed here is:

Hence, "Option 2" is the correct answer.

The logic followed here is:​

Option 1) PNK

Option 2) OMJ

Option 3) RTQ

Option 4) BZW

Thus, out of all the options 'RTQ' is the odd one out.

Hence, "Option 3" is the correct answer.

Here’s the solution using the format you requested:

Given:

Exports from three companies A, B, and C over the years (in Rs. crore).

Formula used:

Average export of company C = Sum of exports of company C / Number of years

Calculation:

Sum of exports of company C = 140 + 158 + 160 + 166 + 178 = 802

Number of years = 5

Average export of company C = 802 / 5 = 160.4 crore

Exports of company C in given years:

1995: 140 crore

1996: 158 crore

1997: 160 crore

1998: 166 crore

1999: 178 crore

Years where exports were less than average: 1995, 1996, 1997

⇒ Number of years = 3

∴ The correct answer is 3 years.

Given:

A shopkeeper marks up his goods 32% above the cost price and gives a discount of 21% on the marked price.

Formula used:

Gain% = $\dfrac{Selling Price - Cost Price}{Cost Price} \times 100$

Calculations:

Let Cost Price (CP) = ₹100

Marked Price (MP) = ₹100 + 32% of ₹100

⇒ MP = ₹100 + ₹32

⇒ MP = ₹132

Discount = 21% of ₹132

⇒ Discount = ₹132 × $\dfrac{21}{100}$

⇒ Discount = ₹27.72

Selling Price (SP) = ₹132 - ₹27.72

⇒ SP = ₹104.28

Gain% = $\dfrac{₹104.28 - ₹100}{₹100} \times 100$

⇒ Gain% = $\dfrac{₹4.28}{₹100} \times 100$

⇒ Gain% = 4.28%

∴ The correct answer is option (1).

Given:

∆ABC and ∆DEF are similar

Area of ∆ABC = 0.64 m²

Area of ∆DEF = 0.0121 m²

EF = 0.154 m

Formula used:

If two triangles are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding sides.

Calculations:

$\dfrac{Area ,of ,∆ABC}{Area ,of ,∆DEF} = \left(\dfrac{BC}{EF}\right)^2$

⇒ $\dfrac{0.64}{0.0121} = \left(\dfrac{BC}{0.154}\right)^2$

⇒ $\dfrac{64}{1.21} = \left(\dfrac{BC}{0.154}\right)^2$

⇒ $\dfrac{64 \times 100}{121} = \left(\dfrac{BC}{0.154}\right)^2$

⇒ $\dfrac{6400}{121} = \left(\dfrac{BC}{0.154}\right)^2$

⇒ $\dfrac{6400}{121} = \left(\dfrac{BC}{0.154}\right)^2$

⇒ $\dfrac{6400}{121} = \left(\dfrac{BC}{0.154}\right)^2$

⇒ $\dfrac{BC}{0.154} = \sqrt{\dfrac{6400}{121}}$

⇒ $\dfrac{BC}{0.154} = \dfrac{80}{11}$

⇒ $\dfrac{BC}{0.154} = 7.2727$

⇒ $BC = 0.154 \times 7.2727$

⇒ BC = 1.12 m

∴ The correct answer is option (3).

Given:

A chord of length 12 units in a circle of radius 10 units

Formula used:

Using the perpendicular distance from the center to the chord formula:

$d = \sqrt{r^2 - (\frac{l}{2})^2}$

Where, r = radius of the circle, l = length of the chord, d = distance from the center to the chord

Calculation:

Given: r = 10, l = 12

⇒ d = $\sqrt{10^2 - (\frac{12}{2})^2}$

⇒ d = $\sqrt{100 - 6^2}$

⇒ d = $\sqrt{100 - 36}$

⇒ d = $\sqrt{64}$

⇒ d = 8

∴ The correct answer is option 2.

Given:

The base of the triangle is two-thirds of its height.

Area = 363 cm²

Formula used:

Area of a triangle = 1/2 × base × height

Let height = h cm

Then, base = 2/3 × h cm

Calculation:

Area = 1/2 × base × height

⇒ 363 = 1/2 × (2/3 × h) × h

⇒ 363 = 1/2 × (2/3) × h²

⇒ 363 = 1/3 × h²

⇒ h² = 363 × 3

⇒ h² = 1089

⇒ h = √1089

⇒ h = 33 cm

∴ The correct answer is option (3).

Shortcut Trick

Let initial Income = 100, Spending = 80, Savings = 20.

Income ↑ 20% → 120.

Spending ↑ 10% → 80 + 8 = 88.

New Savings = 120 − 88 = 32.

Savings % increase = ((32 − 20) ÷ 20) × 100 = 60%.

60% in decimal = 0.6.

∴ The correct option is C.

Alternate Method

Given:

Spending = 80% of Income

Income increase = 20%

Spending increase = 10%

Formula Used:

Income = Expenditure + Savings

Percentage change = (New Value − Old Value) ÷ Old Value × 100

Initial State (Income = 100)

Spend: 80

Save: 20 New State (Income = 120)

Spend: 88 (+10%)

Save: 32

Savings Increase: 20 → 32 (60%)

Calculations:

⇒ Let original Income = 100 units

⇒ Original Expenditure = 80% of 100 = 80 units

⇒ Original Savings = 100 − 80 = 20 units

⇒ New Income = 100 × (1 + 20/100) = 120 units

⇒ New Expenditure = 80 × (1 + 10/100) = 80 + 8 = 88 units

⇒ New Savings = 120 − 88 = 32 units

⇒ Increase in Savings = 32 − 20 = 12 units

⇒ Percentage Increase = (12 ÷ 20) × 100 = 60%

⇒ Value in decimal = 60 ÷ 100 = 0.6

∴ The correct option is C.

Additional Information

Income-Expenditure Alligation

This problem can also be solved using alligation between expenditure and savings where the mean value is the percentage increase in income.

Percentage Change Relation

Net Income Change % = (Exp % × Exp Change %) + (Sav % × Sav Change %). In this case: 20 = (0.8 × 10) + (0.2 × x), solving for x gives 60%.

Rule of Base

When calculating percentage increase, always use the original value as the denominator (e.g., original savings of 20).

Shortcut Trick

Sum of the existing digits in 7_7624 = 7 + 7 + 6 + 2 + 4 = 26.

The next multiple of 3 after 26 is 27.

Smallest digit required = 27 − 26 = 1.

∴ The correct answer is 1.

Alternate Method

Given: The number is 7_7624. Let the missing digit be x.

Divisibility Rule of 3: A number is divisible by 3 if the sum of its digits is divisible by 3.

⇒ Sum of digits = 7 + x + 7 + 6 + 2 + 4

⇒ Sum = 26 + x

For the number to be divisible by 3, (26 + x) must be 27, 30, 33, etc.

⇒ Case 1: 26 + x = 27 → x = 1

⇒ Case 2: 26 + x = 30 → x = 4

⇒ Case 3: 26 + x = 33 → x = 7

The possible digits are {1, 4, 7}. Among these, the smallest digit is 1.

∴ The correct answer is 1.

Additional Information

Divisibility Rule of 3

A number is divisible by 3 if and only if the sum of its digits is a multiple of 3.

Divisibility Rule of 9

Similar to 3, a number is divisible by 9 if the sum of its digits is divisible by 9.

Smallest vs Largest Digit

When finding the smallest digit, test values starting from 0. For the largest digit, test values downwards from 9.

Given:

Diameter of the base (d) = 28 cm

Radius (r) = d/2 = 28/2 = 14 cm

Height (h) = 42 cm

Formula used:

Curved Surface Area (CSA) of a cylinder = 2πrh

Calculations:

CSA = 2 × π × 14 × 42

⇒ CSA = 2 × 22/7 × 14 × 42

⇒ CSA = 2 × 22 × 2 × 42

⇒ CSA = 3696 cm²

∴ The correct answer is option (4).

Given:

The average age of 24 workers and their supervisor is 41 years. If the supervisor's age is excluded, the average reduces by 0.75 years.

Formula used:

Average = Total Sum / Number of Individuals

Calculation:

Let the supervisor's age be S years.

Total Sum of Ages including the supervisor = 41 × 25

⇒ 41 × 25 = 1025

Total Sum of Ages excluding the supervisor = 40.25 × 24

⇒ 40.25 × 24 = 966

Supervisor's age, S = Total Sum including the supervisor - Total Sum excluding the supervisor

⇒ S = 1025 - 966

⇒ S = 59 years

∴ The correct answer is option (2).

Given:

Ramendra purchased watermelons for Rs. 1,500

He sold one-fourth of them at a loss of 12%

He wants to gain 25% on the whole transaction

Formula used:

Total Cost Price (CP) = Rs. 1,500

CP of 1/4 watermelons = 1500/4 = Rs. 375

Loss on 1/4 watermelons = 12%

CP of remaining 3/4 watermelons = 1500 - 375 = Rs. 1125

Overall Gain = 25%

Total Selling Price (SP) = CP × (1 + Overall Gain%)

Calculations:

SP of 1/4 watermelons = CP - Loss

⇒ SP of 1/4 watermelons = 375 - (12/100 × 375)

⇒ SP of 1/4 watermelons = 375 - 45

⇒ SP of 1/4 watermelons = Rs. 330

Total SP for 25% overall gain = 1500 × (1 + 25/100)

⇒ Total SP = 1500 × 1.25

⇒ Total SP = Rs. 1875

SP of remaining 3/4 watermelons = Total SP - SP of 1/4 watermelons

⇒ SP of remaining 3/4 watermelons = 1875 - 330

⇒ SP of remaining 3/4 watermelons = Rs. 1545

Gain on remaining 3/4 watermelons = SP - CP

⇒ Gain = 1545 - 1125

⇒ Gain = Rs. 420

Gain Percentage on remaining 3/4 watermelons = (Gain/CP) × 100

⇒ Gain Percentage = (420/1125) × 100

⇒ Gain Percentage = 37.33%

∴ The correct answer is option 3.

Given:

A number is first increased by 44% and then decreased by 30%.

Formula used:

Net Percentage Change = $(1 + \frac{a}{100}) \times (1 - \frac{b}{100}) - 1 × 100$

Where, a = 44 and b = 30

Calculation:

Net Percentage Change = $(1 + \frac{44}{100}) \times (1 - \frac{30}{100}) - 1 × 100$

⇒ Net Percentage Change = $(1 + 0.44) \times (1 - 0.30) - 1 × 100$

⇒ Net Percentage Change = $(1.44) \times (0.70) - 1 × 100$

⇒ Net Percentage Change = (1.008 - 1) × 100

⇒ Net Percentage Change = 0.008 × 100

⇒ Net Percentage Change = 0.8%

Rounding off to the nearest integer, Net Percentage Change ≈ 1%

∴ The correct answer is option (4).

Shortcut Trick

To find the inverse ratio M : N : O from 1/M : 1/N : 1/O = 3 : 4 : 5, use the hide-and-multiply method.

For M, hide 3 and multiply others: 4 × 5 = 20

For N, hide 4 and multiply others: 3 × 5 = 15

For O, hide 5 and multiply others: 3 × 4 = 12

∴ The correct answer is 20 : 15 : 12.

Alternate Method

Given:

1/M : 1/N : 1/O = 3 : 4 : 5

Formula Used:

If 1/x : 1/y : 1/z = a : b : c, then x : y : z = 1/a : 1/b : 1/c.

Calculations:

⇒ M : N : O = 1/3 : 1/4 : 1/5

⇒ To convert the fractional ratio to integers, multiply by the LCM of 3, 4, and 5.

⇒ LCM(3, 4, 5) = 60

⇒ M = (1/3) × 60 = 20

⇒ N = (1/4) × 60 = 15

⇒ O = (1/5) × 60 = 12

⇒ M : N : O = 20 : 15 : 12

∴ The correct answer is 20 : 15 : 12.

Additional Information

Inverse Ratio

The inverse ratio of a : b is 1/a : 1/b, which simplifies to b : a. For three terms a : b : c, it is 1/a : 1/b : 1/c.

Compound Ratio

The compound ratio of a : b and c : d is calculated by multiplying the corresponding terms, resulting in ac : bd.

Duplicate Ratio

The duplicate ratio of a : b is obtained by squaring both terms of the ratio, expressed as a² : b².

Ratio Property

Multiplying or dividing all terms of a ratio by the same non-zero constant does not change the value of the ratio.

Given:

An equal sum of money was lent to P and Q at 8.6% per annum for a period of 7 years and 8 years, respectively.

Difference in interest paid by them = Rs. 172

Formula used:

Simple Interest (SI) = $\frac{P \times R \times T}{100}$

Calculation:

Interest paid by P: $SI_P = \frac{P \times 8.6 \times 7}{100}$

Interest paid by Q: $SI_Q = \frac{P \times 8.6 \times 8}{100}$

Given, $SI_Q - SI_P = 172$

⇒ $\frac{P \times 8.6 \times 8}{100} - \frac{P \times 8.6 \times 7}{100} = 172$

⇒ $\frac{P \times 8.6 \times (8 - 7)}{100} = 172$

⇒ $\frac{P \times 8.6}{100} = 172$

⇒ $P \times 8.6 = 172 \times 100$

⇒ $P \times 8.6 = 17200$

⇒ $P = \frac{17200}{8.6}$

⇒ $P = 2000$

∴ The correct answer is option (4).

Given:

D takes 45 minutes to reach the destination at 60 km/h.

Formula used:

Speed = Distance / Time

Calculation:

Distance = Speed × Time

Distance = 60 km/h × (45/60) h

⇒ Distance = 60 × 0.75

⇒ Distance = 45 km

To reach in 30 minutes:

Speed = Distance / Time

Time = 30 minutes = 30/60 hours = 0.5 hours

⇒ Speed = 45 km / 0.5 h

⇒ Speed = 90 km/h

∴ The correct answer is option 3.

Given:

The graph shows the higher secondary result of a particular school for the years 2019, 2020, and 2021. The total percentage of students who passed in the year 2020 is required.

Formula used:

Percentage of students who passed = [(Total students passed in First, Second, and Third Divisions) / (Total students)] * 100

Calculation:

In 2020, from the graph:

First Division: 70

Second Division: 80

Third Division: 95

Failed: 5

Total students = 70 + 80 + 95 + 5 = 250

Students who passed = 70 + 80 + 95 = 245

⇒ Percentage of students who passed = (245 / 250) × 100 = 98%

∴ The correct answer is option (1), 98%.

Given:

XR = 12 cm (the length of the tangent)

PQ = x cm (the length of the chord)

QR = x - 2 cm (the external part of the secant)

Formula used:

According to the Power of a Point Theorem:

$XR^2 = PR \times QR$

Where PR = PQ + QR = (x + (x - 2)) = 2x - 2

Substitute into the formula:

Calculations:

12² = (2x - 2)(x - 2)

⇒ 144 = 2x(x - 2) - 2(x - 2)

⇒ 144 = 2x² - 4x - 2x + 4

⇒ 144 = 2x² - 6x + 4

Move everything to one side:

⇒ 2x² - 6x + 4 - 144 = 0

⇒ 2x² - 6x - 140 = 0

Simplify the equation by dividing through by 2:

⇒ x² - 3x - 70 = 0

Factoring the quadratic equation:

(x - 10)(x + 7) = 0

So, x = 10 or x = -7

Conclusion:

Since x represents the length of PQ, it must be positive, so we discard x = -7.

∴ x = 10 cm.

Given:

If sin(X - Y) = sin X cos Y - cos X sin Y, then the value of (sin (A-B))/(cos A cos B)+(sin (B-C))/(cos B cos C) is:

Formula used:

sin(X - Y) = sin X cos Y - cos X sin Y

Calculation:

We need to find the value of (sin (A-B))/(cos A cos B)+(sin (B-C))/(cos B cos C)

⇒ (sin (A-B))/(cos A cos B) + (sin (B-C))/(cos B cos C)

Using the identity sin(X - Y) = sin X cos Y - cos X sin Y, we get:

⇒ (sin A cos B - cos A sin B)/(cos A cos B) + (sin B cos C - cos B sin C)/(cos B cos C)

⇒ (sin A cos B)/(cos A cos B) - (cos A sin B)/(cos A cos B) + (sin B cos C)/(cos B cos C) - (cos B sin C)/(cos B cos C)

⇒ (sin A)/(cos A) - (sin B)/(cos B) + (sin B)/(cos B) - (sin C)/(cos C)

⇒ tan A - tan B + tan B - tan C

⇒ tan A - tan C

⇒ $\frac{\sin (A-C)}{\cos A \cos C}$

∴ The correct answer is option 4.

Given:

Shobhita can complete a painting work in 20 hours

Saroj can complete the same work in 15 hours

Formula used:

If A can complete the work in a hours and B can complete the same work in b hours, then working together they can complete the work in $\dfrac{ab}{a+b}$ hours

Calculation:

Shobhita's time (a) = 20 hours

Saroj's time (b) = 15 hours

⇒ Time taken together = $\dfrac{20 \times 15}{20 + 15}$

⇒ Time taken together = $\dfrac{300}{35}$

⇒ Time taken together = $8\dfrac{4}{7} hours$

∴ The correct answer is option 2.

Shortcut Trick

Winner gets = 72%

Loser gets = 100% − 72% = 28%

Winning margin = 72% − 28% = 44% of total votes.

Margin in votes = 44% × 1000 = 440

∴ The correct answer is 440 votes.

Alternate Method

Given:

Total votes cast = 1000

Winner's share = 72% of total votes

Winner: 72% Loser: 28%

Total Votes = 1000 (100%)

Winning Margin = 44%

Equal to Loser (28%)

44% of 1000 = 440 votes

Calculations:

⇒ Total percentage of votes = 100%

⇒ Loser's share = 100% − 72% = 28%

⇒ Difference in percentage = 72% − 28% = 44%

⇒ Winning margin = 44% of total votes

⇒ Winning margin = (44 ÷ 100) × 1000

⇒ Winning margin = 440

∴ The correct answer is 440 votes.

Additional Information

Majority Margin in Elections

In a two-candidate election, the majority by which the winner wins is always the difference between the winner's and loser's percentages: Margin = Winner % − Loser %.

Valid vs Invalid Votes

If an election has invalid votes, the percentages are usually calculated on the valid votes alone. Valid Votes = Total Cast Votes − Invalid Votes.

Base of Percentage

It is vital to identify the correct base on which the percentage is calculated. Here, both candidates' shares are direct percentages of the total votes cast.

Given:

A solid copper sphere of radius 9 cm is drawn into a wire of radius 4 mm.

Formula used:

Volume of Sphere = Volume of Cylinder

Volume of Sphere = (4/3)πr³

Volume of Cylinder = πr²h

Calculation:

Volume of Sphere = Volume of Cylinder

⇒ (4/3)π(9)³ = π(0.4)²h

⇒ (4/3)π(729) = π(0.16)h

⇒ 972 = 0.16h

⇒ h = 972/0.16

⇒ h = 6075 cm

⇒ h = 60.75 m

∴ The correct answer is option 1.

Given:

The table shows the number of pizzas sold by four different bakeries (X, Y, Z, and W) in five different months. We need to find the ratio of the total number of pizzas sold by bakeries Y and Z together in November to the total number of pizzas sold by bakeries X and W together in the same month.

Formula used:

Ratio = (Total pizzas by Y and Z in November) : (Total pizzas by X and W in November)

Calculation:

Total pizzas sold by Y and Z in November = 104 + 106 = 210

Total pizzas sold by X and W in November = 120 + 105 = 225

⇒ Ratio = 210 : 225

⇒ Simplified ratio = 42 : 45

∴ The correct answer is option (2), 42 : 45.

Calculation:

$\frac{\frac{1}{2} \div \frac{3}{4} \text { of } \frac{5}{6}}{\frac{1}{2} \div \frac{3}{4} \times \frac{5}{6}}+\frac{2+2 \times 2}{2 \div 2 \times 2}$

⇒ $\frac{\frac{1}{2} \div \frac{5}{8}}{\frac{1}{2} \times \frac{4}{3} \times \frac{5}{6}}+\frac{2+4}{1\times 2}$

⇒ $\frac{\frac{1}{2} \times \frac{8}{5}}{\frac{1}{2} \times \frac{4}{3} \times \frac{5}{6}}+\frac{6}{2}$

⇒ $\frac{\frac{4}{5}}{\frac{5}{9}}+\frac{6}{2}$

⇒ $\frac{4}{5}\times\frac{9}{5}$ + 3

⇒ $\frac{36}{25}$+ 3

⇒ 111/25

∴ The correct answer is option (3).

Shortcut Trick

For two concentric circles, the length of the chord of the larger circle that is tangent to the smaller circle is given by:

Length of chord = 2 × √(R² − r²)

Here, R = 35 cm and r = 21 cm.

⇒ Length = 2 × √(35² − 21²)

⇒ Length = 2 × √((35 + 21) × (35 − 21)) = 2 × √(56 × 14) = 2 × √(784) = 2 × 28 = 56 cm.

∴ The correct answer is 56 cm.

Alternate Method

Given: Radius of larger circle (R) = 35 cm, Radius of smaller circle (r) = 21 cm.

Formula Used: Pythagoras Theorem in a right-angled triangle: Hypotenuse² = Base² + Perpendicular².

Let the two concentric circles have center O. Let AB be the chord of the larger circle that is tangent to the smaller circle at point M.

⇒ OM ⊥ AB (Radius is perpendicular to the tangent at the point of contact).

⇒ In larger circle, OM ⊥ chord AB, ∴ M bisects AB (Perpendicular from center to chord bisects the chord).

⇒ AM = MB and AB = 2 × AM.

⇒ In right-angled ▵OMA, OA = 35 cm and OM = 21 cm.

⇒ OA² = OM² + AM²

⇒ 35² = 21² + AM²

⇒ 1225 = 441 + AM²

⇒ AM² = 1225 − 441 = 784

⇒ AM = √784 = 28 cm.

⇒ AB = 2 × 28 = 56 cm.

∴ The correct answer is 56 cm.

Additional Information

Concentric Circles

Circles that share the same center point but have different radii are called concentric circles.

Tangent-Radius Property

A tangent at any point of a circle is perpendicular to the radius through the point of contact.

Chord Bisection Property

The perpendicular drawn from the center of a circle to a chord bisects the chord into two equal segments.

Pythagorean Triplets

The set (21, 28, 35) is a Pythagorean triplet as they are multiples of (3, 4, 5) scaled by 7.