CRPF Head Constable Ministerial Official Paper (Held On: 22 Feb 2023 Shift 1) (Previous Year Paper)

The correct answer is 'His mother prayed for his longivity when he fell ill.'.

Key Points

• The option that has a spelling error is 1) "His mother prayed for his longivity when he fell ill." The correct spelling is "longevity" and not "longevity".
• The word "longivity" does not exist in the English language, and the correct spelling is "longevity."
• "Longevity" refers to a long duration of life or existence, and it is often used in the context of living organisms, such as humans or animals.
• In the given option, the spelling of "longivity" is incorrect, and it should be spelled as "longevity."
• Therefore, the correct option is: His mother prayed for his longevity when he fell ill.

Additional Information

• The other options do not have any spelling errors:
• Orthodox people are victims of myopic views about life. (Correct spelling)
• A mammoth rally was held to protest against the crime. (Correct spelling)
• The kernel of the fruit is always tasty. (Correct spelling)

The correct answer will be 'To be the first to do something new and important'.

Key Points

• The idiom "blaze a trail" means to pioneer a new path or method, to be the first to do something or to create a new path for others to follow.
• It is often used to describe someone who sets a new trend or discovers a new way of doing something.
• Hence, the correct answer will be Option 2- 'To be the first to do something new and important'.

The correct option to fill in the blank is "my".

Key Points

• The word "my" indicates that the book belongs to the person speaking.
• Here, the speaker is saying that 'that book belongs to him/her'. No gender is mentioned in the question.
• The other options are incorrect as "hers" would indicate that the book belongs to a female, "mine" indicates that the book belongs to the speaker, "ours" indicates that the book belongs to a group of people, not just the speaker.

So the complete sentence would be: "This is my book and I am reading it now."

The correct answer is 'extracted; whispered; ruined'.

Key Points

• The given passage describes a situation where someone has performed a magic trick with eggs and has amazed the audience, but suddenly someone from the audience says that the performer has a hen up his sleeve, which reveals the trick behind the magic.
• The first blank requires a verb that indicates the performer's action towards the eggs. The verb "extracted" fits well here as it means to remove something carefully from a particular place, which could be used to describe the process of taking out the eggs for the trick.
• The second blank requires a verb that indicates the action of the quick man who reveals the trick behind the magic. The verb "whispered" fits well here as it means to speak in a quiet voice, which could be used to describe the quick man's action of passing on the information quietly to those around him.
• The third blank requires an adjective that describes the egg trick after it has been exposed. The adjective "ruined" fits well here as it means to spoil or damage something completely, which could be used to describe how the egg trick lost its charm and appeal after it was revealed.

The correct words to fill in the blanks are: 3) predispositions, disagreeing, pattern.

Key Points

• Our expectations and predispositions may, however, blind us to what the article and its author is actually saying. If, for example, we are used to disagreeing with the author, we may see only what we expect to see and not what is actually there. Day after day in our routine pattern of life, we expose ourselves to the same newspaper.
• This option is correct because it accurately fills in the blanks with words that make sense in the context of the sentence.
• Expectations are beliefs about what we think will happen or what we expect to see, and predispositions are our pre-existing attitudes or inclinations towards a particular topic or perspective. Therefore, "predispositions" is an appropriate word to use in the context of the sentence, as it suggests that our pre-existing attitudes may influence how we interpret the article.
• The sentence also talks about how we may see only what we expect to see, which implies disagreement with the author's point of view. Therefore, "disagreeing" is the appropriate word to use in the context of the sentence.
• Lastly, the sentence talks about our routine pattern of life, which suggests that "pattern" is an appropriate word to use in the context of the sentence.

The correct answer is 'A'.

Key Points

• The use of the indefinite article "A" implies that Shylock is just one of many individuals living in the speaker's neighborhood. This article is used before singular countable nouns that are not specific or known to the listener.
• For example, "A dog barked outside my house"
• However, in the given sentence, the speaker is introducing the idea of Shylock as a new piece of information.
• Therefore, the use of the indefinite article "A" is more appropriate.
• It's important to note that the use of "A" or "The" depends on the context of the sentence and the speaker's intent. In some cases, the use of either article can be correct, depending on the specific situation.

Confusion Points

• If the speaker was referring to a specific Shylock that the listener or reader was already familiar with, the definite article "The" would be used. For example, "The Shylock who lives on Main Street is my neighbor."
• The use of the indefinite article "A" implies that Shylock is not a specific or previously mentioned individual. Instead, it suggests that Shylock is just one of the many people living in the speaker's neighborhood. This could be the case if the speaker is just introducing the idea of Shylock to the listener or reader, or if Shylock is not a well-known figure in the neighborhood.

The correct answer is "had been playing."

Key Points

• The sentence is referring to a past event that took place yesterday, and it indicates that the action of playing chess started at some point in the past and continued for a period of time. This implies that a past continuous tense would be appropriate to use in this context.
• option 3) "had been playing" is the most appropriate option to fill in the blank since it correctly conveys the past continuous tense and indicates that the action of playing chess started at some point in the past and continued for a period of time.
• Hence, the correct answer will be Option 3.

Additional Information

• Option 1) "has been playing" is in present perfect continuous tense, which is used to describe an action that started in the past and is still continuing up to the present moment.
• This tense would not be appropriate in this context since the action of playing chess occurred entirely in the past.
• Option 2) "is playing" is in present continuous tense, which is used to describe an action that is happening at the present moment.
• This tense would not be appropriate in this context since the sentence is referring to a past event.
• Option 4) "plays" is in present simple tense, which is used to describe actions that are habitual or routine.
• This tense would not be appropriate in this context since the sentence is referring to a specific past event.

The most appropriate option to fill in the blanks would be "exodus; deplorable."

Key Points

• The word "exodus" refers to a mass departure or emigration of people from a particular place, and it suggests that the community was compelled to leave the valley involuntarily.
• The word "deplorable" means something that is deserving of condemnation or strong disapproval, and it conveys a negative connotation that is appropriate in the context of the sentence.
• Therefore, option 2) "exodus; deplorable" is the most appropriate option to fill in the blanks since it conveys the involuntary mass departure of the community from the valley and the negative connotation that is appropriate in this context.

Additional Information 

• Option 1) "acceptance; lamentable" does not fit the context of the sentence as it implies that the community voluntarily accepted to leave the valley, which is not the case.
• Option 3) "salutation; reprehensible" does not fit the context of the sentence either as "salutation" means a greeting or an expression of respect, which is not appropriate in this context.
• Option 4) "ovation; regrettable" does not fit the context of the sentence as "ovation" means a loud and enthusiastic show of appreciation, which is not appropriate in this context.

Option 1) It is the birthplace of a maroon jellyfish that reaches a weight of 500 pounds. is the correct alternative.

Key Points

• In the original sentence, the verb "have been reaching" is grammatically incorrect.
• "Have been reaching" is the present perfect continuous tense, which implies an ongoing action that started in the past and continues into the present.
• Example- I have been playing cricket for 4 hours. This means that i'm still playing.
• However, in this context, we're referring to a characteristic of the maroon jellyfish, which is its ability to reach a weight of 500 pounds. This is better expressed in the simple present tense.
• Therefore, option 1 correctly uses the simple present tense verb "reaches" to convey this characteristic. The sentence structure and verb tense are both appropriate for describing a general fact or characteristic about the maroon jellyfish.

The most appropriate option to fill in the blanks would be "granaries; arsenals."

Key Points

• The word "granaries" refers to a storehouse for grain, and it implies that a country needs to have sufficient food supplies to sustain its troops during a war.
• The word "arsenals" refers to a place where weapons and military equipment are stored, and it implies that a country needs to have a well-stocked arsenal to equip and arm its troops during a war.
• Therefore, option 3) "granaries; arsenals" is the most appropriate option to fill in the blanks since it conveys the necessary supplies of food and weapons that are required for a country to succeed in a war.

Additional Information

• Option 1) "menageries; infirmaries" does not fit the context of the sentence as "menageries" means a collection of wild animals kept in captivity for exhibition, and "infirmaries" refers to a place where sick or injured people are treated, which are not relevant to the context of the sentence.
  

Option 2) "sculleries; tanneries" does not fit the context of the sentence either as "sculleries" means a small room adjoining a kitchen where washing up is done, and "tanneries" refers to a place where animal hides are processed into leather, which are not relevant to the context of the sentence.

Option 4) "mortuaries; morgues" does not fit the context of the sentence as "mortuaries" refers to a place where dead bodies are kept before burial or cremation, and "morgues" refers to a place where dead bodies are kept for identification and autopsy, which are not relevant to the context of the sentence.

The most appropriate synonym of the word "Poise" is "Equanimity."

Key Points

• The word "Poise" refers to the state of being balanced and composed, especially in difficult situations.
• The word "Equanimity" means calmness and composure, especially in difficult situations, and it is a synonym of "Poise."

Therefore, the most appropriate synonym of the word "Poise" is option 1) "Equanimity."

Additional Information

• Option 4) "Frenzy" does not fit the context of the word "Poise" as it means a state of being uncontrollably excited or agitated, which is not synonymous with being balanced and composed.
• Option 2) "Excitement" does not fit the context of the word "Poise" as it means a feeling of enthusiasm or eagerness, which is not synonymous with being balanced and composed.
• Option 3) "Confusion" does not fit the context of the word "Poise" as it means a state of being bewildered or unclear, which is not synonymous with being balanced and composed.

The correct answer is 'revealed; exposed; extracted'.

Key Points

"In September 2011, The Hindustan Times did a study in Delhi and reported that the number of malaria cases at the time were actually thrice as many as revealed by the city authorities. Earlier, in Mumbai, a municipal claim that 145 people died due to malaria in 2010 was exposed a lie after Praja, a city NGO, extracted figures from the municipality itself."

• Option 3 - revealed; exposed; extracted - provides the most appropriate words to fill in the blanks.
• The sentence talks about the mismatch between the number of malaria cases reported by the city authorities and the actual number of cases, which was revealed in a study done by The Hindustan Times.
• The second part of the sentence talks about how a municipal claim in Mumbai was proven to be a lie after figures were extracted from the municipality itself by Praja, a city NGO.
• The words 'revealed', 'exposed', and 'extracted' accurately convey the meaning of the sentence.

The correct answer is 'imperative, existence, predators'.

Key Points

• Imperative (अनिवार्य): Refers to something that is essential or of utmost importance. In this context, it signifies that the caterpillar's primary focus is survival.
• Existence (अस्तित्व): This represents the caterpillar's state of being or life. The sentence conveys that survival is fundamental to the caterpillar's life.
• Predators (शिकारी): These are animals that hunt and feed on other animals. The caterpillar faces the risk of being eaten by predators.
• The phrase "To eat and not be eaten" emphasizes the survival strategy of caterpillars.
• The leaf roller caterpillar constructs a shelter to protect itself while eating to minimize the risk of predation, aligning with the use of "predators".

Therefore, the correct answer is 'Option 1'.

Additional Information

• Vision, purview, cannibals: Incorrect usages, as "vision" (दृष्टि), "purview" (परिधि), and "cannibals" (नरभक्षी) do not fit the context of survival and shelter construction.
• Motto, species, carnivores: Although "motto" (सूक्ति) and "species" (प्रजाति) might somewhat fit, "carnivores" (मांसाहारी) refers specifically to meat-eating animals, which is contextually less accurate than "predators."
• Mission, peers, herbivores: "Mission" (मिशन) and "peers" (साथी) are contextually inappropriate; "herbivores" (शाकाहारी) are plant-eaters, not typically predators of caterpillars.

The most appropriate option to fill in the blank is: had.

Key Points

"Vishal had intended to set up his own business but could not."

• Option 3, 'had', is the correct choice because it indicates that Vishal had a plan to set up his own business, but he was unable to do so.
• The use of the past perfect tense 'had intended' shows that this plan was made in the past and is now completed.
• Therefore, the sentence is correctly constructed using the past perfect tense 'had' and the past participle 'intended'. Options 1, 2 and 4 are incorrect as they use the present tense 'is', the past tense 'was', and the present perfect tense 'has', respectively, which do not fit the context of the sentence.

The correct answer is 'They were afraid that the problem will have serious repurcussion on the country’s politics and economy.'.

Key Points

• The sentence with a spelling error is: They were afraid that the problem will have serious repurcussion on the country’s politics and economy.
• The correct spelling of the word is "repercussion" with a "e" instead of the letter "u".
• The correct sentence would be: "They were afraid that the problem will have serious repercussions on the country's politics and economy."
• Hence, the correct answer will be Option 2.
  

The correct option to fill in the blank is "from".

 Key Points

• The word "abstain" means to refrain from or avoid doing something, especially something that is considered to be pleasurable or enjoyable but might be harmful.
• In this case, the doctor has asked the person to avoid or refrain from drinking.
• Therefore, the correct preposition to use with "abstain" in this context is "from".
• The other options ("with", "against", and "upon") do not convey the same meaning and are not appropriate in this context.

The correct answer is 'No matter what difficult situation you’re in, there is always a positive side to be seen.'.

Key Points

• The most appropriate meaning of the proverb "Every cloud has a silver lining" is: No matter what difficult situation you're in, there is always a positive side to be seen.
• The proverb is used to express the idea that even in difficult or negative situations, there is usually something positive that can be found or learned.
• Just like how every dark cloud has a silver lining, every negative situation also has something positive that can be taken from it.
• Hence, the correct answer will be Option 2.
  

The correct answer is 'Herbivores have different digestive systems than omnivores, so omnivores usually cannot eat all of the plants that an herbivore can.'.

Key Points

• The original sentence has a syntax error in the second sentence where "Herbivores having most different digestive systems than omnivores" is an incomplete sentence.
• The corrected sentence should be "Herbivores have different digestive systems than omnivores, so omnivores usually cannot eat all of the plants that an herbivore can."
• Specifically, it is a subject-verb agreement error.
• The sentence "Herbivores having most different digestive systems than omnivores, so omnivores usually are cannot eat all of the plants that an herbivore can" contains an incorrect verb form.
• The verb "are" should be removed, as it does not agree with the subject "omnivores."

The antonym of the given word "Corpulent" is "Slight".

Key Points

• "Corpulent" means excessively overweight or fat.
• On the other hand, "Slight" means slender or thin in build.
• So, "Slight" is the opposite of "Corpulent".

Additional Information

• "Obese" is a synonym of "corpulent," meaning extremely overweight or having a high amount of body fat. It is not an antonym.
• "Awkward" means lacking grace or skill; clumsy or ungainly. It is not related to the meaning of "corpulent," and therefore, it is not an antonym.
• The word "blimp" generally refers to a large, non-rigid airship that is used for advertising, surveillance, or transportation.

The correct article to fill in the blank is 'an'.

Key Points

• The correct sentence is: He is an LLB student and is aiming to go abroad to pursue further education.
• The article 'an' is used before a word that begins with a vowel sound, such as 'LLB', to make the sentence grammatically correct.
• The use of articles is governed by specific rules of grammar.
• The definite article 'the' is used when the speaker or writer is referring to a specific person, place, thing, or concept.
• On the other hand, the indefinite articles 'a' and 'an' are used to refer to something that is not specific or known.

In the given sentence, the word "LLB" begins with a vowel sound ('el-el-bee'), so the correct article to use is "an" (option 1).

Therefore, the sentence should read, "He is an LLB student and is aiming to go abroad to pursue further education."

The correct answer is 'Europe is already going through a phase of recession, which will escalate further in 2012.'.

Key Points

• The correct answer to the question is option 1) Europe is already going through a phase of recession, which will escalate further in 2012.
• The given passage discusses the global economic scenario and provides some positive and negative factors that may impact the growth prospects of various countries.
• According to the passage, Europe is "certainly in a spot of trouble" and is "likely to post mildly negative growth" in 2012.
• This suggests that Europe is already going through a phase of recession, and the situation may worsen in 2012.
• The passage also mentions that peripheral economies like Greece, Italy, and Spain have new governments in place and have made progress towards genuine economic reform, which suggests that there are some efforts being made to address the economic challenges in Europe. However, these efforts may not be enough to avert a recession or negative growth in 2012.

The correct answer is 'Steady improvement in the employment scenario'.

Key Points

• The positive aspect of the 2012 US economy mentioned in the passage is the steady improvement in the employment scenario, reflected in retail expenditures on discretionary items like electronics and clothes, has picked up.
• The passage states that if these trends sustain, the US might post better growth numbers for 2012 than the current forecast of 1.5%–1.8%.
• Therefore, option 2) is the correct answer.

The correct answer is 'Fiscal'.

Key Points

• The word in the passage that means 'relating to government revenue, especially taxes' is "fiscal". It is mentioned in the sentence, "Japan is likely to pull out of a recession in 2012, as post-earthquake reconstruction efforts gather momentum and the fiscal stimulus announced in 2011 begins to pay off."
• Here, fiscal refers to the fiscal stimulus announced by the government.

Additional Information

 Here are the meanings of all the options:

• Retail: Refers to the sale of goods to the public for personal or household consumption.
• Fiscal: Relating to government revenue, especially taxes.
• Forecasts: Predictions or estimates of future events or conditions.
• Recession: A period of temporary economic decline, typically characterized by a decrease in GDP, income, employment, and trade.

The correct answer is 'Analytical'.

Key Points

• Analytical: The tone of the passage is analytical as it examines different factors affecting the global economy in 2012 and provides an analysis of each of them, including the potential impact on various countries and regions.
• Humorous: The passage does not have a humorous tone. It is a serious analysis of the global economy in 2012 and the potential positive and negative factors that could impact it.
• Negative: The passage does have some negative elements, particularly with regard to Europe, which is said to be in a spot of trouble and likely to post mildly negative growth in 2012. However, the overall tone is not entirely negative, as there are also positive factors examined, such as the potential for good growth in the US and Japan, and the potential for a correction in commodity prices.
• Farcical: The passage is not farcical, as it is a serious analysis of the global economy and does not contain any elements of absurdity or exaggerated humor.

The correct answer is 'A deep analysis of the 2012 global economy'.

Key Points 

• The central theme of a passage is the main idea or message that the author is trying to convey. It is the underlying concept or topic that ties together all the different ideas and arguments presented in the passage.
• In this particular passage, the central theme is the author's analysis and forecast of the global economy in 2012. The author presents a comparison of different countries' economic scenarios and makes predictions based on current trends and events.
• The passage is not solely focused on negative aspects but also highlights positive developments such as the improvement in the US employment situation and the potential growth of Japan's economy.
• Therefore, options 1, 3, and 4 can be eliminated. The correct answer is option 2, as the passage can be considered as an analytical piece that examines the 2012 global economy and provides insights and predictions based on the author's analysis.

The correct answer is Prabha Atre.

Key Points

• Prabha Atre is an Indian classical vocalist.
• Prabha Atre was awarded the Padma Vibhushan in January 2022.
• The award was not given posthumously.
• She is from the Kirana gharana.
• She holds the world record to have released 11 books.
• She was given the Sangeet Natak Akademi Award in the year 1991.
• She was given the Padma Shri in 1990 and Padma Bhushan in 2002.

• Kirana Gharana:
• It is located in Awadh.
• Abdul Wahid Khan was the founder.

Additional Information

• The Padma Vibhushan is the second-highest civilian award of the Republic of India, after the Bharat Ratna. Instituted on 2 January 1954.
• All persons without distinction of race, occupation, position or sex are eligible for these awards.
• The first recipients of the award were Satyendra Nath Bose, Nand Lal Bose, Zakir Hussain, Balasaheb Gangadhar Kher, Jigme Dorji Wangchuck, and V. K. Krishna Menon, who were honoured in 1954.

The correct answer is 'Steeplechase'.

Key Points

• Avinash Mukund Sable is an Indian track and field athlete who specializes in 3000 metres steeplechase.
• Avinash Sable finally ended the Kenyan hegemony in the men’s 3000m steeplechase at the Commonwealth Games, the East African nation that had monopolised the CWG podium since 1988, to win a silver medal with a time of 8:11.20 at the Alexander Stadium, Birmingham.
• Sable, separated from gold medal winner Kenya’s Abraham Kibiwot by five microseconds, was disappointed at missing out on the chance to be at the top of the podium.

Additional Information 

 Arjuna Award

• Arjuna Award is one of the famous sports awards given to individuals for their exemplary performance in various sports.
• The Ministry of Youth Affairs and Sports, Government of India extends this award.
• It is the second-highest sporting honor in India, the highest being the Major Dhyan Chand Khel Ratna Award.
• It started in 1961.
• A total of 25 Sportspersons will receive their awards this year.

The correct answer is 1989.

Key Points 

• SIDBI is the principal development financial institution for promotion, financing, and development of Micro, Small, and Medium Enterprises (MSME) sector in India.
• It was established on April 2, 1990, under an Act of Parliament 1989.
• The headquarters of the SIDBI is located in Lucknow, Uttar Pradesh.
• It aims to facilitate and strengthen credit flow to MSMEs and address both financial and developmental gaps in the MSME eco-system across the country.
• It coordinates the functions of institutions engaged in similar activities.

• Housing and Urban Affairs Ministry and Small Industries Development Bank of India, SIDBI has signed an MoU to engage SIDBI as the implementation agency for PM Street Vendor’s AtmaNirbhar Nidhi (PM SVANidhi).
• The Ministry had launched the PM SVANidhi on 1st June 2020 for providing affordable Working Capital loan to street vendors.
• This scheme targets to benefit over 50 lakh Street Vendors.

The correct answer is 15 Lakh.

Key Points

• Technology Development Board (TDB) is a statutory body of Department of Science & Technology (DST).
• As part of National Technology Day celebration on 11th May every year, TDB present National Awards to industrial concerns for successful commercialization of indigenous technology.
• The second category of award was introduced for the first time in 2000 for SSI units which has been renamed as MSME Award. From 2017 onwards, a new category of award called ‘National Award for Start-Up’ has been introduced to encourage & promote technologies developed by start-ups having potential for commercialization.

AWARD CATEGORIES: There are three categories of award, which are as following-

• NATIONAL AWARD FOR THE SUCCESSFUL COMMERCIALIZATION OF INDIGENOUS TECHNOLOGY
• This award will be given to an industrial concern which has successfully developed & commercialized an indigenous technology  In case, the technology developer / provider and technology commercializer are two different organizations, each one would be eligible for award of ₹25 Lakh and a trophy.
• Cash Award of ₹25 Lakh
• Number of awards: One*

• NATIONAL AWARD FOR MSMEs
• This award will be given to MSMEs which have successfully commercialized a product based on indigenous technology.
• Cash Awards of ₹15 Lakh
• Number of awards: Three*

• NATIONAL AWARD FOR TECHNOLOGY START-UPs
• This award will be given to a technology start-up for promising new technology with potential for commercialization.
• Cash Awards of ₹15 Lakh

• • Selection Committee may change the number of awards under each category to be given or may defer if the entries are not found suitable.

The correct answer is ​Gujarat.

Key Points

• The Harappan site of Dholavira is located in Gujarat.
• In the great ran of Kutch of Gujarat, at Bhachau taluka, Dholavira is a village.
• On Khadir Island, the site is located.
• The site can be 4000 years BCE.
• From 2900-2400 BCE, the site expanded very fast.
• For the construction of the house, the people of Dholavira switched from the mud-brick to stone brick.
• Potteries and ornaments were made by the people of the region.
• Dholavira is the largest excavated Harappan site.
• The continuous settlement at one given place is recorded in Dholavira.
• Excellent city planning, wide roads, and architecture with geometric precision can be seen here.
• On Mansar and Manhar River, the dams were built by the people of Dholavira.

Additional Information

• Harappan civilization
• Harappan civilization is also called as Indus Valley Civilization (IVC).
• John Marshall was the first researcher to use the term, ‘Indus Valley Civilization’.
• Indus Valley Civilization (IVC) is one of the four great civilizations of the world.
• It flourished along the flood plains of Indus and Ghaggar-Hakra.
• It was spread across the western part of South Asia that now lies in India, Pakistan and Afghanistan.
• Indus Valley Civilization spread from the year 2500 – 1750 BC according to radio-carbon dating.
• The capital cities were Mohenjodaro and Harappa.

The correct answer is Cyclone ASANI

Key Points

• Cyclone Asani formed in the Bay of Bengal on 8 May 2022.
• The name Asani has been given by Sri Lanka which means 'wrath' in Sinhalese.
• Cyclone Asani is the first storm in the North Indian Ocean region in 2022.
• The cyclone has been predicted to strengthen into a very severe cyclonic storm, with wind speeds reaching 118 to 220 km/hour, and remaining over the east-central Bay of Bengal.

Additional Information Favourable Conditions for Cyclone:

• Large sea surface with a temperature higher than 27° C.
• Presence of the Coriolis force is enough to create a cyclonic vortex.
• Small variations in the vertical wind speed.
• A pre-existing weak low-pressure area or low-level cyclonic circulation.
• Upper divergence above the sea level system.

The IMD’s four colour codes are:

• Green: This code means that “all is well” there is no likelihood of any adverse weather-related and there are no advisories issued.
• Yellow: The colour yellow signals authorities to “be aware” or on their guard.
• Orange: Meaning “Be prepared”, the IMD issues the orange alert as a warning for extremely bad weather, electricity blackouts and the possibility of communication disruptions, including road and rail closures.
• Red: The IMD issues the highest level of warning—indicating authorities should “take action”.

The correct answer is Droupadi Murmu.

• President Droupadi Murmu laid the foundation stone of state-owned energy firm SJVN’s 1,000 MV Bikaner Solar Power Project.
• The event was done virtually by the President of India in Jaipur, Rajasthan.
• The project is being implemented by SJVN Limited through its owned subsidiary SJVN Green Energy Limited (SGEL).
• The solar power project is being developed on 500 acres near the village of Banderwala, district Bikaner of Rajasthan.
• It is one of the highest solar yield areas in India.
• The project is scheduled to be commissioned by March 2024, he said, adding the project will generate 2,454.55 million units (MU) in the first year and approximately 56,838 MU would be generated on a cumulative basis over a period of 25 years.
• The project would also lead to a reduction in carbon emissions of 27,85,077 tonnes.

The correct answer is Fifth.​

Key Points

• India has overtaken Britain to become the world’s fifth largest economy.

Additional Information 

• GDP is the final value of all the goods and services produced in a country in a given year.
• Nominal gross domestic product is the gross domestic product (GDP) evaluated at current market prices.
• Real GDP, on the other hand, is calculated by taking a base year as a determinant.
• Real GDP adjusts for price changes due to inflation/deflation.
• The main difference between nominal GDP and real GDP is the adjustment for inflation.
• A cryptocurrency is a digital or virtual currency designed to work as a medium of exchange.
• It uses cryptography functions to secure and verify transactions as well as to control the creation of new units of a particular cryptocurrency.

The correct answer is ₹1 lakh crore.

Key Points

• Smt. Sitharaman proposed to allocate Rs. 1 lakh crore to assist the States in catalyzing overall investments in the economy for 2022-23.
• These fifty-year interest free loans are over and above the normal borrowings allowed to the states, she said. This allocation will be used for PM Gati Shakti related and other productive capital investment of the States including components for:
• Supplemental funding for priority segments of PM Gram Sadak Yojana, including support for the States’ share,
• Digitization of the economy, including digital payments and completion of OFC network, and
• Reforms related to building byelaws, town planning schemes, transit-oriented development, and transferable development rights.

Additional InformationPM Gati Shakti

• PM GatiShakti National Master Plan was launched on 13th October 2021 for providing multimodal connectivity infrastructure to various economic zones
• PM GatiShakti is a transformative approach to economic growth and sustainable development. The approach is driven by 7 engines, namely: Railways Roads, Ports, Waterways, Airports, Mass TransportLogistics Infrastructure
• PM GatiShakti National Master Plan provides a comprehensive database of the ongoing & future projects of various Ministries i.e. Infrastructure Ministries & Ministries and States involved in the development of Economic Zones, integrated with 200+ GIS layers thereby facilitating planning, designing and executing of the infrastructure projects with a common vision.
• PM Gati Shakti Master Plan for Expressways will be formulated in 2022-23 to facilitate the faster movement of people and goods. The national highways network will be expanded by 25,000 km in 2022-23.

The correct answer is Morarji Desai.

Key Points

• The Gold Control Act of 1962 was introduced by Morarji Desai, who was the Finance Minister of India at the time.
• Morarji Desai served as the Finance Minister of India twice, from 1959 to 1963 and from 1967 to 1970.
• He was known for his conservative economic policies and played a significant role in shaping India's economic landscape during his tenure.

Additional Information 

• Under the Gold Control Act of 1962, the government of India had the power to regulate the manufacture, possession, sale, transport, import, and export of gold and other precious metals.
• The act prohibited the holding of gold by individuals, except in the form of jewelry, and required them to declare any gold holdings above a certain limit.

The correct answer is 2000.

Key Points

About Pandit Jasraj:

• He was born on 28 January 1930 in Pili Mandori, Village in Hisar District of Haryana State. Pandit Jasraj was an Indian classical vocalist, belonged to the Mewati Gharana.
• Pandit Jasraj Musical Career spanned over 75 years resulting in International and National fame. He accoladed with many National and International Awards.
• He conferred with some of the major awards of India they were Padma Bhushan in 1990, Padma Vibhushan 2000, Padma Shri 1975, Sangeet Natak Akademi award 1987, etc.
• He died on 17th August 2020. He trained under some of the veterans like Ghulam Qadir Khan of Mewati Gharana, and Classical Vocalist Pandit Maniram.

The correct answer is 'Sikkim'.

Key Points 

• The Indian Census 2011 can be referred to as the seventh census operation after Indian independence.
• According to the State Census 2011,
• The most populated state in India is Uttar Pradesh with a population of 19.96 crores.
• The least populated state in the country is Sikkim with a population of 60, 7688.
• Mizoram is the second least populous state in India with around 1,091,014 population.
• Arunachal Pradesh is the third least populous state.

Hence, the correct answer is Sikkim.

Additional InformationCensus in India:

• It was done for the first time in 1872 under the British Viceroy Lord Mayo.
• After that, it is conducted at intervals every 10 years.
• However, the first complete census of India was conducted in 1881.
• Since 1949, it is conducted by the Registrar General and Census Commissioner of India under the Ministry of Home Affairs, Government of India.
• All censuses after 1951 were conducted under the 1948 Census Act.
• As of 2011, the Census of India has been conducted 15 times.

The Correct answer is Jahanara.

Key Points 

• Jahanara Begum Sahib was the eldest daughter of Shah Jahan and Mumtaz Mahal.
• Together with her brother Dara Shikoh. she was a disciple of Mullah Shah Badakhshi, who initiated her into the Qadiriyya Sufi order in 1641.
• Jahanara Begum made such progress on the Sufi path that Mullah Shah would have named her his successor in the Qadiriyya, but the rules of the order did not allow this.
• She wrote a biography of Moinuddin Chishti, the founder of the Chishtiyah order, titled "Mu’nis al-Arwāḥ", as well as a biography of Mullah Shah, titled Risālah-i Ṣāḥibīyah, in which she also described her initiation by him.
• Her biography of Moinuddin Chishti is highly regarded for its judgment and literary quality. In it, she regarded him as having initiated her spiritually four centuries after his death, described her pilgrimage to Ajmer, and spoke of herself as a faqīrah to signify her vocation as a Sufi woman.

The correct answer is 8.6%.

Key Points

A census is a procedure of systematically calculating, acquiring, and recording information about the members of a given population

• According to Census 2011, the number of scheduled tribes in India is 10, 42, 81,034, which is 8.6% of the total population of India.
• The number of Scheduled Castes is 20,13, 78086, which is 16.6%.

Additional Information

• The Census of India is conducted every 10 years.
• Census 2011 was the 15th National census survey conducted by the Registrar General and Census Commissioner of India.
• Mr. C. Chandramouli is the Commissioner & Registrar General of the Indian 2011 Census.

Hence, According to the Census of India 2011, the Scheduled Castes and the Scheduled Tribes were 16.6% and 8.6% of the country’s population, respectively.

The correct answer is Justice S Abdul Nazeer.

Key Points

• Justice Abdul Nazeer has been appointed as the Governor of Andhra Pradesh, a month after retiring from the Supreme Court.
• He was the lone minority judge in the bench which gave the judgement in Ayodhya case and paved the way for the construction of Ram temple.
• The Ram Jannabhoomi temple- Babri Masjid was a long-drawn dispute between the two communities which the Supreme Court finally decided on November 9, 2019.
• Justice S. Abdul Nazeer was one of the five-member Supreme Court Bench that gave the final verdict.
• The landmark 2019 judgment in the Ayodhya Ram Mandir-Babri Masjid dispute, pronounced by a five-judge bench of former CJI Ranjan Gogoi, Justice SA Bobde, Justice DY Chandrachud, Justice Ashok Bhushan and Justice S. Abdul Nazeer.

The correct answer is Nagaland.

Key Points 

• The Family Courts (Amendment) Bill, 2022 was introduced in Lok Sabha on July 18, 2022.
• This bill was passed by Lok Sabha on 26th July 2022, and it seeks to amend the Family Courts Act, 1984.
• The bill was passed by Rajya Sabha on 4 Aug 2022.
• This bill has granted statutory cover to already established family courts in Himachal Pradesh and Nagaland.
• The Bill seeks to extend the scope of the Act for the establishment of Family Courts in the State of Himachal Pradesh with effect from the 15th of February 2019 and in the State of Nagaland with effect from the 12th of September 2008.
• Every order of appointment of a person as a Judge of a Family Court and every order of posting, promotion or transfer, as the case may be, made under this Act in the States of Himachal Pradesh and Nagaland prior to the commencement of the Family Courts (Amendment) Act, 2022 shall be deemed to be validly made under the provisions of this Act.

The correct answer is Janata Small Finance Bank Limited.

Key Points

• Small Finance Banks:
• They are the financial institutions that provide financial services to the unserved and unbanked region of the country.
• They are registered as a public limited company under the Companies Act, 2013.
• The minimum paid-up equity capital for small finance banks shall be Rs. 100 crore.
• The promoter’s minimum initial contribution to the paid-up equity capital of such a small finance bank shall at least be 40 per cent and gradually brought down to 26 per cent within 12 years from the date of commencement of business of the bank.

 According to RBI, currently, 12 small finance banks are operating in India.

• They are as follows:
• Au Small Finance Bank Ltd.
• Capital Small Finance Bank Ltd
• Fincare Small Finance Bank Ltd.
• Equitas Small Finance Bank Ltd
• ESAF Small Finance Bank Ltd.
• Suryoday Small Finance Bank Ltd.
• Ujjivan Small Finance Bank Ltd.
• Utkarsh Small Finance Bank Ltd.
• North East Small finance Bank Ltd
• Jana Small Finance Bank Ltd
• Shivalik Small Finance Bank Ltd
• Unity Small Finance Bank Ltd

Additional Information

Payments Bank

• The minimum paid-up equity capital for payment banks shall be Rs. 100 crore.
• The promoter’s minimum initial contribution to the paid-up equity capital of such payments bank shall at least be 40 per cent for the first five years from the commencement of its business.

The correct answer is CO2.

Key Points 

• Life rafts are typically equipped with a carbon dioxide cylinder that is used to inflate the raft in case of an emergency.
• When the valve on the CO₂ cylinder is opened, the gas flows into the inflatable chambers of the raft and expands them, quickly inflating the raft to its full size.
• Carbon dioxide is a good choice for inflating life rafts because it is non-flammable and non-toxic.
• It is readily available and easy to store in cylinders.

Additional Information 

• H₂O₂ (hydrogen peroxide) is not typically used to inflate life rafts, as it is highly reactive and can be dangerous to handle.
• N₂ (nitrogen) is an inert gas and does not react with other substances, but it is not commonly used to inflate life rafts.
• C₂H₂ (acetylene) is a highly flammable gas and is not suitable for inflating life rafts.

CONCEPT:

• Ampere’s Law: Line integral of the magnetic field B around any closed curve is equal to μ0 times the net current I threading through the area enclosed by the curve i.e.

$\oint \vec B \cdot \overrightarrow {dl} = {\mu _o}I$

where I - current flowing

EXPLANATION:

• In a simplified form, Ampere's circuital law states that if the field is directed along the tangent to every point on the perimeter L of a closed curve and its magnitude is constant along the curve, then BL = μoI

where I = the net current enclosed by the closed circuit.

• The closed curve is called the Amperean loop which is a geometrical entity and not a real wire loop.
• According to this law, magnetic fields are related to the electric current produced in them.
• The law specifies the magnetic field that is associated with a given current or vice-versa, provided that the electric field doesn’t change with time.
• It can be applied outside the conductor only.

The correct answer is 1872​.

Key Points 

​The Indian Christian Marriage Act, 1872 -

• ​The Indian Christian Marriage Act, 1872 also called the Native Marriage Act.
• This is an act of the Parliament of India regulating the legal marriage of Indian Christians. Hence statement 1 is incorrect.
• According to the act, marriage is legitimate if at least one of the parties is Christian.
• An ordained minister of any church in India, a clergyman of the Church of Scotland, a marriage registrar or a special licensee may get an aspiring couple married under the act.
• The marriage performer issues a marriage certificate.
• This certificate is recorded with the Registrar of Marriage
• It was enacted on July 18, 1872, and applies throughout India, excluding territories such as Cochin, Manipur and Jammu and Kashmir.

The correct answer is North-East.

Key Points

• Satriya Nritya is the classical dance form of the North-Eastern State of Assam which represents the Satriya culture, the basis of the religious and cultural fabric of Assam.
• It is a dance-drama performance art with origins in the Krishna-centered Vaishnavism monasteries of Assam and attributed to the 15th-century Bhakti movement scholar and saint Mahapurush Srimanta Sankardev.
• Dance historian Dr. Sunil Kothari has recently been bestowed with the Madhabdev Award by the Government of Assam for popularising the Sattriya dance.
• Sattriya was given the status of classical dance in the year 2000 by the Sangeet Natak Akademi.

Important Points 

• Other classical dances of India are:
• Bharatnatyam (Tamil Nadu), Kathakali (Kerala), Kuchipudi (Andhra Pradesh), Kathak (North India), Mohiniyattam (Kerala), Manipuri (Manipur) and Odissi (Odisha).

The correct answer is Article 19(1) (d).

Key Points

• Article 19(1)
• In the original text of the constitution, Art. 19 contained seven rights.
• Under the original Constitution Article 19(1)(f) and 31 provide for the protection of property rights that included acquiring and disposing of the property.
• Later they were repealed and Article 300A was inserted.
• Six rights under Art. 19 are protected against only state action and not private individuals.
• These rights are available only to the citizens not to foreigners or legal persons like companies or corporations, etc.
• The State is empowered to impose “reasonable” restrictions on the enjoyment of these six rights only on the grounds mentioned in the Art. 19 itself and not on any other grounds

Article 19 (1) states:

• All citizens shall have the right
• a) To freedom of speech and expression
• b) To assemble peaceably and without arms
• c) To form associations or unions
• d) To move freely throughout the territory of India
• e) To reside and settle in any part of the territory of India and
• f) The right to acquire, hold and dispose of property Omitted by the 44th Amendment Act
• g) To practice any profession, or to carry on any occupation, trade, or business
• Hence, Option 3 is correct.

The correct answer is West Bengal.

Key Points 

• Singalila National park is located in the Darjeeling districts of West Bengal.
• The Singalila Ridge is a north-south mountain ridge running from northwestern West Bengal.
• The Singalila National Park is a high-altitude park with virgin Rhododendron forests—declared a wildlife sanctuary in 1986, it became a national park in 1992.
• The four highest peaks in this ridge are
• Falut (3,600 m).
• Sandakphu (3,636 m) - the highest point in West Bengal.
• Tonglu (3,036 m).
• Sabargram (3,543 m).

Additional Information

• Wildlife sanctuaries and national parks in West Bengal have included Jaldapara Wildlife Sanctuary, Buxa National Park, Gorumara National Park, Chapramari Wildlife Reserve, and the Mahananda Wildlife Sanctuary.

The Correct answer is Communist Party of India.

Key Points 

• Indrajit Gupta was the longest-serving member having been elected eleven times to the Lok Sabha the lower house of Indian Parliament.
• Indrajit Gupta belongs to Communist Party of India, often referred to as the "Father of the House", His constituency was Kolkata South West.
• Somnath Chatterjee was the leader of the CPI in Lok Sabha from 1989 to 2004.
• Somnath Chatterjee lost just one Lok Sabha election and was a ten-time MP.
• Atal Bihari Vajpayee was a member of the Indian Parliament for over five decades, having been elected ten times to the Lok Sabha.
• PM Sayeed was a member of Indian National Congress. He has been elected ten times to the Lok Sabha.

The correct answer is Oyster.

Key Points 

• Phylum Porifera, also known as sponges, is a group of aquatic animals that are characterized by their porous bodies and lack of true tissues and organs.
• Sponges are filter feeders, meaning they feed on small particles suspended in water that pass through their bodies.
• Glass sponges and Demosponges both belong to phylum Porifera.
• Glass sponges are a type of sponge with a skeleton made of silica, while demosponges have a skeleton made of collagen fibers.
• Stromatoporoidea, also known as stromatoporoids, are a separate phylum of extinct aquatic animals that lived during the Paleozoic era.
• Although they have a porous body structure similar to sponges, they are not classified within the phylum Porifera.
• Oysters belong to phylum Mollusca, which is a separate group of animals that includes snails, clams, and octopuses.
• Mollusks have a distinct body structure that includes a muscular foot, a mantle, and a shell.

Statement:

1. All apples are oranges.
2. Some oranges are mangoes.
3. All mangoes are yellow.

Conclusion:

I. Some apples are mangoes → False (because no direct relationship given between apples and mangoes so it may be possible but not defined)

II. Some oranges are yellow → True (because some oranges are mangoes and all mangoes are yellow so some oranges are definitely yellow)

Hence, the correct answer is "Only conclusion II follows".

Position values of the letters according to the English alphabet series,

The logic followed here is,

PARK ∶ 16011811

Similarly,

SELF ∶ ?

So, SELF ∶ ? → SELF ∶ 19051206 

Hence, the correct answer is "19051206".

Tuesday, Thursday, and Saturday all are alternate days but Monday does not make any pattern with other days.

Given:

Eight friends A, B, C, D, E, F, G and H

1) A is taller than F but shorter than D.

D > A > F 

2. G is shorter than B but taller than H.

B > G > H

3. E is taller than B.

E > B

4. C is shorter than F but taller than E.

F > C > E 

By combining all the arrangements :

D > A > F > C > E > B  > G > H

So, 'A' is the second tallest friend.

Hence, the correct answer is 'option (1)'.

The pattern followed here is as follows:

So, the number '312' doesn't follow the pattern.

Hence, "312" is incorrect here.

After unfolding the given paper the figure formed is as shown below :

Hence, the correct answer is "Option 3".

Logic: We have to eliminate the odd pair of the following:

Option 1: Author ∶ Pen

Pen is used by the Author for writing a book.

Option 2: Chef ∶ Knife 

A Knife is used by Chef for cutting vegetables.

Option 3: Doctor ∶ Patient

The Doctor treats the Patient.

Option 4: Tailor ∶ Needle

The needle is used by Tailor for stitching the clothes.

As it can be seen that all options are analogous except "Option 3".

Hence, the correct answer should be "Option 3 : Doctor ∶ Patient".

Given equation: 16 G 8 E 17 F 52 H 13 = ?  

After replacing the symbols by their meaning, we get:

16 × 8 + 17 - 52 ÷ 13 = ?  

= 16 × 8 + 17 - 4

= 128 + 17 - 4

= 145 - 4

= 141

Hence, ‘141’ is the correct answer.

The figure that will next in the following figure series is shown below:

• One by one line incraseing in figure.

Hence, ‘option 4’ is the correct answer.

The pattern followed here is:

Given:

"LAND" is written as "LBPG"

And,

"JEAN" is written as "JFCQ"

Similarly,

"HOME" be written as '?'

Hence, the correct answer is "HPOH".

The logic followed here is:

In figure 3rd and 4th:

• Three similar figures are in the diagram. one similar figure is increasing.

Similarly, 

In figure C and D:

• One similar figure is increasing.

Hence, "Option 1" is the correct answer.

Given:

Five members of a panel D, E, F, G and H are sitting in a row, not necessarily in the same order.

1. G is sitting immediately next to E who sits in the extreme left corner.

2. D sits immediately next to F.

3. H is not an immediate neighbour of D. H does not sit next to G.

So, 'D' sits to the immediate left of F 

Hence, the correct answer is "D".

Given:

Sarah is going to her dance class from Monday to Friday on five different days.

Every day she learns different dance forms such as Ghumar, Hip-Hop, Belly, Salsa and Kathak.

1. She attends the class of Kathak and the class of Ghumar on consecutive days.

2. Where the Salsa class take place immediately after the Ghumar class.

3. Sarah learns Kathak on Tuesday.

4. There is a gap of two days between the class of Salsa and the class of Hip-Hop.

So, Sarah attend the class of Salsa on Thursday.

Hence, the correct answer is “Thursday”.

Given:

Expression:- V & W # T @ X % Y $ Z

Here,

V & W means V is the son of W.

W # T means W is the father of T.

T @ X means T is the brother of X.

X % Y means X is the sister of Y.

Y $ Z means Y is the daughter of Z

Thus, the following family tree can be drawn:

W is the husband of Z.

Hence, the correct answer is Husband.

Given:

Raju ranked sixteenth from the top and forty-ninth from the bottom among those who passed an examination

Total number of students who passed the examination = 16 + 49 - 1 = 65 -1 = 64

Seven students did not appear in the examination and two failed.

Therefore, the total number of students in the class = 64 + 7 + 2 = 73

Hence, the correct answer is 73.

Vikas said. "I have no brother or sister but Ravi's father is my father's son"

The family tree diagram is shown below: 

Thus, Vikas is the father of Ravi.

Hence, "Father" is the correct answer.

Given:-

(Left) 7 0 2 5 6 4 7 4 3 1 6 9 8 9 6 4 9 8 0 2 5 0 4 1 4 8 2 7 3 4 6 (Right)

'4' that is immediately followed by an even number and immediately preceded by an odd number:

7 0 2 5 6 4 7 4 3 1 6 9 8 9 6 4 9 8 0 2 5 0 4 (1 4 8) 2 7 (3 4 6)

Thus, there are two such numbers '4' that is immediately followed by an even number and immediately preceded by an odd number.

Hence, the correct answer is Two.

Given:

1. Vikas started walking towards East.

2. He took a left turn after walking 2 km.

3. He again took a left turn after walking 5 km.

Distance traveled by Vikas:

Now, he is facing in the West direction.

Hence, the correct answer is West.

Given Word: OUTSCREAMING

After rearranging the letters of the given word as they appear in the English alphabet, we get

ACEGIMNORSTU

There is no such letter whose position has remained unchanged after rearrangement. The position of all letters has changed after rearrangement.

Hence, the correct answer is Zero.

BODMAS Rule:

Given:-

8 $ 14 @ 5 # 56 % 7 = ? 

Replacing the codes with mathematical symbols, we get,

8 + 14 × 5 - 56 ÷ 7 = ? 

Solving using the BODMAS Rule, we get,

8 + 70 - 8 = 78 - 8 = 70

Hence, the correct answer is 70.

Given:

Six Friends - Charu, Manu, Prakash, Pari, Varun and Vishal 

Sitting in a circle and facing the center.

Now,

1) Prakash is to the immediate left of Pari.

The arrangement will be -

2) Only Varun is between Vishal and Pari. It means Varun is sitting to the immediate right of Pari and Vishal is sitting to the immediate right of Varun.

3)  Only Vishal is between Charu and Varun. It means Charu is sitting to the immediate right of Vishal and the remaining Manu is sitting between Charu and Prakash.

The final arrangement will be as follows - 

Charu is to the immediate left of Manu.

Hence, the correct answer is Charu.

The figure given in the first option can be formed from the cut-pieces given in the question figure.

Hence, the figure given in the option 1 is the correct answer.

Given Word: EAGER

The first letter is E which is a vowel and the last letter is R which is a consonant.

Thus, the condition applicable in this case is -

If the first letter is a vowel and the last letter is a consonant, the codes for the first and the last alphabet are to be interchanged.

So, the code for E (first letter) and R will be interchanged. E (first letter) will be coded as # and the R will be coded as α.

Therefore, the code for the word EAGER will be #¥£αα.

Hence, the correct answer is #¥£αα.

The pattern followed is:

Hence, ‘QQP’ is the correct answer.

The pattern given in the series is the addition of consecutive odd numbers starting from 3.

The consecutive odd numbers are 3, 5, 7, 9, 11, and so on.

So,

211 + 3 = 214

214 + 5 = 219

219 + 7 = 226

226 + 9 = 235

235 + 11 = ? = 246

So, the number which will replace the question mark (?) in the given numerical series is 246.

Hence, the correct answer is 246.

Formula used:

Area of equilateral triangle = $\frac{√3}{4}$(side)²

Calculation:

Let the side of the triangle be 'a'

Using the above formula 

Area = $\frac{\sqrt3}{2}$ × 84.5

$\frac{√3}{4}$(a²) = $\frac{\sqrt3}{2}×\frac{169}{2}$

a² = 169

a = 13 

∴ The length of each side of the triangle is 13cm.

Formula used:

Simple interest = (P × R × T)/100

Calculation:

SI₁ = (2400 × 14 × n)/100                    -----(1)

SI₂ = [2800 × 8 × (n + 3)]/100              -----(2)

According to the question

⇒ SI₁ / SI₂ = 8/7

⇒ (2400 × 14 × n)/[2800 × 8 × (n + 3)] = 8/7

⇒ 3n/2(n+3) = 8/7

⇒ 21n = 16n + 48

⇒ 5n = 48

⇒ n =  48/5 = 9.6

∴ The value of n is 9.6 years.

Shortcut Trick

Distance covered by Train 1 from 6:00 A.M. to 7:00 A.M. = 50 km/h × 1 hr = 50 km.

Remaining distance at 7:00 A.M. = 275 − 50 = 225 km.

Relative speed (opposite directions) = 50 + 62.5 = 112.5 km/h.

Time to meet = 225 ÷ 112.5 = 2 hours.

Meeting time = 7:00 A.M. + 2 hours = 09:00 A.M.

∴ The correct answer is 09:00 A.M.

Alternate Method

Given:

Total distance between station A and station B = 275 km

Speed of Train 1 = 50 km/h, starting time = 6:00 A.M.

Speed of Train 2 = 62.5 km/h, starting time = 7:00 A.M.

Formula Used:

Distance = Speed × Time

Relative Speed (when moving in opposite directions) = S₁ + S₂

Time = Distance ÷ Relative Speed

Calculations:

⇒ Distance covered by Train 1 in 1 hour (from 6:00 A.M. to 7:00 A.M.) = 50 × 1 = 50 km

⇒ Remaining distance between the two trains at 7:00 A.M. = 275 − 50 = 225 km

⇒ Relative speed of the trains = 50 + 62.5 = 112.5 km/h

⇒ Time required to meet after 7:00 A.M. = 225 ÷ 112.5 = 2 hours

⇒ Therefore, they will meet 2 hours after 7:00 A.M.

⇒ Meeting time = 7:00 A.M. + 2 hours = 09:00 A.M.

∴ The correct answer is 09:00 A.M.

Additional Information

Relative Speed (Opposite Directions)

When two bodies move towards each other, their relative speed is the sum of their individual speeds: S_rel = S₁ + S₂.

Relative Speed (Same Direction)

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

Average Speed

If equal distances are covered at different speeds x and y, the average speed for the whole journey is given by (2 × x × y) ÷ (x + y).

Concept:

Orthocenter of a triangle: it is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle cut each other.

Centroid: The point where all three medians of the triangle intersect each other.

Circumcenter: The point where the perpendicular bisectors of the sides of the triangle intersect each other. The vertices of the triangle are equidistant from the circumcenter.

Note: Centroid divides the orthocenter and the circumcenter internally in a ratio 2:1

Formula used:

Section Formula: Let A (x1, y1) and B (x2, y2) be the two given points and the point P (x, y) divide the line joining the points A and B in the ratio m : n, then

The point of internal division is given as:

 $\left( {x,;y} \right) = \left( {\frac{{m{x_2} + n{x_1}}}{{m + n}},\frac{{m{y_2} + n{y_1}}}{{m + n}}} \right)$

Calculation:

Given that, the coordinates  of the orthocentre and centroid of a triangle are O(6, -1) and G(4, 1)

Let, the coordinates of Circumcenter are C(x, y) & it is also equidistant from the vertices of the triangle.

By using the above concept, the centroid divides the orthocenter and the circumcenter internally in a ratio 2:1

By using the section formula 

⇒ 4 = $\frac{2x+6\times 1}{2+1}$

⇒ 4 = (2x + 6)/3

⇒ 2x + 6 - 12

⇒ x = 3

Again, 

⇒ 1 = $\frac{2y+1 \times (-1)}{2+1}$

⇒ 2y - 1 = 3

⇒ y = 2

∴ (3, 2) are the coordinates of a point that is equidistant from the vertices of the triangle.

Given:

The ratio of the monthly income of Marc and Jason is 5 ∶ 6, respectively,

The ratio of the monthly income of Tanya and Jason is 4 ∶ 3, respectively.

The monthly income of Lorenz is twice that of the total monthly income of all the remaining 3 employees.

Their monthly income of Lorenz is 26600

Calculation:

M      :        J       :        T

(5       :        6       :        _ )

 ( _     :       3       :        4)  × 2 

___________________________

5         :      6         :        8

Sum  = 5 + 6 + 8 = 19 unit

According to the question,     

income of Lorenz = 2 × 19 = 38 unit

But it is given that

38 unit =  26600    

1 unit = 700

8 unit  = 700 × 8 = 5600

∴ The highest monthly income out of the remaining 3 employees is 5600.

Given:

P and Q can complete a work in 14 days and 21 days, respectively.

They started doing the work but after 4 days

Q alone completed the remaining work. 

Calculation:

Efficiency (work/day)           Days                Total Work

42/14 = 3 unit/days     P     ----->  14  

                                                                42 =  LCM of (14, 21)  

42/21 = 2 unit/days     Q     ----->  21  

One day work of P & Q = 3 + 2 = 5 unit

4 days work of P & Q = 5 × 4 = 20 unit

Remaining work = 42 - 20 = 22 unit

Time taken by Q to complete the required work = 22/2 = 11 days

Total time taken  = (4 days work of P & Q) + 11 days work of Q

∴ The required time is 15 days.

Formula used:

a² - b² = (a - b)(a + b)

Calculation:

$\frac{(0.8)^4 - (0.4)^4}{(0.8)^2 + (0.4)^2}$

By using the above identity

⇒ $\frac{[(0.8)^2 - (0.4)^2][(0.8)^2 + (0.4)^2]}{(0.8)^2 + (0.4)^2}$

⇒ (0.8)² - (0.4)² 

⇒ 0.64 - 0.16 = 0.48

∴ $\frac{(0.8)^4 - (0.4)^4}{(0.8)^2 + (0.4)^2}$ = 0.48

Calculation:

Let's denote the initial population of the city as "x".

The population of the city increased by 12%, which means that the new population became:

x + 0.12x = 1.12x

However, due to COVID like a virus, the population decreased by 12%. This means that the current population is 88% of the increased population:

⇒ 0.88(1.12x) = 295680

⇒ 0.9856x = 295680

⇒ x = 300000

Therefore, the initial population of the city was 300000.

Calculation:

Given that 

x * y = x + y - $√{xy}$,

Let x = 32, y = 8

⇒ 32 * 8 = 32 + 8 -  √(32×8) 

⇒ 32 * 8 = 40 - √(256)

 32 * 8 = 40 - 16 = 24

∴ The required value is 24.

Given:

Three numbers P, Q, and R are in the ratio of 15 ∶ 17 ∶ 20.

The sum of these numbers is 3640

Calculation:

(Difference between Q and P) : (Difference between R and Q)

(17 - 15) : (20 - 17) = 2 : 3

Important Point

According to the question

15 + 17 + 20 unit = 3640

52 unit = 3640

1 unit = 70

But this information has no use to find the required value.

Calculation:

Let's denote the minimum marks required to pass the exam as "m" and the maximum marks that can be scored in the exam as "M".

From the problem statement, we know that:

Candidate 1 failed by 21 marks from the minimum required to pass, which means that they scored (m - 21) marks.

Candidate 2 scored 147 marks more than the minimum required to pass, which means that they scored (m + 147) marks.

The difference in percentage secured by both candidates is 40%, which means that:

(m + 147)/(M) - (m - 21)/(M) = 40/100

(168)/(M) = 2/5

M = (168 * 5)/2 = 420

Therefore, the maximum mark that can be scored in the exam is 420.

Formula used:

Average Speed = Total Distance covered / Total time 

Calculation:

Let "d " be the total distance covered by the man.

Total time = (84/42) + (d - 84)/65

Substituting this value of total time into the equation above, we get:

52 = d / [(84/42) + (d - 84) / 65]

⇒ 52 = d/[2 +  (d - 84)/65]

⇒ 52 = 65d / (65 × 2 + d - 84)

⇒ 52 = 65d / (d + 46)

⇒ 52d + 2392 = 65d

⇒ d = 184

Therefore, the total distance covered by the man is 184 km.

Given:

Principle = Rs. 20,000

Rate of Interest = 10%

Time = 1.5 years

Condition = Half yearly

Concept used:

Condition = Half yearly

New Rate = Rate/2

New time = Time × 2

Formula used:

A = P(1 + R/100)T

C.I. = A – P

Where, A → Amount, P → Principal, R → Rate,

T → Time, C.I. → Compound interest

Calculations:

New rate = 10/2 = 5%

New Time = 1.5 × 2 = 3 years

Amount = 20,000 [1 + 5/100]3

⇒ 20000 × (105/100) × (105/100) × (105/100)

⇒ Rs. 23,152.50

C.I. = 23,152.50 – 20,000

C.I. = Rs. 3152.50

Shortcut Trick

Area of sector = (θ ÷ 360) × πr²

Given θ = 90° and r = 6 cm

⇒ Area = (90 ÷ 360) × π × 6²

⇒ Area = (1 ÷ 4) × 36π = 9π cm²

∴ The correct answer is 9π cm².

Alternate Method

Given:

⇒ Radius (r) = 6 cm

⇒ Sector Angle (θ) = 90°

Formula Used:

⇒ Area of Sector = (θ ÷ 360°) × π × r²

Calculations:

⇒ Area = (90° ÷ 360°) × π × (6)²

⇒ Area = (1 ÷ 4) × π × 36

⇒ Area = 9 × π

⇒ Area = 9π cm²

∴ The correct answer is 9π cm².

Additional Information

Length of Arc

The length of the arc of a sector is given by l = (θ ÷ 360) × 2πr.

Perimeter of Sector

The total perimeter of a sector includes the arc length and two radii: P = l + 2r.

Area in terms of Arc Length

The area of a sector can also be expressed as Area = (1 ÷ 2) × l × r.

Calculation:

Let's assume that the amount of work is one unit.

Denote the amount of work each person can do in one day by D for Dinesh, P for Prateek, and M for Prem. Then we have:

D + P = 1/20             ------(1)

P + M = 1/30             ------(2)

M + D = 1/15            ------(1)

Adding equations (1), (2), and (3) gives:

2(D + P + M) = 1/20 + 1/30 + 1/15

2(D + P + M) = 3/20

D + P + M = 3/40

Substituting equation (1) into this last equation, we get:

3/40 = 1/20 + M

M = 1/40

Therefore, Prem can finish the work alone in 40 days.

Calculation:

Let the cost price of the article be 'C'.

Given that the article was sold after giving two successive discounts of 8% and 12% on its marked price of Rs. 650. 

Selling price = Marked price × (1 - 8% of marked price)(1 - 12% of marked price)

Selling price = 650 × (92/100) × (88/100)

Selling price = Rs. 526.24

As the seller gains 60% profit. 

160% of the cost price = selling price

(160/100) x C = 526.24

C = 526.24 x (100/160)

C = Rs. 328.9

Hence, the cost price of the article is Rs. 328.9.

Formula used:

Average Speed = Total distance covered / total time taken

Calculation:

Distance covered in the first 4 hours = 18 km/h × 4 h = 72 km

Distance remaining = 152 km - 72 km = 80 km

Time is taken to cover the remaining distance at 16 km/h = 80/16 = 5 h

Total time taken = 4 h + 5 h = 9 h

Average speed = 152 km / 9 h = $16\frac{8}{9}$ km/h

Calculation:

Let the number of mobile phones be N

Mobile phone sold in January = 18% of N = 0.18N

Mobile phone sold by B in January

⇒ [4/(5+4)] of 0.18N 

⇒ (4/9) × 0.18N = 0.08N

Mobile phone sold in June = 10% of N = 0.1N

Mobile phone sold by B in June

⇒ [6/(4+6)] of 0.1N 

⇒ (6/10) × 0.1N = 0.06N

Required ratio = 0.08N/0.06N = 4/3

∴ The required ratio is 4 : 3.

Shortcut Trick

From condition 1: (x + 2) / 2y = 1 / 2 ⇒ y − x = 2.

We need the sum x + y. We can quickly test the given options to find integers x and y with a difference of 2.

Checking option 4 (Sum = 8): x + y = 8 and y − x = 2 ⇒ 2y = 10 ⇒ y = 5, x = 3.

This gives the original fraction as 3 / 5.

Testing condition 2: (3 × 2) / (5 + 2) = 6 / 7, which strictly satisfies the second given condition.

∴ The correct answer is 8.

Alternate Method

Let the original fraction be x / y.

Step 1: First Condition

⇒ (x + 2) / 2y = 1 / 2

⇒ 2(x + 2) = 2y

⇒ x + 2 = y

⇒ y − x = 2   --- (Equation 1)

Step 2: Second Condition

⇒ 2x / (y + 2) = 6 / 7

⇒ 14x = 6(y + 2)

⇒ 7x = 3y + 6   --- (Equation 2)

Step 3: Solving the equations

⇒ Substitute y = x + 2 from Equation 1 into Equation 2:

⇒ 7x = 3(x + 2) + 6

⇒ 7x = 3x + 6 + 6

⇒ 4x = 12

⇒ x = 3

⇒ Substitute x = 3 in Equation 1:

⇒ y = 3 + 2 = 5

The original fraction is 3 / 5.

⇒ Sum of numerator and denominator = x + y = 3 + 5 = 8.

∴ The correct answer is 8.

Additional Information

Linear Equations in Two Variables

When solving fractional word problems, replacing the unknown numerator and denominator with separate variables (x and y) creates a basic linear system that can be efficiently solved using substitution.

Equivalent Fractions

A fraction's proportional value remains unchanged if both terms are multiplied by the same non-zero integer, but adding absolute values directly alters the ratio composition entirely.

Calculation:

1. (A + B)2 - (A - B)2 = 4AB
2. (A4 + B4)  = (A2 - B2)2 + 2A2B2
3. (A - B)(A + B) = A² - B²

Calculation:

Given that 

a + b = √12              -----(1)

a - b = √8                -----(2)

We know that 

(a + b)² - (a - b)² = 4ab

(√12)² - (√8)² = 4ab

4ab = 12 - 8 = 4

ab = 1                 

Again, using the formula

(a⁴ + b⁴)  = (a² - b²)² + 2a²b²

(a4 + b⁴) = [(a - b)(a + b)]2 + 2a2b2

(a4 + b⁴)  = 12 × 8 + 2 × 1            (∵ ab = 1)

(a4 + b4)  = 98

∴ The required answer is 98.

Formula used:

Heron's formula: It states that if a triangle has sides of length a, b, and c, then its area, A, is given by:

A = √(s(s - a)(s - b)(s - c))

Where s is the semiperimeter, given by:

s = (a + b + c) / 2

Calculation:

Using this formula, 

⇒ s = (8 + 15 + 17) / 2 = 20

⇒ A  = √(20(20 - 8)(20 - 15)(20 - 17))

⇒ ​A  = √(20 × 12 × 5 × 3)

⇒ ​A  =  √(3600)

⇒ ​A = 60 cm²

∴ Required area is 60 cm²

Formula used:

Speed = Distance / time

Calculation:

Let x be the speed for the rest of the distance.

Time taken to cover the first 100 km = 100 km / 50 km/h = 2 hours.

Time taken to cover the rest of the distance = 65 km / x hours.

Total time taken = 5 hours.

2 + (65/x) = 5

65/x = 3

x = 65/3 km/hr

Hence, the speed for the rest of the distance is 65/3 km/h.

Calculation:

12 = 2² × 3

16 = 2⁴

35 = 5 × 7

42 = 2 × 3 × 7

LCM = 2⁴ × 3 × 5 × 7  = 1680

Hence, 1680 is the least number that is exactly divisible by12, 16, 35 and 42

Also, 12 - 5 = 7, 16 - 9 = 7, 35 - 28 = 7, 42 - 35 = 7

Therefore, the common remainder is 7. 

1680 - 7 =  1673 

So, 1680k - 7 is the number where k = 1, 2, 3...... 

To find the smallest 5-digit number, let's put k = 6 (you can check in other values as well)

1680 × 6 - 7 = 10073

Sum of digits = 1 +  0 + 0 + 7 + 3 = 11

Shortcut Trick

Equate the ratio of Selling Price (SP) and Cost Price (CP) using the given condition: 18 × SP = 21 × CP.

SP / CP = 21 / 18 = 7 / 6.

Here, CP = 6 units and SP = 7 units, so Profit = 7 − 6 = 1 unit.

Gain % = (Profit / CP) × 100 = (1 / 6) × 100 = 16(2/3) %.

∴ The correct answer is 16(2/3) % gain.

Alternate Method

Given:

Selling Price of 18 articles = Cost Price of 21 articles.

Formula Used:

Gain % = [(SP − CP) / CP] × 100

Calculations:

⇒ Let the Cost Price of 1 article be ₹x.

⇒ Cost Price of 21 articles = ₹21x.

⇒ Since Selling Price of 18 articles = Cost Price of 21 articles,

⇒ Selling Price of 18 articles = ₹21x.

⇒ Cost Price of 18 articles = ₹18x.

⇒ Gain = Selling Price − Cost Price = 21x − 18x = 3x.

⇒ Gain % = (3x / 18x) × 100

⇒ Gain % = (1 / 6) × 100

⇒ Gain % = 50 / 3 % = 16(2/3) %.

∴ The correct answer is 16(2/3) % gain.

Additional Information

Profit and Loss on Quantity

When the cost price of 'm' articles is equal to the selling price of 'n' articles, the profit or loss percent is given by [(m − n) / n] × 100. If positive, it is a gain; if negative, it is a loss.

Basic Profit Percentage

Profit Percentage is always calculated on the Cost Price unless specified otherwise. Formula: Profit % = (Profit / CP) × 100.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount. Discount % = (Discount / MP) × 100.

Formula used:

Average  = Sum of all observations / Number of observations

Calculation:

The sum of the yield of the crop for state C from 2017 to 2021

= 260 + 260 + 230 + 250 + 280 = 1280

By using the above formula 

Average  = 1280 / 5 = 256

The yield of the crop for state B in 2018  = 220

Required % = [ (256 - 220)/256 ] × 100

Required % = (36/256) × 100 = 14.06 ≈ 14%.