\subsection*{Step 1: Analyzing the Subject
The core of this question lies in correctly identifying the grammatical subject and its number (singular or plural). The full subject phrase is \textit{"He, as well as his friends". While it might appear to be a compound subject, the phrase "as well as" acts as an interrupter. Grammatically, such phrases do not alter the number of the main subject. The true subject of the sentence is "He", which is a singular pronoun. Therefore, the verb that follows must also be in its singular form to maintain subject-verb agreement.

\subsection*{Step 2: Analyzing the Options
With the understanding that the verb must be singular and agree with "He," we can evaluate the given choices:

(A) aren't: This is the contraction for "are not," which is a plural verb form. Since our subject is singular, this option is incorrect.
(B) were: This is a plural past tense verb. As the subject is singular, this choice is grammatically incorrect.
(C) was: This is the singular past tense form of the verb "to be." It correctly agrees with the singular subject "He."
(D) has: This is a singular present perfect or present tense verb. While it is singular, the context of the sentence implies a past action, making the past tense "was" a more appropriate choice. Without the full sentence, we rely on the provided analysis that a past tense verb is required.


\subsection*{Step 3: Conclusion
The only option that satisfies the requirements of both number (singular) and tense (past) is (C) was. It correctly agrees with the singular subject "He," disregarding the interrupting phrase "as well as his friends." Quick Tip: When the subject is singular, use a singular verb form such as "was," even if the subject is compound with "as well as."

\subsection*{Step 1: Understanding the Sentence
The sentence in question describes an event (Chanakya's life) that occurred within a specific period (the reign of Chandragupta Maurya). The goal is to select the preposition that accurately conveys this relationship of an event happening within a defined timeframe.

\subsection*{Step 2: Analyzing the Options
Let's examine the function of each preposition in the context of time:

(A) under: This preposition is typically used to denote a position or hierarchy (e.g., "under the table," "under his command") and is not the standard choice for indicating a period of time.
(B) since: "Since" marks the starting point of an action or state that continues up to the present. It is often used with perfect tenses (e.g., "He has been king since 2010"). This does not fit the context of an event that is completed in the past.
(C) during: This preposition is used to indicate that something happens within a specific period of time or event. It perfectly describes Chanakya living within the span of Chandragupta Maurya's reign.
(D) no change / no error: This option implies the original preposition ("for") was correct. "For" is used to express the duration of time (e.g., "he reigned for twenty years"). While Chanakya lived "for" a certain number of years, the sentence aims to place his life "during" a specific reign. Therefore, a change is necessary.


\subsection*{Step 3: Conclusion
The preposition (C) during is the most accurate choice as it correctly expresses that the event of Chanakya's life transpired within the specific historical period of Chandragupta Maurya's reign. Quick Tip: Use "during" when referring to events or actions that happen within a particular time frame.

\subsection*{Step 1: Analyzing the Possessive Form
The sentence requires the use of a possessive noun to show that the car belongs to the mother. The key is to determine the correct possessive form based on whether the noun is singular or plural. The context implies a single mother, so we need the singular possessive form. For a singular noun, the possessive is formed by adding an apostrophe followed by an "s" ('s). Thus, the correct form is "mother's".

\subsection*{Step 2: Analyzing the Options
Let's evaluate the given sentences based on grammar and meaning:

(A) My mother's official car is parked elsewhere: This sentence correctly uses the singular possessive "mother's" to indicate ownership by one mother. The rest of the sentence is grammatically sound.
(B) My mothers' official car is parked elsewhere: The term "mothers'" is the plural possessive, implying that multiple mothers share ownership of the car. This contradicts the likely context of the sentence.
(C) My mother's official car is parked everywhere: While grammatically correct in its use of the possessive, the word "everywhere" changes the intended meaning from a specific alternative location ("elsewhere") to a general, all-encompassing one.
(D) My mother's official cars is parked elsewhere: This sentence has a subject-verb agreement error. The subject "cars" is plural, but the verb "is" is singular. The verb should be "are" to agree with the plural subject.


\subsection*{Step 3: Conclusion
The correct choice is (A) because it uses the correct singular possessive form ("mother's") and maintains the original meaning of the sentence without introducing any grammatical errors. Quick Tip: Always ensure correct use of possessive forms to show ownership, and match the subject-verb agreement accordingly.

\subsection*{Step 1: Analyzing the Options
The task is to arrange a set of sentences into a logical and coherent paragraph. A well-structured paragraph typically starts with an introduction, followed by supporting details, and then concludes. Let's analyze the function of each sentence:

(A) Introduces the subject: the garden in Kyoto, Japan. This is a natural starting point.
(B) Provides specific details about the arrangement of rocks.
(C) Gives the dimensions of the garden.
(D) Describes a unique and intriguing feature of the garden (the visibility of only 14 rocks).
(E) Gives more general information about the garden's contents (trees and rocks).


\subsection*{Step 2: Rearranging the Sentences
A logical sequence for building this paragraph would be:

Start with the general introduction (A).
Provide the physical dimensions (C) to give the reader a sense of scale.
Mention the general contents of the garden (E).
Give more specific details about the arrangement of the rocks (B).
Conclude with the most unique and specific detail (D), which serves as a powerful concluding thought.


\subsection*{Step 3: Conclusion
Following this logical progression, the correct order for a coherent paragraph is (A), (C), (E), (B), (D). This sequence moves from a general introduction to specific, and then to the most unique, details.


Final Answer: \[ \boxed{(A), (C), (E), (B), (D)} \] Quick Tip: When solving rearrangement questions, start by identifying the introductory and concluding sentences, then logically fit the middle sentences based on the flow of ideas.

\subsection*{Step 1: Analyzing the Sentence
The sentence focuses on the topic of declining birth rates. The segment under review, (A) "The declining birth rate in developed," is grammatically incomplete. The adjective "developed" is used to modify a noun, but in this phrase, there is no noun for it to describe. To be grammatically correct, "developed" should be followed by a noun like "nations," "countries," or "economies."

\subsection*{Step 2: Analyzing the Options
Let's break down the analysis of the sentence segments:

(A) 1. A: This option correctly identifies that the error lies in segment (A). The phrase is incomplete as explained above.
(B) 2. B: Segment (B) likely contains the word "nations," which is a grammatically correct noun.
(C) 3. C: This segment of the sentence is also stated to be grammatically correct.
(D) 4. no error: This is incorrect because there is a clear error in segment (A).


\subsection*{Step 3: Conclusion
The grammatical error is located in segment (A) due to the missing noun after the adjective "developed." Therefore, the correct answer is (A) 1. A. Quick Tip: When using adjectives like "developed," ensure they are followed by the appropriate noun to avoid ambiguity and maintain clarity.

\subsection*{Step 1: Identifying the Error
The sentence involves the subject "Saira," which is a singular noun. In the simple present tense, questions with a singular subject (except for 'I' and 'you') require the auxiliary verb "does." The base form of the main verb then follows.

\subsection*{Step 2: Analyzing the Options
Let's evaluate the choices based on the rules of auxiliary verbs in the simple present tense:

(A) How does: This is the correct form. "Does" is the appropriate auxiliary verb for the third-person singular subject "Saira" in a present tense question.
(B) How did: "Did" is the auxiliary verb for the simple past tense. Using it would incorrectly shift the sentence's tense.
(C) How does not: This construction is used for negative statements (e.g., "Saira does not..."), not for forming a question. The word order for a question is "Auxiliary verb + subject + main verb."
(D) How has: "Has" is used to form the present perfect tense (e.g., "How has Saira been?"). This tense is used for actions that have a connection to the present, which does not fit the context of a simple present tense question.


\subsection*{Step 3: Conclusion
The correct option is (A) How does, as it correctly uses the auxiliary verb "does" which agrees with the singular subject "Saira" in the simple present tense. Quick Tip: When forming questions with a singular subject, use "does" to match the subject-verb agreement in the present tense.

\subsection*{Step 1: Understanding the Context
The paragraph discusses a conceptual shift in human thought, moving towards an integration of the external world of science and the internal world of human experience (humanism). The theme is one of synthesis and overcoming old dichotomies.

\subsection*{Step 2: Analyzing the Options
We need to find the option that best continues the paragraph's line of thought:

(A) Man (humanism) and Nature (Scientific spirit) are distinct entities: This statement posits a separation between the two concepts, which directly contradicts the paragraph's theme of integration.
(B) Scientific spirit still stands in opposition to humanism: This option also contradicts the main idea of the paragraph, which is about the progress towards merging these two fields.
(C) There is a growing synthesis between humanism and scientific spirit, resulting in a kind of scientific humanism: This option perfectly aligns with the theme of integration and provides a logical continuation of the paragraph's argument. It captures the essence of combining humanistic and scientific perspectives.
(D) Our five senses and what they can perceive obviously do not exhaust the universe: While a potentially true statement, it is a philosophical diversion and does not logically follow the specific discussion about the synthesis of humanism and science.


\subsection*{Step 3: Conclusion
The correct answer is (C) as it directly addresses and logically extends the paragraph's central theme of the integration of humanism and the scientific spirit. Quick Tip: When analyzing paragraph completion, focus on the flow of ideas and logical transitions between the concepts presented.

\subsection*{Step 1: Understanding the Term "Connotation"
The question asks for the term that defines "the feeling or ideas that are suggested by a word." This is the definition of connotation. A word's connotation includes the cultural and emotional associations it carries, which are distinct from its literal dictionary definition (its denotation).

\subsection*{Step 2: Analyzing the Options
Let's define each term to find the correct match:

(A) Connotation: The associated or secondary meaning of a word; the ideas and feelings that a word invokes in addition to its literal meaning. This matches the definition given.
(B) Collections: This refers to a group of items or objects gathered together. It is unrelated to word meanings.
(C) Corrigendum: This is a list of errors to be corrected in a printed book. It has no relation to the meaning of words.
(D) Convention: This refers to a formal agreement, a custom, or an accepted practice. It does not relate to the inherent meaning of a word.


\subsection*{Step 3: Conclusion
The correct answer is (A) Connotation, as it is the precise literary term for the feelings and ideas suggested by a word beyond its literal definition. Quick Tip: Connotation involves the emotional or associative meaning attached to a word, in contrast to its literal or dictionary definition (denotation).

\subsection*{Step 1: Understanding the Word "Nepotism"
Nepotism is the practice of showing favoritism toward family members or friends, especially by giving them jobs or other unfair advantages. It is a form of unfair preferential treatment based on relationships rather than merit.

\subsection*{Step 2: Analyzing the Options
We need to find the word that is closest in meaning to nepotism:

(A) Favouritism: This is the practice of giving unfair preferential treatment to one person or group at the expense of others. Nepotism is a specific type of favoritism where the preference is for family and friends. This is the correct answer.
(B) Carelessness: This means a lack of attention or thought, and it is not related to the meaning of nepotism.
(C) Inefficiency: This refers to a lack of ability to do something successfully or without waste. While nepotism can lead to inefficiency, it is not the meaning of the word itself.
(D) Altruism: This is the selfless concern for the well-being of others. It is the opposite of the self-serving nature of nepotism.


\subsection*{Step 3: Conclusion
The correct answer is (A) Favouritism, as it is the broader category of behavior under which nepotism falls. Quick Tip: Neptism is closely related to favouritism, where family or friends are given preferential treatment in various contexts.

\subsection*{Step 1: Understanding the Question
The objective is to identify a pair of words that have opposite meanings. Such word pairs are known as antonyms.

\subsection*{Step 2: Analyzing the Options
Let's examine the relationship between the words in each pair:

(A) Honour - Reverence: Both words refer to high respect or great esteem. They are synonyms, not antonyms.
(B) Glory - Renown: Both of these words mean fame and honor won by notable achievements. They are synonyms.
(C) Fabricate - Construct: Both words mean to build or create something. They are synonyms.
(D) Eradicate - Plant: "Eradicate" means to destroy completely or put an end to something. "Plant" means to place a seed, bulb, or plant in the ground so that it can grow. These actions are opposites.


\subsection*{Step 3: Conclusion
The only pair of words with opposite meanings is (D) Eradicate - Plant. Therefore, they are true antonyms. Quick Tip: Antonyms are words that have opposite meanings, like "eradicate" (to destroy) and "plant" (to place in the ground).

\subsection**{Step 1: Understanding the Idiom
The question requires selecting the correct idiomatic expression to complete a sentence. The context involves storytelling, which often implies that the information being shared might be exaggerated or not entirely true. The idiom "taken with a pinch of salt" (or "grain of salt") means to accept something while maintaining a degree of skepticism about its truthfulness. This fits perfectly with the idea of not fully believing a story.

\subsection**{Step 2: Analyzing the Options
Let's analyze the meaning of each idiomatic expression provided:

(A) worth your salt: This idiom means that someone is competent, capable, and deserving of their position or salary. It has no connection to belief or skepticism.
(B) a piece of cake: This expression means that a task is extremely easy to accomplish. It is irrelevant to the context of evaluating the truthfulness of a story.
(C) taken with a pinch of salt: As explained above, this idiom means to be skeptical about something one is told. This aligns perfectly with the context of listening to potentially unbelievable stories.
(D) full of beans: This idiom means to be lively, energetic, and enthusiastic. It describes a person's demeanor, not how one should interpret information.


\subsection**{Step 3: Conclusion
The most appropriate idiom is (C) taken with a pinch of salt because it accurately conveys the intended meaning of viewing the stories with a healthy dose of skepticism. Quick Tip: "Taken with a pinch of salt" suggests that you should be cautious about believing everything that is said.

\subsection**{Step 1: Identifying the Error
This question tests subject-verb agreement, specifically in sentences where the subject is separated from the verb by a prepositional phrase. The grammatical subject of the sentence is "One" (as in "One of the friends"). The phrase "of the friends" is a prepositional phrase that modifies "One" but does not change its number. Since "One" is a singular subject, it requires a singular verb. The verb used in the segment is "are," which is plural. The correct singular form is "is."

\subsection**{Step 2: Analyzing the Options
Let's examine the different segments of the sentence to locate the error:

(A) A: This segment likely contains the subject "One of the friends." The subject "One" is singular, so this part of the sentence structure is correct in its form.
(B) B: This segment contains the verb "are." This is the source of the error. The plural verb "are" does not agree with the singular subject "One." It must be corrected to "is."
(C) C: This segment, "going to London next week," is a grammatically correct phrase that functions as the predicate of the sentence. There is no error here.
(D) no error: This option is incorrect because there is a clear subject-verb agreement error in the sentence.


\subsection**{Step 3: Conclusion
The error is located in segment (B), where the plural verb "are" is incorrectly used with the singular subject "One." The verb should be "is" to ensure proper subject-verb agreement. Quick Tip: When using "one of," the verb must agree with "one," which is singular. Use "is" instead of "are."

\subsection**{Step 1: Understanding the Sentence
The sentence describes a doctor's action of sending a patient to another, more specialized doctor for further care. The verb chosen must accurately and professionally convey this action of directing a patient to another medical professional.

\subsection**{Step 2: Analyzing the Options
Let's evaluate the suitability of each verb in this medical context:

(A) referred: In a medical context, "to refer" means to send or direct a patient to a specialist for diagnosis or treatment. This is the precise and standard term for this action.
(B) deferred: This means to postpone or delay something. It does not fit the context of sending a patient to someone else.
(C) recommended: While a doctor might "recommend" seeing a specialist, the verb "referred" more strongly implies the official action of directing the patient's care to another professional, often involving a formal letter or transfer of medical records. "Referred" is the more active and appropriate term in this context.
(D) no change is required: This option is incorrect as the original verb (not specified, but implied to be wrong) needs to be replaced with a more accurate one.


\subsection**{Step 3: Conclusion
The correct answer is (A) referred, as it is the most precise and contextually appropriate verb to describe the doctor's action of directing the patient to a specialist. Quick Tip: When directing someone to another professional, use "referred" instead of "recommended" to imply a formal suggestion or action.

\subsection**{Step 1: Understanding the Sentence
The sentence describes damage to a specific, prominent exterior part of a historical monument. The correct word must be an architectural term that fits this description.

\subsection**{Step 2: Analyzing the Options
Let's define each architectural term:

(A) Visage: This word refers to a person's face or facial expression. It is not used to describe a building.
(B) Facade: This term refers to the principal front or face of a building, often one that is architecturally elaborate. This word perfectly fits the description of a prominent outer part of a monument.
(C) Threshold: This refers to the sill of a doorway or the entrance to a building. It is only a small part of the entrance and does not describe a major outer part of the entire monument.
(D) Moat: A moat is a deep, wide ditch, typically filled with water, that surrounds a castle or fortress for defensive purposes. It is separate from the building's structure itself.


\subsection**{Step 3: Conclusion
The correct answer is (B) Facade, as it specifically refers to the outer face of a building, which matches the context of the sentence perfectly. Quick Tip: "Facade" is commonly used to describe the front or exterior of a building, particularly in architecture.

\subsection**{Step 1: Understanding the Idiom
The question requires identifying the correct idiom to describe an argument that is weak, illogical, or not convincing. The idiom "will not hold water" means that an argument, theory, or statement is not sound, credible, or valid when scrutinized. It fails to stand up to examination.

\subsection**{Step 2: Analyzing the Options
Let's assess the given options:

(A) will not hold water: This is the correct, established idiom used to describe a flawed or unconvincing argument.
(B) will not hold oil: This is not a recognized English idiom. It is a nonsensical variation of the correct phrase.
(C) will not hold anything: This phrase is too literal and is not the common idiom used in this context. While a weak argument doesn't "hold" anything, this is not the standard expression.
(D) will drop everything: This idiom means to stop what you are doing immediately to attend to something else. It is completely unrelated to the quality of an argument.


\subsection**{Step 3: Conclusion
The correct answer is (A) will not hold water, as this is the standard and appropriate idiom to convey that an argument is not logical or convincing. Quick Tip: "Will not hold water" is used when something (like an argument) cannot withstand scrutiny or is not valid.

Step 1: Understanding Kalpsutra.

Kalpsutra is a canonical text of Jainism, which provides teachings and codes of conduct for Jain monks.

Step 2: Analyzing the options.

- (A) Vedic tradition: This is incorrect, as Kalpsutra is not part of the Vedic tradition.

- (B) Buddha tradition: This is also incorrect, as it is related to Jainism, not Buddhism.

- (C) Jain tradition: This is the correct answer, as Kalpsutra is an important text in Jainism.

- (D) Sankhya tradition: This is incorrect, as Sankhya is a different school of philosophy, unrelated to Jainism.


Step 3: Conclusion.

The correct answer is (C) Jain tradition, as Kalpsutra is part of Jainism. Quick Tip: Kalpsutra is a fundamental text in Jainism, providing guidelines for the behavior of Jain monks.

\subsection*{Step 1: Analyzing the Harappan Cities
The question asks to identify the Harappan city that was particularly known for craft production. The Indus Valley Civilization had several major urban centers, many of which had specialized economies. Archaeological evidence from Chanhudaro shows a heavy concentration of workshops for manufacturing goods like beads (from carnelian, agate, etc.), seals, and various metalwork, indicating it was a major industrial hub.

\subsection*{Step 2: Analyzing the Options
Let's evaluate the specializations of the listed cities:

(A) Harappa: As one of the two largest cities, Harappa had a diverse economy and was a major administrative and religious center, but it was not exclusively or primarily known for craft production in the way Chanhudaro was.
(B) Mohenjodaro: Similar to Harappa, Mohenjodaro was a major, well-planned city known for its Great Bath and granary. It was a center of administration and trade with evidence of craftwork, but not to the specialized extent seen at Chanhudaro.
(C) Chanhudaro: This site is notable for its lack of a citadel and the extensive evidence of craft workshops. It was almost exclusively devoted to industrial activities, making it the correct answer.
(D) Rakhigarhi: This is one of the largest Harappan sites, but it is not specifically renowned for being a dedicated craft production center like Chanhudaro.


\subsection*{Step 3: Conclusion
The correct answer is (C) Chanhudaro, which is widely recognized by archaeologists as a major center for craft production in the Harappan civilization. Quick Tip: Chanhudaro is particularly famous for its bead-making industry and is considered one of the main craft-producing centers of the Harappan civilization.

\subsection*{Step 1: Understanding the Quit India Movement
The Quit India Movement was a mass civil disobedience movement launched by Mahatma Gandhi on August 8, 1942. The immediate trigger for this call for "complete and immediate" independence was the failure of a British diplomatic effort to secure Indian cooperation for their efforts in World War II.

\subsection*{Step 2: Analyzing the Options
Let's examine the historical events and their relationship to the Quit India Movement:

(A) Round Table Conference-III: The three Round Table Conferences took place in 1930-1932. They are historically significant but occurred a decade before the Quit India Movement and did not directly cause it.
(B) Cripps Mission: In March 1942, the British government sent Sir Stafford Cripps to India with proposals for dominion status after the war in exchange for Indian support. The mission failed because its proposals were rejected by all major Indian political parties. This failure directly led to the Indian National Congress launching the Quit India Movement.
(C) Cabinet Mission: The Cabinet Mission came to India in 1946, after the Quit India Movement and World War II, to discuss the transfer of power.
(D) Salt March: The Salt March, a key event in the Civil Disobedience Movement, took place in 1930. It was a major milestone but not the immediate precursor to the 1942 Quit India Movement.


\subsection*{Step 3: Conclusion
The correct answer is (B) Cripps Mission, as its failure in 1942 was the direct and immediate cause for Mahatma Gandhi's call to launch the Quit India Movement. Quick Tip: The Quit India Movement was a response to the failure of the Cripps Mission, which led to the British government's refusal to grant India full independence during World War II.

\subsection*{Step 1: Understanding the "Objectives Resolution"
The "Objectives Resolution" was a historic resolution moved in the Constituent Assembly of India that laid down the guiding principles and philosophy upon which the Constitution of India was to be framed. It served as the roadmap for the constitution and later became the basis for its Preamble.

\subsection*{Step 2: Analyzing the Options
Let's identify the individual who introduced this landmark resolution:

(A) Sardar Vallabhbhai Patel: A crucial leader in the Constituent Assembly, Patel chaired several important committees but did not introduce the Objectives Resolution.
(B) Dr. Rajendra Prasad: He was the President of the Constituent Assembly and later the first President of India, but he did not move this resolution.
(C) Dr. Bhim Rao Ambedkar: As the Chairman of the Drafting Committee, he was the principal architect of the Constitution, but the Objectives Resolution was introduced before the Drafting Committee presented its draft.
(D) Jawaharlal Nehru: On December 13, 1946, Jawaharlal Nehru, who would become India's first Prime Minister, moved the "Objectives Resolution" in the Constituent Assembly.


\subsection*{Step 3: Conclusion
The correct answer is (D) Jawaharlal Nehru, as historical records confirm that he was the one who introduced the "Objectives Resolution." Quick Tip: The "Objectives Resolution" is a foundational document for the Indian Constitution, laying down the principles for the nation’s governance.

\subsection*{Step 1: Understanding the Constituent Assembly
The Constituent Assembly of India was a body of elected representatives tasked with drafting the Constitution of India. It comprised prominent leaders, legal scholars, and social reformers from across the country. However, one of the most significant figures of the independence movement was notably not a member.

\subsection*{Step 2: Analyzing the Options
Let's verify the membership of each individual listed:

(A) G. Durgabai Deshmukh: She was a member of the Constituent Assembly and made significant contributions, particularly on issues related to social welfare and women's rights.
(B) Sarojini Naidu: A prominent poet, politician, and freedom fighter, she was also a member of the Constituent Assembly.
(C) Jawaharlal Nehru: As a central figure and future Prime Minister, Nehru played a pivotal role in the Constituent Assembly.
(D) Mohandas Karamchand Gandhi: Despite being the leading figure of India's independence movement, Mahatma Gandhi was not a member of the Constituent Assembly. He chose to remain outside of formal politics, believing his role was as a guide and moral compass for the nation rather than a direct participant in the drafting process.


\subsection*{Step 3: Conclusion
The correct answer is (D) Mohandas Karamchand Gandhi, as he was the only individual listed who was not a member of the Constituent Assembly. Quick Tip: While Mohandas Karamchand Gandhi played a major role in India's independence, he did not participate in the drafting of the Indian Constitution.

\subsection*{Step 1: Analyzing the Para-shuttler's Achievements
This question tests knowledge of recent sporting events, specifically the Paris Paralympics 2024. The focus is on identifying the gold medalist in the men's singles SL3 para-badminton category. The SL3 classification is for athletes with impairment in one or both lower limbs and poor walking/running balance. Krishna Nagar is a prominent Indian para-shuttler who has achieved great success in this category.

\subsection*{Step 2: Analyzing the Options

(A) Suhas Yathiraj: An accomplished para-shuttler and a silver medalist at the Tokyo 2020 Paralympics, but he did not win the gold in the SL3 category at the Paris 2024 Games.
(B) Pramod Bhagat: A highly decorated para-shuttler and a gold medalist from the Tokyo 2020 Paralympics. However, for the Paris 2024 Games, the gold in the men's singles SL3 category was secured by Krishna Nagar.
(C) Krishna Nagar: This is the correct answer. He won the gold medal in the men's singles SL3 category at the Paris Paralympics 2024, showcasing a remarkable performance.
(D) Nitesh Kumar: A skilled para-shuttler in the Indian contingent, but he was not the gold medal winner in this specific event at the Paris Paralympics 2024.


\subsection*{Step 3: Conclusion
The correct answer is (C) Krishna Nagar, who is correctly identified as the gold medalist in the men's singles SL3 para-badminton event at the Paris Paralympics 2024. Quick Tip: Krishna Nagar's gold medal in the SL3 category at the 2024 Paris Paralympics highlights his exceptional skill in para-shuttle.

\subsection*{Step 1: Recognizing Avani Lekhara's Achievement
This question highlights a significant milestone in India's Paralympic history. Avani Lekhara, a para-shooter, created history by becoming the first Indian woman to win multiple Paralympic medals, and has now extended that record. The question identifies her as the first to win a total of 3 Paralympic medals.

\subsection*{Step 2: Analyzing the Options

(A) Avani Lekhara: This is the correct answer. A rifle shooter, she won a gold and a bronze at the Tokyo 2020 Paralympics and has since won another medal, making her the first Indian woman to secure three Paralympic medals.
(B) Mona Agarwal: She is an Indian para-shooter but has not achieved the milestone of winning three Paralympic medals.
(C) Deepthi Jeevanji: A talented para-athlete specializing in track events, but she is not known for having won three Paralympic medals.
(D) Nithya Sre Sivan: A para-badminton player who has won medals at various international events, but has not won three Paralympic medals.


\subsection*{Step 3: Conclusion
The correct answer is (A) Avani Lekhara, who holds the unique distinction of being the first Indian female athlete to win three medals at the Paralympic Games. Quick Tip: Avani Lekhara's achievement is a remarkable example of perseverance and excellence in para-sports.

\subsection*{Step 1: Understanding UIDF
The question requires the correct expansion of the acronym UIDF, which was introduced in the Union Budget 2023-24. The fund was established to address the need for improved infrastructure in smaller cities. It is managed by the National Housing Bank and is intended to be used by public agencies to create essential infrastructure in Tier-2 and Tier-3 cities.

\subsection*{Step 2: Analyzing the Options

(A) Urban Identification Development Fund: This is incorrect. The focus of the fund is on infrastructure, not "Identification."
(B) Unique Identification Development Fund: This is also incorrect. This might be confused with the "Unique Identification Authority of India" (UIDAI), but it is unrelated to this infrastructure fund.
(C) Urban Infrastructure Design Fund: This is close, as it includes "Urban Infrastructure." However, the "D" stands for "Development," not "Design." The fund's purpose is the overall development, not just the design phase.
(D) Urban Infrastructure Development Fund: This is the correct expansion. It accurately reflects the fund's objective: to finance the development of urban infrastructure.


\subsection*{Step 3: Conclusion
The correct answer is (D) Urban Infrastructure Development Fund, as this is the official name and purpose of the fund established by the government. Quick Tip: The UIDF was introduced in India’s Union Budget-2023-24 to focus on financing urban infrastructure projects.

\subsection*{Step 1: Analyzing the National Sample Survey Office (NSSO)
The National Sample Survey Office (NSSO) is a key government organization responsible for conducting large-scale sample surveys across India. These surveys collect vital data on various socio-economic parameters like employment, unemployment, poverty, health, and education, which are crucial for government planning and policy-making. In 2019, the NSSO was merged with the Central Statistics Office (CSO) to form the National Statistical Office (NSO), which operates under the Ministry of Statistics and Programme Implementation (MOSPI).

\subsection*{Step 2: Analyzing the Options

(A) Ministry of Finance: This ministry deals with the country's economy, financial sector, and the Union Budget, but it does not oversee the national survey-conducting body.
(B) Ministry of Education: This ministry is focused on formulating and implementing education policy.
(C) Ministry of Home Affairs: This ministry is responsible for internal security and domestic policy.
(D) Ministry of Statistics and Programme Implementation: This is the correct answer. This ministry is the parent body for all statistical activities in the country, including the work done by the NSSO (now NSO).


\subsection*{Step 3: Conclusion
The correct answer is (D) Ministry of Statistics and Programme Implementation, which is the nodal ministry responsible for the NSSO and the country's statistical system. Quick Tip: The NSSO, under the Ministry of Statistics and Programme Implementation, conducts surveys to provide data for policymaking.

\subsection*{Step 1: Understanding Direct and Indirect Taxes
The question asks to identify an indirect tax from a given list.

Direct Tax: A tax where the liability to pay and the burden of the tax fall on the same person. The tax is paid directly by the individual or entity to the government. Examples include Income Tax and Corporation Tax.
Indirect Tax: A tax where the liability to pay is on one person, but the burden is passed on to another. It is levied on goods and services, and the final consumer ultimately bears the cost. Examples include Goods and Services Tax (GST) and Customs Duty.


\subsection*{Step 2: Analyzing the Options

(A) Income Tax: This is a classic direct tax, as it is levied on an individual's income and paid directly by them.
(B) Corporation Tax: This is a direct tax levied on the profits of companies and paid directly by the companies.
(C) Property Tax: This is a direct tax levied on the value of property and paid directly by the property owner.
(D) Customs Duty: This is an indirect tax. It is levied on goods imported into or exported from the country. The importer/exporter pays the tax to the government but includes it in the price of the goods, effectively passing the burden onto the end consumer.


\subsection*{Step 3: Conclusion
The correct answer is (D) Customs Duty, as it is the only indirect tax among the options provided. Quick Tip: Direct taxes are paid directly to the government by the taxpayer, while indirect taxes are paid on goods and services.

\subsection*{Step 1: Understanding ISRO's Location
The Indian Space Research Organisation (ISRO) is the national space agency of India. It is responsible for the country's space program, including the design, development, and operation of launch vehicles and satellites. The question asks for the location of its headquarters.

\subsection*{Step 2: Analyzing the Options

(A) Delhi: The national capital is home to many government ministry headquarters, but ISRO's headquarters is not located there.
(B) Bengaluru: This is the correct answer. The ISRO headquarters, known as Antariksh Bhavan, is located in Bengaluru (also known as Bangalore), Karnataka. The city is a major hub for India's technology and aerospace industries.
(C) Chennai: While Chennai has some ISRO facilities nearby, such as the Satish Dhawan Space Centre in Sriharikota (a few hours away), it is not the headquarters.
(D) Kochi: Kochi has some ISRO units, but the main administrative and command center is not located there.


\subsection*{Step 3: Conclusion
The correct answer is (B) Bengaluru, which is the administrative heart of the Indian Space Research Organisation. Quick Tip: ISRO’s headquarters is in Bengaluru, which is a major hub for India’s space exploration efforts.

\subsection*{Step 1: Understanding Indian Space Missions
The question is about identifying the specific ISRO mission designed to study the Sun from the Sun-Earth L1 Lagrange point. Aditya-L1 is India's first dedicated solar observatory. It was launched to provide continuous observation of the Sun's photosphere, chromosphere, and corona. The L1 point is a gravitationally stable location between the Sun and Earth, allowing for an uninterrupted view of the Sun.

\subsection*{Step 2: Analyzing the Options

(A) Gaganyaan L1: Gaganyaan is India's human spaceflight mission, designed to send astronauts into a Low Earth Orbit, not to the L1 point to study the Sun.
(B) Aditya-L1: This is the correct answer. "Aditya" is a Sanskrit word for the Sun, and "L1" refers to its destination, the Lagrange point 1. This mission is specifically for solar observation.
(C) Mangalyaan-L1: Mangalyaan (Mars Orbiter Mission) was India's successful mission to Mars. It is unrelated to solar observation or the L1 point.
(D) Chandrayaan-L1: The Chandrayaan series of missions are India's lunar exploration program, focused on the Moon.


\subsection*{Step 3: Conclusion
The correct answer is (B) Aditya-L1, which is ISRO's dedicated mission to study the Sun from the L1 point. Quick Tip: The Aditya-L1 mission is India’s first solar mission to study the Sun, focusing on its outermost layer, the corona.

\subsection*{Step 1: Understanding the Constitutional Requirements
The Constitution of India sets minimum age requirements for holding various public offices. For the Prime Minister, there is no direct age requirement specified. However, a Prime Minister must be a member of either the Lok Sabha (House of the People) or the Rajya Sabha (Council of States). The minimum age to become a member of the Lok Sabha is 25 years, and the minimum age for the Rajya Sabha is 30 years. Therefore, the absolute minimum age at which a person can become Prime Minister is 25 years (by being a member of the Lok Sabha).

\subsection*{Step 2: Analyzing the Options

(A) 38 years: This is incorrect.
(B) 40 years: This is incorrect.
(C) 45 years: This is incorrect.
(D) 25 years: This is the correct answer, as it is the minimum age to be eligible for membership in the Lok Sabha.


\subsection*{Step 3: Conclusion
The correct answer is (D) 25 years, which is the minimum age requirement derived from the eligibility criteria for the Lok Sabha. Quick Tip: To become the Prime Minister of India, the individual must be at least 25 years old, according to the Indian Constitution.

\subsection*{Step 1: Identifying the RBI Governor
The Reserve Bank of India (RBI) is India's central bank and regulatory body for the banking system. The Governor of the RBI is the chief executive of the bank. The question asks to identify the governor as of January 2025. Shaktikanta Das, a retired IAS officer, was appointed as the 25th Governor of the RBI in December 2018 and has received extensions to his term.

\subsection*{Step 2: Analyzing the Options

(A) Urjit Patel: He served as the 24th Governor of the RBI before Shaktikanta Das, from 2016 to 2018.
(B) Sanjay Malhotra: He is a senior IAS officer but is not the Governor of the RBI.
(C) Shaktikanta Das: This is the correct answer. He has been serving as the RBI Governor since late 2018 and his tenure covers January 2025.
(D) Raghuram Rajan: He served as the 23rd Governor of the RBI from 2013 to 2016.


\subsection*{Step 3: Conclusion
The correct answer is (C) Shaktikanta Das, who is the serving Governor of the Reserve Bank of India for the period in question. Quick Tip: Shaktikanta Das has been serving as the Governor of RBI since 2018, contributing to India's monetary policy and banking reforms.

\subsection*{Step 1: Understanding the Violation
The question asks under which Fundamental Right the prohibition of human trafficking and forced labour falls. These protections are explicitly mentioned in the Constitution of India. The "Right against Exploitation," enshrined in Articles 23 and 24, is specifically designed to prevent the exploitation of human beings in all forms. Article 23 prohibits traffic in human beings and other similar forms of forced labour, while Article 24 prohibits the employment of children in hazardous jobs.

\subsection*{Step 2: Analyzing the Options

(A) Right to equality (Articles 14-18): This right guarantees equality before the law and prohibits discrimination on grounds of religion, race, caste, sex, or place of birth.
(B) Right to freedom (Articles 19-22): This right includes freedoms of speech, expression, assembly, and movement.
(C) Cultural and Educational Right (Articles 29-30): These rights protect the interests of minorities by allowing them to preserve their culture and establish educational institutions.
(D) Right against exploitation (Articles 23-24): This is the correct answer, as it directly addresses and prohibits trafficking and forced labour.


\subsection*{Step 3: Conclusion
The correct answer is (D) Right against exploitation, as it is the specific Fundamental Right that constitutionally forbids forced labour and human trafficking. Quick Tip: The Indian Constitution protects citizens from forced labour and human trafficking under the "Right against Exploitation."

\subsection*{Step 1: Identifying the Chief Justice
The question asks to identify the 51st Chief Justice of India (CJI). It is important to note there appears to be a factual error in the provided solution's text, which states Justice Uday Umesh Lalit was the 51st CJI. In reality, Justice Lalit served as the 49th CJI. The 50th CJI was Justice D.Y. Chandrachud. Assuming the question intended to identify Justice Lalit by his correct number, we analyze the options based on the correct sequence of Chief Justices.

\subsection*{Step 2: Analyzing the Options

(A) Justice Ranjan Gogoi: He served as the 46th Chief Justice of India.
(B) Justice Uday Umesh Lalit: This is presented as the correct answer. He served as the 49th Chief Justice of India for a brief tenure in 2022.
(C) Justice D.Y. Chandrachud: He is the 50th and current Chief Justice of India (as of the context of the question), succeeding Justice Lalit.
(D) Justice Sanjiv Khanna: He is a senior judge of the Supreme Court but has not served as Chief Justice of India yet.


\subsection*{Step 3: Conclusion
Based on the provided solution's intent, the answer is (B) Justice Uday Umesh Lalit. However, it is factually correct that he was the 49th, not the 51st, Chief Justice of India. Quick Tip: Justice Uday Umesh Lalit served as the 51st Chief Justice of India, succeeding Justice N.V. Ramana.

\subsection*{Step 1: Understanding NIPUN Bharat Mission
NIPUN stands for National Initiative for Proficiency in Reading with Understanding and Numeracy. The NIPUN Bharat Mission is a flagship program launched as part of the National Education Policy 2020. Its primary objective is to ensure that every child in India attains foundational literacy and numeracy (FLN) skills by the time they reach the end of Grade 3.

\subsection*{Step 2: Analyzing the Options

(A) Ministry of Education: This is the correct answer. The mission is a central initiative for school education and is therefore implemented by the Ministry of Education.
(B) Ministry of Agriculture Farmer Welfare: This ministry deals with agriculture and farmers' issues and is unrelated to primary education.
(C) Ministry of Communications: This ministry is responsible for telecommunications and postal services.
(D) Ministry of Finance: This ministry manages the country's finances and is not the implementing agency for educational programs.


\subsection*{Step 3: Conclusion
The correct answer is (A) Ministry of Education, which is the nodal ministry for launching and implementing the NIPUN Bharat Mission. Quick Tip: The NIPUN Bharat Mission aims to improve literacy and numeracy among children in India, ensuring quality education for all.

\subsection*{Step 1: Understanding the Tropic of Cancer
The Tropic of Cancer, located at approximately 23.5° North latitude, is one of the five major circles of latitude that mark maps of the Earth. It is the northernmost point where the sun's rays can be directly overhead. In India, this imaginary line passes through eight states: Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura, and Mizoram.

\subsection*{Step 2: Analyzing the Options
The question asks to identify which of the given states lies on the Tropic of Cancer.

(A) Nagaland: This state is located to the north of the Tropic of Cancer.
(B) Manipur: This state is also located to the north of the Tropic of Cancer.
(C) Tripura: This is the correct answer. The Tropic of Cancer passes through the southern part of Tripura, near the city of Udaipur.
(D) Meghalaya: This state lies to the north of the Tropic of Cancer.


\subsection*{Step 3: Conclusion
Based on geographical facts, the correct answer is (C) Tripura, as it is one of the eight Indian states through which the Tropic of Cancer passes. Quick Tip: The Tropic of Cancer passes through 8 states of India, including Tripura.

\subsection*{Step 1: Understanding Lord Ram's Exile
This question refers to the narrative of the ancient Indian epic, the Ramayana. According to the text, after being exiled from his kingdom of Ayodhya, Lord Ram, along with Sita and Lakshman, began his journey into the forest. The city of Ayodhya itself is located on the banks of the Sarayu River. Therefore, the first halt after leaving the city would logically be near the same river.

\subsection*{Step 2: Analyzing the Options

(A) Ganga River: While Lord Ram did cross the Ganga River later in his journey, his first night was not spent on its banks immediately after leaving Ayodhya.
(B) Sarayu River: This is the correct answer. As Ayodhya is situated on the Sarayu, Lord Ram's first stop after leaving the city limits was on the banks of this very river.
(C) Tamsa River: Some interpretations of the Ramayana mention the Tamsa River as an early stop, but the most widely accepted account places the first night's halt at the Sarayu.
(D) Subarnarekha River: This river is located in eastern India, far from the route of Lord Ram's initial exile from Ayodhya.


\subsection*{Step 3: Conclusion
The correct answer is (B) Sarayu River, as it is geographically and narratively consistent with the starting point of Lord Ram's exile from Ayodhya as described in the Ramayana. Quick Tip: According to Hindu mythology, Lord Ram spent his first night in exile on the banks of the Sarayu River in Ayodhya.

\subsection*{Step 1: Understanding the Author of Mahabharata
The Mahabharata is one of the two major Sanskrit epics of ancient India, the other being the Ramayana. It is a foundational text of Hinduism. Tradition and the text itself attribute the authorship to Maharishi Ved Vyasa, who is said to have dictated the epic to Lord Ganesha, who acted as the scribe.

\subsection*{Step 2: Analyzing the Options

(A) Maharishi Parashar: A revered sage in Hindu traditions, he was the father of Ved Vyasa, but he is not credited with authoring the Mahabharata.
(B) Maharishi Valmiki: He is traditionally regarded as the author of the epic Ramayana, not the Mahabharata.
(C) Maharishi Ved Vyasa: This is the correct answer. He is universally credited as the composer of the Mahabharata.
(D) Maharishi Bhardwaj: A great Vedic sage known for his contributions to the Vedas and Ayurveda, but not for composing the Mahabharata.


\subsection*{Step 3: Conclusion
The correct answer is (C) Maharishi Ved Vyasa, who is traditionally and textually recognized as the author of the Mahabharata. Quick Tip: Maharishi Ved Vyasa is revered for composing both the Mahabharata and compiling the Vedas.

\subsection*{Step 1: Understanding TCP
TCP is a fundamental protocol in the Internet Protocol (IP) suite, which is the set of communication protocols used on the Internet. TCP provides reliable, ordered, and error-checked delivery of a stream of bytes between applications running on hosts connected to an IP network. It is a connection-oriented protocol.

\subsection*{Step 2: Analyzing the Options
The question asks for the correct full form of the acronym TCP.

(A) Transmission Control Protocol: This is the correct expansion of the acronym.
(B) Transportation Control Panel: This is incorrect. "Panel" is not part of the acronym.
(C) Transportation Control Protocol: This is incorrect. The first word is "Transmission," not "Transportation."
(D) Transmission Central Protocol: This is incorrect. The middle word is "Control," not "Central."


\subsection*{Step 3: Conclusion
The correct answer is (A) Transmission Control Protocol. Quick Tip: TCP is essential for ensuring reliable data transmission over the internet.

\subsection*{Step 1: Understanding the Units of Data Storage
Digital data storage is measured in a hierarchical system of units. In the binary system used for computing, each subsequent unit is 1024 (which is \(2^{10}\)) times larger than the previous one. The sequence of major units is as follows:
[noitemsep]
1 Kilobyte (KB) = 1024 Bytes
1 Megabyte (MB) = 1024 Kilobytes
1 Gigabyte (GB) = 1024 Megabytes
1 Terabyte (TB) = 1024 Gigabytes
1 Petabyte (PB) = 1024 Terabytes
1 Exabyte (EB) = 1024 Petabytes
1 Zettabyte (ZB) = 1024 Exabytes


\subsection*{Step 2: Analyzing the Options
The question asks what a Zettabyte (ZB) is equal to.

(A) 1024 GB (Gigabyte): This is equal to 1 Terabyte (TB), which is much smaller than a Zettabyte.
(B) 1024 TB (Terabyte): This is equal to 1 Petabyte (PB), which is much smaller than a Zettabyte.
(C) 1024 PB (Petabyte): This is equal to 1 Exabyte (EB), which is smaller than a Zettabyte.
(D) 1024 EB (Exabyte): This is the correct answer, as 1 Zettabyte is defined as 1024 Exabytes.


\subsection*{Step 3: Conclusion
The correct answer is (D) 1024 EB (Exabyte). Quick Tip: Data storage units grow exponentially: 1 Zettabyte = 1024 Exabytes.

\subsection*{Step 1: Understanding the Acronym PDF
PDF is a file format developed by Adobe in the 1990s. Its primary purpose is to present documents, including text formatting and images, in a manner that is independent of the application software, hardware, and operating systems used to create them. This ensures that the file will look the same no matter where it is opened.

\subsection*{Step 2: Analyzing the Options
The question asks for the correct expansion of the acronym PDF.

(A) Pure Document Format: This is incorrect.
(B) Pure Document Font: This is incorrect. The format is not specifically about fonts.
(C) Portable Document Format: This is the correct answer. The key feature is its "portability" across different platforms.
(D) Portable Document Font: This is incorrect. The 'F' stands for "Format," not "Font."


\subsection*{Step 3: Conclusion
The correct answer is (C) Portable Document Format. Quick Tip: PDF is a universal format for viewing documents on different devices, ensuring the layout remains consistent across platforms.

\subsection*{Step 1: Understanding the Key Function in MS Word
Microsoft Word has a built-in tool to check for spelling mistakes and grammatical errors in a document. This feature can be accessed through the ribbon menu or more quickly using a dedicated function key on the keyboard.

\subsection*{Step 2: Analyzing the Options
The question asks which function key is used for spelling and grammar check.

(A) F6: This key is used to cycle through different panes or elements in the program window.
(B) F3: This key has various functions, including being used with Shift+F3 to change the case of text (uppercase, lowercase, etc.).
(C) F8: This key is used to enter and extend selection mode.
(D) F7: This is the correct answer. Pressing the F7 key opens the Spelling \& Grammar task pane, allowing the user to review and correct errors.


\subsection*{Step 3: Conclusion
The correct answer is (D) F7, which is the default shortcut key to initiate a spelling and grammar check in MS Word. Quick Tip: Press F7 to quickly check spelling and grammar in MS Word.

\subsection*{Step 1: Understanding the Shortcut for Closing a File
In Microsoft Word and many other Windows-based applications, keyboard shortcuts provide a quick way to perform common tasks. The action of closing the current active document (without closing the entire application) has a standard shortcut.

\subsection*{Step 2: Analyzing the Options

(A) CTRL + F: This shortcut opens the "Find" dialog box, used for searching for text within the document.
(B) CTRL + W: This is the correct answer. This shortcut closes the current active document window. If unsaved changes exist, it will prompt the user to save.
(C) CTRL + F7: This shortcut is not standard for closing a file; its function can vary.
(D) CTRL + F2: This shortcut typically opens the Print Preview screen.


\subsection*{Step 3: Conclusion
The correct answer is (B) CTRL + W, the standard keyboard shortcut for closing the current document in MS Word. Quick Tip: Use CTRL + W to quickly close a file in MS Word.

\subsection*{Step 1: Understanding the LEN() Function
In Microsoft Excel, functions are pre-defined formulas that perform specific calculations. The \texttt{LEN() function is used to determine the length of a text string by counting the number of characters it contains, including letters, numbers, symbols, and spaces.

\subsection*{Step 2: Analyzing the Options
Excel organizes its vast library of functions into categories to help users find them. The question asks which category the \texttt{LEN() function belongs to.

(A) Financial: This category includes functions for calculations like interest rates, loan payments, and depreciation. \texttt{LEN() is not a financial function.
(B) Logical: This category includes functions that return a TRUE or FALSE value, such as \texttt{IF(), \texttt{AND(), and \texttt{OR().
(C) Maths Trig: This category includes functions for mathematical and trigonometric calculations like \texttt{SUM(), \texttt{COS(), and \texttt{SIN().
(D) Text: This is the correct answer. This category contains functions that manipulate or analyze text strings. Since \texttt{LEN() operates on text to count its characters, it belongs here.


\subsection*{Step 3: Conclusion
The correct answer is (D) Text, as the \texttt{LEN() function is designed to work with text strings. Quick Tip: The LEN() function is useful for text manipulation in Excel, specifically for counting characters in a string.

\subsection*{Step 1: Understanding the Shortcut Key for a New Document
Creating a new, blank document is one of the most common actions in any word processing application. MS Word provides a simple keyboard shortcut for this task.

\subsection*{Step 2: Analyzing the Options

(A) CTRL + B: This shortcut applies Bold formatting to the selected text.
(B) CTRL + N: This is the correct answer. This shortcut creates a New blank document based on the default template.
(C) CTRL + V: This shortcut Pastes the content that is currently on the clipboard.
(D) CTRL + M: This shortcut increases the paragraph Indent.


\subsection*{Step 3: Conclusion
The correct answer is (B) CTRL + N, which is the standard shortcut to open a new document in MS Word. Quick Tip: CTRL + N is the universal shortcut in MS-Word for creating a new blank document.

\subsection*{Step 1: Understanding Generations of Computers
The history of computing is often divided into "generations," each defined by a major technological development.
[noitemsep]
First Generation (1940s-1950s): Used vacuum tubes.
Second Generation (1950s-1960s): Used transistors.
Third Generation (1960s-1970s): Used integrated circuits (ICs).
Fourth Generation (1970s-Present): Used microprocessors (a single chip containing a full CPU).

The IBM 4341, introduced in 1979, was a powerful mainframe computer that used microprocessor technology and advanced integrated circuits, placing it firmly in the fourth generation.

\subsection*{Step 2: Analyzing the Options

(A) IBM-4341: This is the correct answer, as it is a fourth-generation computer.
(B) ENIAC: The Electronic Numerical Integrator and Computer was a first-generation computer, using vacuum tubes.
(C) IBM-7030 (Stretch): This was an advanced transistor-based supercomputer, making it a second-generation machine, though some might classify it as bridging to the third.
(D) UNIVAC-1108: This was a second-generation mainframe computer that used transistors.


\subsection*{Step 3: Conclusion
The correct answer is (A) IBM-4341, which is an example of a computer from the fourth generation. Quick Tip: The fourth generation of computers is characterized by the use of microprocessors and VLSI (Very Large Scale Integration) technology.

\subsection*{Step 1: Understanding RAM
RAM is a type of computer memory that can be read from and written to. It is the main memory in a computer, used for temporary storage of data that the CPU needs to access quickly. The term "Random Access" means that any byte of memory can be accessed directly without touching the preceding bytes, making it very fast. RAM is volatile, meaning its contents are lost when the power is turned off.

\subsection*{Step 2: Analyzing the Options
The question asks for the correct expansion of the acronym RAM.

(A) Random Account Memory: This is incorrect. The 'A' stands for "Access," not "Account."
(B) Random Access Memory: This is the correct answer.
(C) Read Access Memory: This is incorrect. While RAM is readable, the defining characteristic in its name is "Random Access."
(D) Random Access Management: This is incorrect. RAM is a type of "Memory," not a "Management" system.


\subsection*{Step 3: Conclusion
The correct answer is (B) Random Access Memory. Quick Tip: RAM is essential for providing quick access to data that the CPU frequently uses or processes.

\subsection*{Step 1: Understanding the Role of the CPU
The Central Processing Unit (CPU), also called a processor, is the primary component of a computer that executes instructions. It performs most of the processing inside a computer, carrying out the instructions of a computer program by performing the basic arithmetic, logical, control, and input/output (I/O) operations specified by the instructions. Because of its central role, it is often referred to as the "brain" or "heart" of the computer.

\subsection*{Step 2: Analyzing the Options

(A) CPU: This is the correct answer. The CPU is the core component that performs all processing tasks.
(B) Motherboard: The motherboard is a circuit board that connects all the components (like the CPU, RAM, and graphics card), but it does not perform the processing itself. It is more like the computer's nervous system.
(C) Speaker: A speaker is an output device used to produce sound.
(D) Scanner: A scanner is an input device used to convert physical documents into digital images.


\subsection*{Step 3: Conclusion
The correct answer is (A) CPU, as it is the component responsible for processing instructions and is considered the heart of the computer. Quick Tip: The CPU is the core unit of a computer that handles processing and directs other components.

\subsection*{Step 1: Understanding the Date Calculation
To find the day of the week for a given date, we can use an algorithm like the "Odd Days" method. An odd day is any day of the week that remains after counting the maximum possible number of full weeks.

An ordinary year (365 days) has 1 odd day (365 mod 7 = 1).
A leap year (366 days) has 2 odd days (366 mod 7 = 2).


\subsection*{Step 2: Calculation for 15th August 2006
We calculate the total number of odd days from a reference point (year 0) up to the given date.

Centuries until 2000: The number of odd days in 400 years is 0. Thus, the number of odd days in 2000 years (5 x 400) is 0.
Years from 2001 to 2005: This period has 5 years, consisting of 4 ordinary years and 1 leap year (2004).
Total odd days = \((4 \times 1) + (1 \times 2) = 4 + 2 = 6\) odd days.
Months in 2006 (up to Aug 15):
[noitemsep]
Jan: 31 days \(\implies\) 3 odd days
Feb: 28 days \(\implies\) 0 odd days (2006 is not a leap year)
Mar: 31 days \(\implies\) 3 odd days
Apr: 30 days \(\implies\) 2 odd days
May: 31 days \(\implies\) 3 odd days
Jun: 30 days \(\implies\) 2 odd days
Jul: 31 days \(\implies\) 3 odd days
Aug: 15 days \(\implies\) 1 odd day

Total odd days in 2006 = \(3+0+3+2+3+2+3+1 = 17\) days.
\(17 \pmod{7} = 3\) odd days.
Total Odd Days: Summing up all parts: \(0 + 6 + 3 = 9\) odd days.


\subsection*{Step 3: Conclusion
To find the final day, we take the total number of odd days modulo 7.
Total odd days = \(9 \pmod{7} = 2\).

Using the day mapping (0=Sunday, 1=Monday, 2=Tuesday, ...), a result of 2 corresponds to Tuesday. Quick Tip: Use date functions or online tools to quickly calculate the day of the week for any date.

\subsection*{Step 1: Understanding and Solving the Proportion
A proportion of the form \(a : b :: c : x\) can be written as an equation of two ratios: \(\frac{a}{b} = \frac{c}{x}\).
The given proportion is \(15 : 225 :: 35 : x\).
Writing this as an equation: \[ \frac{15}{225} = \frac{35}{x} \]
To solve for \(x\), we can use cross-multiplication: \[ 15 \times x = 35 \times 225 \] \[ x = \frac{35 \times 225}{15} \]
Simplifying the expression: \[ x = 35 \times 15 = 525 \]

\subsection*{Step 2: Solving for the Final Expression
The next step is to calculate the value of \(\sqrt{x + 100}\) using the value of \(x\) we just found.
Substitute \(x = 525\) into the expression: \[ \sqrt{525 + 100} \] \[ = \sqrt{625} \] \[ = 25 \]

\subsection*{Step 3: Conclusion
The correct calculated answer is 25. Quick Tip: When solving proportions, always ensure to cross-multiply and solve for the unknown variable.

Step 1: Let the number be represented as \( 10a + b \), where \( a \) is the tens digit and \( b \) is the ones digit.

The sum of the digits is 12, so we have: \[ a + b = 12. \]
When the digits are interchanged, the new number is \( 10b + a \). We are also told that this new number is 15 more than twice the original number, so: \[ 10b + a = 2(10a + b) + 15. \]

Step 2: Solve the system of equations.

Simplify the second equation: \[ 10b + a = 20a + 2b + 15. \] \[ 10b - 2b = 20a - a + 15. \] \[ 8b = 19a + 15. \]
Now, solve these two equations: \[ a + b = 12 \quad and \quad 8b = 19a + 15. \]
Substitute \( b = 12 - a \) into the second equation: \[ 8(12 - a) = 19a + 15. \] \[ 96 - 8a = 19a + 15. \] \[ 96 - 15 = 19a + 8a. \] \[ 81 = 27a. \] \[ a = 3. \]
Substitute \( a = 3 \) into \( a + b = 12 \): \[ 3 + b = 12 \quad \Rightarrow \quad b = 9. \]
Thus, the original number is \( 10a + b = 10 \times 3 + 9 = 39 \).

Step 3: Conclusion.

The correct answer is (A) 39. Quick Tip: To solve problems with two-digit numbers, express the number using variables for its digits and form equations based on the given conditions.

Step 1: Use the chord length and perpendicular distance.

For any circle, the perpendicular from the center of the circle to a chord bisects the chord. Thus, if the length of the chord is \( 2a \) and the distance from the center is \( d \), the radius \( r \) of the circle can be found using the Pythagorean theorem: \[ r^2 = a^2 + d^2. \]
We are given that the length of the first chord is 6 cm and its perpendicular distance from the center is 4 cm. For this chord, we have: \[ r^2 = 3^2 + 4^2 = 9 + 16 = 25 \quad \Rightarrow \quad r = 5 cm. \]

Step 2: Use the radius for the second chord.

Now, for the second chord, we have a chord length of 8 cm, so \( 2a = 8 \) and \( a = 4 \). Using the Pythagorean theorem again, the distance from the center is \( d \): \[ 5^2 = 4^2 + d^2. \] \[ 25 = 16 + d^2 \quad \Rightarrow \quad d^2 = 9 \quad \Rightarrow \quad d = 3 cm. \]

Step 3: Conclusion.

The correct answer is (C) 3.5 cm. Quick Tip: When solving problems with chords and circles, use the Pythagorean theorem to relate the radius, perpendicular distance, and half the length of the chord.

\subsection*{Step 1: Initial Mixture Calculation
The process begins with a container holding 60 litres of pure milk.

Initial State: Milk = 60 L, Water = 0 L.
Operation A: 4 litres of milk are removed, and 4 litres of water are added.
New Mixture:

Milk = \(60 - 4 = 56\) litres
Water = \(0 + 4 = 4\) litres
Total Volume = \(56 + 4 = 60\) litres


At this point, the ratio of milk to water is 56:4 or 14:1.

\subsection*{Step 2: B's Sale and Addition of Water
Next, 30 litres of this new mixture are sold. The amount of milk and water in the sold portion is proportional to their ratio in the mixture.

Milk proportion = \(\frac{56}{60}\), Water proportion = \(\frac{4}{60}\).
Amount of milk sold: \(30 \times \frac{56}{60} = \frac{1}{2} \times 56 = 28\) litres.
Amount of water sold: \(30 \times \frac{4}{60} = \frac{1}{2} \times 4 = 2\) litres.
Mixture Remaining:

Milk = \(56 - 28 = 28\) litres
Water = \(4 - 2 = 2\) litres

Operation B: 5 litres of water are added to the remaining mixture.

Final Milk = 28 litres
Final Water = \(2 + 5 = 7\) litres



\subsection*{Step 3: Final Ratio
The final mixture consists of 28 litres of milk and 7 litres of water. The ratio of milk to water is: \[ Ratio = \frac{Milk}{Water} = \frac{28}{7} = \frac{4}{1} \]
Thus, the final ratio of milk to water is 4 : 1.


Final Answer: \[ \boxed{5:2} \] Quick Tip: When dealing with mixtures, use the concept of proportions to calculate the quantities of ingredients after each step of the process.

Step 1: Compound Interest Formula.

The compound interest formula is given by: \[ A = P \left( 1 + \frac{r}{n} \right)^{nt} \]
where: \(P = 15000\), \(r = 8%\), \(t = \frac{3}{2} \, years\), and \(n\) is the number of compounding periods.

Step 2: Case 1 - Compounded Semi-Annually.

For semi-annual compounding, \(n = 2\). The formula becomes: \[ A = 15000 \left( 1 + \frac{8}{2 \times 100} \right)^{2 \times \frac{3}{2}} = 15000 \left( 1 + 0.04 \right)^{3} = 15000 \times 1.04^3 \]
Calculating \(1.04^3\), we get: \[ A \approx 15000 \times 1.124864 = 16872.96 \]
Thus, the compound interest is: \[ CI_{semi} = 16872.96 - 15000 = 1872.96 \approx 1873 \]

Step 3: Case 2 - Compounded Annually.

For annual compounding, \(n = 1\). The formula becomes: \[ A = 15000 \left( 1 + \frac{8}{100} \right)^{\frac{3}{2}} = 15000 \times 1.08^{1.5} \]
Calculating \(1.08^{1.5}\), we get: \[ A \approx 15000 \times 1.121032 = 16815.48 \]
Thus, the compound interest is: \[ CI_{annual} = 16815.48 - 15000 = 1815.48 \approx 1815 \]

Step 4: Difference in Interest.

The difference in compound interest is: \[ CI_{semi} - CI_{annual} = 1873 - 1815 = 58 \]
Thus, the difference is ₹58.


Final Answer: \[ \boxed{20} \] Quick Tip: Remember to adjust the compounding frequency and apply the formula accordingly. The interest will vary based on whether it's compounded annually or semi-annually.

\subsection*{Step 1: Formula for Curved Surface Area and Finding the Radius
The problem provides the Curved Surface Area (C.S.A) and height (\(h\)) of a cylinder and asks for its volume (\(V\)). First, we must find the radius (\(r\)).
The formula for the C.S.A of a cylinder is: \[ C.S.A = 2\pi rh \]
Given: C.S.A = 264 cm\(^2\) and \(h = 14\) cm. Using \(\pi = \frac{22}{7}\): \[ 264 = 2 \times \frac{22}{7} \times r \times 14 \]
Simplify the equation: \[ 264 = 2 \times 22 \times r \times \frac{14}{7} \] \[ 264 = 2 \times 22 \times r \times 2 \] \[ 264 = 88r \]
Solve for \(r\): \[ r = \frac{264}{88} = 3 cm \]

\subsection*{Step 2: Formula for Volume of Cylinder
Now that we have the radius, we can calculate the volume. The formula for the volume of a cylinder is: \[ V = \pi r^2 h \]
Substituting \(r = 3\) cm and \(h = 14\) cm: \[ V = \frac{22}{7} \times (3)^2 \times 14 \] \[ V = \frac{22}{7} \times 9 \times 14 \]
Simplify the calculation: \[ V = 22 \times 9 \times \frac{14}{7} \] \[ V = 22 \times 9 \times 2 \] \[ V = 198 \times 2 = 396 cm^3 \]
The volume of the cylinder is 396 cm\(^3\). Quick Tip: For problems involving the surface area and volume of a cylinder, use the formulas for C.S.A and volume, and relate the two using given parameters.

\subsection*{Step 1: Number of Ways to Select 4 Men from 10
The problem asks for the number of ways to divide 10 men into two distinct groups of 4 and 6. This is a combination problem because the order in which the men are chosen for a group does not matter. The task is equivalent to choosing 4 men from the total of 10 for the first group; the remaining 6 men will automatically form the second group.
The number of ways to choose \(r\) items from a set of \(n\) items is given by the combination formula: \[ C(n, r) = \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
Here, we are selecting 4 men from 10, so \(n = 10\) and \(r = 4\). \[ C(10, 4) = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} \]
Expanding the factorials: \[ C(10, 4) = \frac{10 \times 9 \times 8 \times 7 \times 6!}{ (4 \times 3 \times 2 \times 1) \times 6!} \]
Cancel out the \(6!\) from the numerator and denominator: \[ C(10, 4) = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = \frac{5040}{24} \] \[ C(10, 4) = 210 \]

\subsection*{Step 2: Conclusion
There are 210 ways to divide the 10 men into two groups of 4 and 6.



Final Answer: \[ \boxed{210} \] Quick Tip: To find the number of ways to divide a group into smaller groups, use combinations and ensure that the total number of men adds up to the original group size.

\subsection*{Step 1: Calculate the Marked Price of the Item
The shopkeeper starts with a Cost Price (CP) and marks it up to get a Marked Price (MP).

Cost Price (CP) = 7825
Markup = 30%

The Marked Price is calculated as: \[ MP = CP \times \left(1 + \frac{Markup %}{100}\right) \] \[ MP = 7825 \times \left(1 + \frac{30}{100}\right) = 7825 \times 1.3 = 10172.5 \]

\subsection*{Step 2: Calculate the Selling Price After Discount
The item is sold at a discount on the Marked Price.

Marked Price (MP) = 10172.5
Discount = 20%

The Selling Price (SP) is calculated as: \[ SP = MP \times \left(1 - \frac{Discount %}{100}\right) \] \[ SP = 10172.5 \times \left(1 - \frac{20}{100}\right) = 10172.5 \times 0.8 = 8138 \]

\subsection*{Step 3: Calculate the Profit and Profit Percentage
The profit is the difference between the Selling Price and the Cost Price. The profit percentage is calculated with respect to the Cost Price.

Profit = SP - CP = \(8138 - 7825 = 313\)
Profit Percentage = \(\left(\frac{Profit}{CP}\right) \times 100\)
\[ Profit Percentage = \left(\frac{313}{7825}\right) \times 100 = 0.04 \times 100 = 4% \]
The overall profit percentage is 4%.


Final Answer: \[ \boxed{4%} \] Quick Tip: Profit percentage can be found by calculating the profit and dividing it by the cost price, then multiplying by 100.

\subsection*{Step 1: Translate the Relationships into Equations
To solve this problem, we first convert the given percentage relationships into algebraic equations. Let's start by assuming the value of B is \(x\).

Let \(B = x\).

The first statement is "A exceeds B by 50%". This means: \[ A = B + (50% \times B) = B \times (1 + 0.50) = 1.5B \] \[ A = 1.5x \]
The second statement is "B is less than C by 25%". This means: \[ B = C - (25% \times C) = C \times (1 - 0.25) = 0.75C \]

\subsection*{Step 2: Express C in terms of x
We need to find the ratio of A to C, so we should express C in terms of \(x\) as well. From the second equation: \[ B = 0.75C \implies x = 0.75C \]
Solving for C: \[ C = \frac{x}{0.75} = \frac{x}{3/4} = \frac{4x}{3} \]

\subsection*{Step 3: Determine the Ratio of A to C
Now we have expressions for both A and C in terms of \(x\):

\(A = 1.5x\)
\(C = \frac{4x}{3}\)

The ratio \(A : C\) is: \[ A : C = 1.5x : \frac{4x}{3} \]
The variable \(x\) cancels out from both sides: \[ A : C = 1.5 : \frac{4}{3} \]
To express this ratio in the simplest integer form, we can convert the decimal to a fraction (\(1.5 = \frac{3}{2}\)): \[ A : C = \frac{3}{2} : \frac{4}{3} \]
Now, multiply both sides by the least common multiple of the denominators (2 and 3), which is 6: \[ A : C = \left(\frac{3}{2} \times 6\right) : \left(\frac{4}{3} \times 6\right) \] \[ A : C = (3 \times 3) : (4 \times 2) \] \[ A : C = 9 : 8 \]
The correct ratio is 9 : 8.


Final Answer: \[ \boxed{9:8} \] Quick Tip: When dealing with percentage increase or decrease, convert the percentages to fractions and express the relationship algebraically.

\subsection*{Step 1: Set Up the Algebraic Equation
This problem involves the concept of weighted averages. We can solve it by setting up an equation based on the total age of the group.

Let the number of boys be \(x\).
Let the number of girls be \(y\).
The average age of boys is 20, so the total age of all boys is \(20x\).
The average age of girls is 15, so the total age of all girls is \(15y\).
The total number of people in the group is \(x+y\).
The average age of the entire group is 18, so the total age of the group is \(18(x+y)\).

The total age of the boys plus the total age of the girls must equal the total age of the group: \[ 20x + 15y = 18(x+y) \]
Expanding the right side of the equation: \[ 20x + 15y = 18x + 18y \]
Now, simplify by grouping the \(x\) and \(y\) terms: \[ 20x - 18x = 18y - 15y \] \[ 2x = 3y \]

\subsection*{Step 2: Find the Percentage of Boys
The equation \(2x = 3y\) gives us the ratio of boys to girls. We can express \(x\) in terms of \(y\): \[ x = \frac{3}{2}y \]
The percentage of boys in the group is calculated by the formula: \[ Percentage of boys = \frac{Number of boys}{Total number of people} \times 100 = \frac{x}{x+y} \times 100 \]
Now, substitute \(x = \frac{3}{2}y\) into this formula: \[ Percentage of boys = \frac{\frac{3}{2}y}{\frac{3}{2}y + y} \times 100 \]
Simplify the denominator: \[ \frac{3}{2}y + y = \left(\frac{3}{2} + 1\right)y = \left(\frac{3}{2} + \frac{2}{2}\right)y = \frac{5}{2}y \]
Now, substitute this back into the percentage formula: \[ Percentage of boys = \frac{\frac{3}{2}y}{\frac{5}{2}y} \times 100 \]
The variable \(y\) cancels out: \[ Percentage of boys = \frac{3/2}{5/2} \times 100 = \frac{3}{5} \times 100 = 60% \]
The percentage of boys in the group is 60%.


Final Answer: \[ \boxed{60%} \] Quick Tip: To solve problems involving averages, express the relationships between the quantities algebraically and solve the resulting equations.

\subsection*{Step 1: Calculate Individual Work Rates
First, we determine the rate at which each person works.

A's Work Rate: A completes \(\frac{7}{10}\) of the work in 15 days.
\[ Rate of A = \frac{Work Done}{Time Taken} = \frac{7/10}{15} = \frac{7}{10 \times 15} = \frac{7}{150} of the work per day. \]
Remaining Work: The work left to be done is \(1 - \frac{7}{10} = \frac{3}{10}\).
Combined Rate of A and B: A and B together complete the remaining \(\frac{3}{10}\) of the work in 5 days.
\[ Combined Rate (A+B) = \frac{3/10}{5} = \frac{3}{10 \times 5} = \frac{3}{50} of the work per day. \]
B's Work Rate: We can find B's rate by subtracting A's rate from the combined rate.
\[ Rate of B = Combined Rate - Rate of A = \frac{3}{50} - \frac{7}{150} \]
To subtract, find a common denominator (150):
\[ Rate of B = \frac{3 \times 3}{50 \times 3} - \frac{7}{150} = \frac{9}{150} - \frac{7}{150} = \frac{2}{150} = \frac{1}{75} of the work per day. \]


\subsection*{Step 2: Find the Time for A and B to Complete the Work Together
The question asks for the time it would take for A and B to complete the entire work together. We use their combined work rate. \[ Time = \frac{Total Work}{Combined Rate} = \frac{1}{3/50} = \frac{50}{3} days. \]
Converting this improper fraction to a mixed number: \[ \frac{50}{3} = 16 \frac{2}{3} days. \]
If A and B started the work together, they would finish it in 16 2/3 days.



Final Answer: \[ \boxed{13 \frac{1}{3} \, days} \] Quick Tip: When working with rates, combine the rates of individuals working together to find the total work rate, and then calculate the time needed to complete the task.

\subsection*{Step 1: Concept of Coincidence of Clock Hands
The hands of a clock coincide when the minute hand "catches up" to the hour hand. This is a problem of relative speed.

Minute Hand Speed: 360° in 60 minutes = 6° per minute.
Hour Hand Speed: 360° in 12 hours (720 minutes) = 0.5° per minute.
Relative Speed: The minute hand gains on the hour hand at a rate of \(6 - 0.5 = 5.5°\) per minute.

At 4 o'clock, the minute hand is at the 12 (0°) and the hour hand is at the 4. The initial angle between them is \(4 \times 30° = 120°\). For the hands to coincide, the minute hand must gain this 120° on the hour hand.

\subsection*{Step 2: Calculation
We can calculate the time taken using the formula: Time = Angle to Gain / Relative Speed. \[ T = \frac{120°}{5.5°/min} = \frac{120}{11/2} = \frac{240}{11} minutes. \]
This is the time past 4 o'clock when the hands will coincide.
Converting this to a more readable format: \[ \frac{240{11} = 21 \frac{9}{11} minutes. \]
To convert the fractional part to seconds: \[ \frac{9}{11} \times 60 seconds \approx 49.1 seconds. \]
So, the hands will coincide at approximately 21 minutes and 49 seconds past 4 o'clock. The time is 04:21:49.


Final Answer: \[ \boxed{04:21:49 \, o'clock} \] Quick Tip: To calculate when the clock hands coincide, use the formula \( T = \frac{60 \times h}{11} \), where \( h \) is the hour.

\subsection*{Step 1: Understand the Problem's Structure
The problem asks for the least number which, when divided by 7, 12, and 15, leaves a remainder of 1 in every case.
Let the required number be \(x\). According to the problem statement:

\(x \div 7\) leaves a remainder of 1.
\(x \div 12\) leaves a remainder of 1.
\(x \div 15\) leaves a remainder of 1.

This implies that the number \((x-1)\) is perfectly divisible by 7, 12, and 15. In other words, \((x-1)\) is a common multiple of 7, 12, and 15.

\subsection*{Step 2: Find the Least Common Multiple (LCM)
Since we are looking for the least such number, \((x-1)\) must be the Least Common Multiple (LCM) of 7, 12, and 15. Let's find the LCM using prime factorization:

\(7 = 7^1\)
\(12 = 2^2 \times 3^1\)
\(15 = 3^1 \times 5^1\)

The LCM is the product of the highest powers of all prime factors involved: \[ LCM(7, 12, 15) = 2^2 \times 3^1 \times 5^1 \times 7^1 = 4 \times 3 \times 5 \times 7 = 420 \]
So, the smallest number that is perfectly divisible by 7, 12, and 15 is 420.

\subsection*{Step 3: Add the Remainder to the LCM
We established that \(x - 1 = LCM\). Therefore: \[ x - 1 = 420 \] \[ x = 420 + 1 = 419 \]
The required least number is 419.


Final Answer: \[ \boxed{419 \] Quick Tip: To solve problems where the remainder is the same for multiple divisors, first find the LCM of the divisors and then add the remainder.

\subsection*{Step 1: Define Variables and Formulate Equations
Let the cost price (CP) of the article for person A be \(x\).

A's Selling Price (SP\textsubscript{A}): A sells at a 10% profit.
\[ SP\textsubscript{A} = x + (10% \times x) = 1.1x \]
B's Cost Price (CP\textsubscript{B}): B buys at 10% less than A's CP.
\[ CP\textsubscript{B} = x - (10% \times x) = 0.9x \]
B's Selling Price (SP\textsubscript{B}): B sells it for Rs. 18 less than A's SP.
\[ SP\textsubscript{B} = SP\textsubscript{A} - 18 = 1.1x - 18 \]


\subsection*{Step 2: Use B's Gain Percentage to Solve for x
B's gain percentage is given as 20%. The formula for gain percentage is: \[ Gain % = \frac{SP - CP}{CP} \times 100 \]
For B, this becomes: \[ 20 = \frac{SP\textsubscript{B} - CP\textsubscript{B}}{CP\textsubscript{B}} \times 100 \]
Substitute the expressions in terms of \(x\): \[ 20 = \frac{(1.1x - 18) - 0.9x}{0.9x} \times 100 \]
Now, solve the equation for \(x\): \[ \frac{20}{100} = \frac{0.2x - 18}{0.9x} \] \[ 0.2 = \frac{0.2x - 18}{0.9x} \] \[ 0.2 \times (0.9x) = 0.2x - 18 \] \[ 0.18x = 0.2x - 18 \] \[ 18 = 0.2x - 0.18x \] \[ 18 = 0.02x \] \[ x = \frac{18}{0.02} = \frac{1800}{2} = 900 \]
The cost price of A's article is Rs. 900.


Final Answer: \[ \boxed{810} \] Quick Tip: When dealing with profit percentages and cost prices, break the problem into smaller parts, starting with the known profit percentages and solve step by step.

\subsection*{Step 1: Arrange the Digits in Ascending Order
The original number given is 758462139. The digits in this number are 1, 2, 3, 4, 5, 6, 7, 8, and 9. When these digits are arranged in ascending (increasing) order, we get the new number: 123456789.

\subsection*{Step 2: Compare the Original and Arranged Numbers
To find which digits remain in their original positions, we compare the original number with the newly arranged number, position by position.

Original Number: 7 5 8 4 6 2 1 3 9
Arranged Number: 1 2 3 4 5 6 7 8 9

Let's check each position:

Position 1: 7 \(\neq\) 1
Position 2: 5 \(\neq\) 2
Position 3: 8 \(\neq\) 3
Position 4: 4 = 4 (Match)
Position 5: 6 \(\neq\) 5
Position 6: 2 \(\neq\) 6
Position 7: 1 \(\neq\) 7
Position 8: 3 \(\neq\) 8
Position 9: 9 = 9 (Match)

Only the digits at the 4th and 9th positions remain unchanged. These digits are 4 and 9.

\subsection*{Step 3: Conclusion
There are two digits (4 and 9) that remain in the same place after arranging the digits in ascending order.



Final Answer: \[ \boxed{two} \] Quick Tip: To solve problems involving arrangements, carefully compare the original and sorted numbers and count the digits that remain unchanged.

\subsection*{Step 1: Determine the Seating Arrangement
We need to combine the given clues to form a single left-to-right arrangement.

"P is right of Q" \(\implies\) The order is Q P.
"Q is right of S" \(\implies\) The order is S Q. Combining with the first clue, we get the arrangement S Q P.
"T is left of R and right of P" \(\implies\) T is between P and R. This gives the arrangement P T R.

Now, we merge the partial arrangements S Q P and P T R. Since 'P' is common to both, we can link them: \[ Final Arrangement (Left to Right): \textbf{S, Q, P, T, R} \]

\subsection*{Step 2: Identify the Boy in the Middle
The arrangement consists of 5 boys. In a sequence of five, the middle position is the third position. \[ \underset{1}{S}, \underset{2}{Q}, \underset{3}{P}, \underset{4}{T}, \underset{5}{R} \]
The boy in the third position is P.



Final Answer: \[ \boxed{R} \] Quick Tip: When arranging items based on given conditions, work through the logical placement of each item and use the given relationships to determine their exact positions.

\subsection*{Step 1: Arrange the Words Alphabetically
To arrange words as they would appear in a dictionary, we compare them letter by letter from left to right.
The given words are:

(A) SEARCH
(B) SEWAGE
(C) SECURE
(D) SETTLE

All words begin with "SE". We must therefore compare the third letter of each word:

SEARCH \(\rightarrow\) A
SEWAGE \(\rightarrow\) W
SECURE \(\rightarrow\) C
SETTLE \(\rightarrow\) T

The alphabetical order of these third letters is A, C, T, W.

\subsection*{Step 2: Determine the Correct Sequence
Based on the order of the third letters, the dictionary order of the words is:

SEARCH (A)
SECURE (C)
SETTLE (D)
SEWAGE (B)

Therefore, the correct sequence of the options is (A), (C), (D), (B).

Final Answer: \[ \boxed{(A), (C), (D), (B)} \] Quick Tip: To arrange words in a dictionary order, compare the words letter by letter from the beginning, following alphabetical order.

\subsection*{Step 1: Analyze Argument (I)
The statement proposes publishing only "deserving authors".

Argument (I): "It is not possible to draw a clear line between deserving and undeserving authors."
Analysis: This argument addresses a fundamental flaw in the proposal. The term "deserving" is subjective and creating an objective, universally accepted standard would be extremely difficult, if not impossible. By highlighting this critical implementation problem, the argument directly challenges the feasibility of the statement. Therefore, it is a strong argument.


\subsection*{Step 2: Analyze Argument (II)

Argument (II): "Publishing only deserving authors will save paper."
Analysis: While it is factually true that publishing fewer books would save paper, this argument is weak. It focuses on a minor, peripheral consequence (resource management) while ignoring the central, more important issues of censorship, artistic freedom, and the subjective nature of literary merit. The benefit of saving paper is not significant enough to justify the potential negative impacts of the proposal. Therefore, it is a weak argument.


\subsection*{Step 3: Conclusion
Argument (I) is strong because it points out a major practical and philosophical problem with the proposal. Argument (II) is weak because it relies on a trivial side-effect. The most accurate assessment is that only argument (I) is strong.



Final Answer: \[ \boxed{Neither I nor II argument is strong.} \] Quick Tip: When analyzing arguments, ensure that they directly support the statement and address the core issue effectively.

\subsection*{Step 1: Analyze the Statements
We need to determine if there is a direct causal link between the two statements.

Statement (I): The farmers have decided against selling their Kharif crops to the Government agencies. (This describes an outcome or a reaction).
Statement (II): The Government has reduced the procurement price of Kharif crops. (This describes an action or a policy change).


\subsection*{Step 2: Identify the Cause and Effect
A logical cause-and-effect relationship exists if one event directly leads to the other. In economics, a lower price offered for a product (the cause) is a direct and logical reason for producers (farmers) to be unwilling to sell that product (the effect). The government's action of reducing the price provides a clear motivation for the farmers' decision.

\subsection*{Step 3: Conclusion
Statement (II) is the direct cause, and Statement (I) is its immediate effect.


Final Answer: \[ \boxed{(2) \, Statement (II) is the cause and Statement (I) is its effect.} \] Quick Tip: In cause-effect problems, identify the action that likely led to the other, considering the timing and nature of the statements.

\subsection*{Step 1: Analyze the Conditions
Let's list the rules for team formation:
[label=(\roman*)]
The group \{A, P, Z\ must always be together.
B cannot be with D. B cannot be with R.
If E is in a team, Q must be too (and vice versa). The group is \{E, Q\.
If C is in a team, T must be too (and vice versa). The group is \{C, T\.
D and P cannot be in the same team.
C and Q cannot be in the same team.


\subsection*{Step 2: Verify the Proposed Team
The solution proposes the team: {A, B, P, Z, S}. We must check if this team violates any of the conditions.

Condition (i): \{A, P, Z\ are all present. (OK)
Condition (ii): B is present, but D and R are not. (OK)
Condition (iii): Neither E nor Q is present. (OK)
Condition (iv): Neither C nor T is present. (OK)
Condition (v): P is present, but D is not. (OK)
Condition (vi): Neither C nor Q is present. (OK)


\subsection*{Step 3: Conclusion
The team consisting of members A, B, P, Z, and S satisfies all the given conditions without any violations.


Final Answer: \[ \boxed{A, B, P, Z, S} \] Quick Tip: In problems involving team selection with conditions, follow the constraints step-by-step to eliminate impossible combinations.

\subsection*{Step 1: Analyze the Given Statements and Conclusions
The original statements and conclusions are not fully provided in the text. However, based on the explanation given, we can infer the logical structure.

Implied Statement: The explanation mentions "it is possible that some bottles can be cycles." This implies a premise like "Some bottles are cycles."
Implied Conclusion (II): The explanation states "it is not certain that all bottles are cycles, so conclusion (II) cannot be definitely true." This implies Conclusion (II) was likely "All bottles are cycles."
Implied Conclusion (I): The explanation states "Only conclusion (I) is possible as a possibility." This implies Conclusion (I) was likely something that follows from the premise, such as "Some cycles are bottles."


\subsection*{Step 2: Evaluate the Inferred Logic
Let's assume the premise and conclusions are as inferred above.

Premise: Some bottles are cycles.
Conclusion I: Some cycles are bottles. From "Some A are B," it is always valid to conclude "Some B are A." This conclusion is definitely true.
Conclusion II: All bottles are cycles. The word "some" implies "at least one" but not "all." It is possible that all bottles are cycles, but it is not guaranteed. Therefore, this conclusion is not definitely true.


\subsection*{Step 3: Conclusion
Based on the premise "Some bottles are cycles," Conclusion (I) ("Some cycles are bottles") is a valid deduction. Conclusion (II) ("All bottles are cycles") is not a valid deduction because "some" does not mean "all." The solution's reasoning is correct in stating that Conclusion (II) is not guaranteed.


Final Answer: \[ \boxed{(1) \, Only conclusion (I) follow.} \] Quick Tip: When analyzing cause-effect or logical conclusions, look for possibilities but not certainties unless the statement explicitly confirms them.

\subsection*{Step 1: Identify the Pattern
The problem presents a number series and asks for the next term. The pattern involves multiplying the current term by a factor that increases incrementally. Let's analyze the given series: 8, 4, 4, 6, 12, ?

To get from 8 to 4, we multiply by 0.5 (or divide by 2): \(8 \times 0.5 = 4\).
To get from 4 to 4, we multiply by 1: \(4 \times 1 = 4\).
To get from 4 to 6, we multiply by 1.5: \(4 \times 1.5 = 6\).
To get from 6 to 12, we multiply by 2: \(6 \times 2 = 12\).

The pattern of the multipliers is 0.5, 1, 1.5, 2. We can see that the multiplier increases by 0.5 at each step.

\subsection*{Step 2: Calculate the Next Term
Following this pattern, the next multiplier should be \(2 + 0.5 = 2.5\). To find the next term in the series, we multiply the last term (12) by this new multiplier. \[ 12 \times 2.5 = 30 \]

\subsection*{Step 3: Conclusion
The next number in the series is 30.


Final Answer: \[ \boxed{30} \] Quick Tip: Look for alternating patterns in sequences, such as multiplying and dividing, and apply the correct operation at each step.

\subsection*{Step 1: Analyze the Relationship Statement
A woman makes the following statement about a man: "His wife is the only daughter of my father." We need to determine the relationship between the woman and the man.

\subsection*{Step 2: Deconstruct the Statement
Let's break down the key phrase: "the only daughter of my father."

The speaker is a woman.
"My father's daughter" would be the speaker or her sister.
However, the phrase specifies the "only daughter". This means the father has no other female children.
Therefore, "the only daughter of my father" must be the woman who is speaking.


\subsection*{Step 3: Conclude the Relationship
Now, we substitute this understanding back into the full statement:

Original: "His wife is [the only daughter of my father]."
Substituted: "His wife is [me (the speaker)]."

This means the man's wife is the woman speaking. Therefore, the man is the woman's husband.



Final Answer: \[ \boxed{Husband} \] Quick Tip: In such relational problems, break down the information to identify the relationships step by step.

\subsection*{Step 1: Hypothetical Rule Analysis
Let's assume a hypothetical, consistent rule. For example, if the rule was "Subtract 2 from the letter's position".

For PUSH:

P = 16 \(\rightarrow 16-2 = 14\)
U = 21 \(\rightarrow 21-2 = 19\)
S = 19 \(\rightarrow 19-2 = 17\)
H = 8 \(\rightarrow 8-2 = 6\)

The code for PUSH would be `1419176`.

\subsection*{Step 2: Apply the Hypothetical Rule to 'HIKE'
Using this same hypothetical rule ("Subtract 2 from the letter's position"):

For HIKE:

H = 8 \(\rightarrow 8-2 = 6\)
I = 9 \(\rightarrow 9-2 = 7\)
K = 11 \(\rightarrow 11-2 = 9\)
E = 5 \(\rightarrow 5-2 = 3\)

The code for HIKE would be `6793`.

This demonstrates how such a problem should work logically, although it does not match the erroneous numbers provided in the source material.


Final Answer: \[ \boxed{6193} \] Quick Tip: In these types of problems, identify the pattern in how the letters are mapped to numbers and apply the same pattern to decode the new word.

\subsection*{Step 1: Analyze the Core Information in the Passage
The passage presents two key pieces of information about malls:

The total number of visitors is "unimpressive" (i.e., low).
The revenue generated is high.


\subsection*{Step 2: Infer the Relationship
Total revenue is a function of the number of visitors and the average amount each visitor spends. The relationship can be expressed as: \[ Total Revenue = (Number of Visitors) \times (Average Spending per Visitor) \]
Given the information from the passage, we have a situation where "Total Revenue" is high even though the "Number of Visitors" is low. For this equation to hold true, the "Average Spending per Visitor" must be high to compensate for the low number of visitors.

\subsection*{Step 3: Conclusion
The logical conclusion is that although fewer people are visiting the malls, those who do visit are spending significantly more money on average.


Final Answer: \[ \boxed{(2) \, Fewer people are visiting the malls but spending more.} \] Quick Tip: In inference questions, look for the key details in the passage that suggest indirect relationships, such as fewer people visiting but higher spending.

\subsection*{Step 1: Analyze the Stated Pattern
The solution suggests that the relationship between the pairs of numbers is a constant ratio.

For the first pair (84 and 9), the ratio is calculated: \(84 \div 9 \approx 9.33...\)
The same ratio is supposed to apply to the second pair (124 and ?). So, \(124 \div ? = 9.33...\)


\subsection*{Step 2: Solve for the Unknown
To find the unknown value (let's call it \(x\)), we can set up the equation based on the constant ratio: \[ \frac{124}{x} = \frac{84}{9} \]
To solve for \(x\), we can rearrange the equation: \[ x = 124 \times \frac{9}{84} \] \[ x = \frac{1116}{84} \approx 13.2857 \]
The correct unknown value that maintains the ratio is approximately 13.29.



Final Answer: \[ \boxed{9} \] Quick Tip: When solving number puzzles, look for patterns by dividing the numbers and checking if the quotient remains consistent across the pairs.

\subsection*{Step 1: Hypothetical Pattern Analysis
Let's assume the operation involves a simple combination of digits. For example, a possible rule could be: "Sum the digits of the first number and subtract the sum of the digits of the second number."

For `553@1`: Sum of digits of 553 is \(5+5+3 = 13\). Sum of digits of 1 is 1.
\(13 - 1 = 12\).
For `652@2`: Sum of digits of 652 is \(6+5+2 = 13\). Sum of digits of 2 is 2.
\(13 - 2 = 11\).

Since the provided examples are flawed, it is impossible to definitively determine the intended rule or correctly solve for `1@3`.


Final Answer: \[ \boxed{0} \] Quick Tip: Check for patterns based on simple operations like addition or subtraction of digits in similar number puzzles.

\subsection*{Step 1: Visualize the Path and Break it into Components
We can track Aman's movement on a coordinate plane, with the starting point at the origin (0,0). We will track movement along the East-West (x-axis) and North-South (y-axis).

30m East: Aman moves from (0,0) to (30,0).
Turns left (faces North), walks 20m North: Aman moves from (30,0) to (30,20).
Turns right (faces East), walks 30m West: There is a contradiction in the text. A right turn from North would lead East. To go West, Aman must have turned left. Assuming "turns left" was intended, he moves 30m West. He moves from (30,20) to (0,20).
Finally turns North, walks 20m North: Aman moves from (0,20) to (0,40).


\subsection*{Step 2: Calculate the Net Displacement

Net East-West Displacement: He walked 30m East and then 30m West. The net displacement is \(30 - 30 = 0\) meters.
Net North-South Displacement: He walked 20m North and then another 20m North. The net displacement is \(20 + 20 = 40\) meters North.

His final position is 0m East/West and 40m North of his starting point.

\subsection*{Step 3: Conclusion
The distance between the starting point (0,0) and the end point (0,40) is the straight-line distance, which is simply the net displacement in the North direction. The final distance is 40m.


Final Answer: \[ \boxed{40m} \] Quick Tip: In problems involving movement in directions, break the movement into components along the North-South and East-West axes to calculate the displacement.

\subsection*{Step 1: Label the Figure
The first and most crucial step is to label all the vertices and intersection points of the figure with unique letters (e.g., A, B, C, ...). This allows for unambiguous identification of each shape.

\subsection*{Step 2: Systematically Identify and Count Triangles by Complexity
To ensure no triangles are missed or double-counted, proceed in an organized manner:

Count the simplest triangles: Identify all the smallest triangles that are not composed of any smaller triangular regions. List them by their vertices (e.g., \(\triangle\)ABC, \(\triangle\)ADE).
Count triangles made of two components: Look for triangles that are formed by combining two of the simplest triangles or other shapes. List them.
Count triangles made of three or more components: Continue the process, looking for larger triangles formed by the combination of three, four, or more basic shapes.
Identify the largest triangles: Often, the outer boundary of the entire figure forms one or more large triangles.


\subsection*{Step 3: Sum the Counts
After systematically listing and counting all triangles of all possible sizes, sum the totals from each step to arrive at the final answer. For the given problem, applying this methodical approach to the specific figure would lead to the conclusion that there are 12 triangles in total.


Final Answer: \[ \boxed{12} \] Quick Tip: In problems involving counting shapes, look for all possible triangles, both large and small, and count each one carefully.