CUET PG 2026 General Question Paper with Solutions - Available

Step 1: Understanding the Question:


This question requires us to identify the major contribution of the invention of the telephone as highlighted in the provided comprehension passage.

We need to analyze the options and find the one that matches the passage's description of the telephone's broader impact.



Step 2: Detailed Explanation:


The passage explicitly states: ``This strange instrument known as Telephone was to revolutionize life in the years to come.''

While option (A) describes the functional capability of the device, the author presents the primary societal contribution as a revolutionary transformation of human life.

Option (B) is incorrect because the passage does not limit the usage or communication of the telephone to wealthy individuals.

Option (C) mentions a specific experimental event with Watson, which was a step toward the invention rather than the overall contribution of the invention to society.

Therefore, the overarching contribution of the telephone is its power to revolutionize human life globally.



Step 3: Final Answer:

The correct option is (D).
Quick Tip: Look for the author's broad statements regarding the long-term impact of an invention rather than focusing on specific localized incidents described in the text.

Step 1: Understanding the Question:


The question asks for the primary underlying driver or motivation that led Alexander Graham Bell to invent the telephone.

We must refer to the text to find what intrinsic or extrinsic factor initiated his inventive activities.



Step 2: Detailed Explanation:


According to the passage, ``Bell was fond of scientific inventions and was ever engaged in making some machines in his spare time.''

This direct statement highlights his personal passion and keen interest in scientific research as the primary catalyst for his creative endeavors.

Although he was dedicated to teaching and serving the deaf and dumb (options A and B), these activities represent his humanitarian career rather than the direct motivation for building communication machines like the telephone.

Watson (Option D) was his assistant and companion during the later testing phases, but he was not the source of motivation that drove Bell to start inventing.

Thus, his innate curiosity and fondness for scientific inventions led to the creation of the telephone.



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Identify keywords in the text like ``fond of'' or ``engaged in making... in his spare time'' to connect personal habits directly to motivations.

Step 1: Understanding the Question:


This question requires us to identify the specific geographic location where the historic demonstration call to the Emperor of Brazil took place.

We need to isolate different locations mentioned in the text and match them with the correct event.



Step 2: Detailed Explanation:


The passage starts with the description of the Emperor of Brazil expressing amazement: ``My God, it speaks''.

It then explicitly connects this event to a specific time and location: ``This incident goes back to 1876 when at an exhibition in Philadelphia (USA), Alexander Graham Bell was giving a demonstration of his new invention.''

Let us review the other locations mentioned in the passage:

Edinborough (Option A) was Bell's birthplace in Scotland.

Brazil (Option C) was the country ruled by the Emperor, not the place where the call was initiated.

Boston (Option D) was the place where Bell conducted experiments over metal wires with Watson, but it was not the venue of the demonstration involving the Emperor.

Hence, the demonstration call was made during the exhibition in Philadelphia.



Step 3: Final Answer:

The correct option is (B).
Quick Tip: Distinguish between the birthplace of a scientist, their experimental headquarters, and the public exhibition venues mentioned in historical accounts.

Step 1: Understanding the Question:


The question asks why Bell's teaching activities were described as a ``noble cause'' in the passage.

We need to analyze the target audience of his teaching work as described in the text.



Step 2: Detailed Explanation:


The passage states that Bell ``was dedicated to the noble cause of teaching the deaf and the dumb.''

Deaf and dumb individuals suffer from physical sensory impairments, making them physically challenged or underprivileged. Special education for these individuals required extreme patience, compassion, and specialized skills in the 19th century.

Option (B) is historically incorrect and unsupported by the text; there were other educators in the world.

Option (C) mentions financial details that are completely absent from the text.

Option (D) describes his scientific reputation, which is unrelated to why his teaching activities themselves were deemed ``noble''.

Thus, the nobility of his work lies in his dedication to educating physically challenged, marginalized children.



Step 3: Final Answer:

The correct option is (A).
Quick Tip: A ``noble cause'' in comprehension passages is often linked to humanitarian efforts, charity, or serving disabled and underprivileged segments of society.

Step 1: Understanding the Question:


The question asks for the primary reason behind Alexander Graham Bell's relocation to Canada in the year 1870.

We need to pinpoint the cause-and-effect relationship detailed in the text regarding this journey.



Step 2: Detailed Explanation:


The passage explicitly notes: ``Due to a severe illness, Bell was sent to Canada in 1870...''

This indicates that his own health issues (severe illness) necessitated the move, likely for recovery, rest, or medical treatment in a healthier climate.

Option (A) is incorrect as he went due to his own illness, not to treat someone else.

Option (B) describes the work he engaged in after arriving in Canada, but this was not the initial reason why he was sent there.

Option (D) is incorrect as his invention phase began in earnest later, and health was the immediate catalyst for the 1870 move.

Therefore, undergoing personal medical treatment and recuperating from a severe illness was the primary reason for his journey.



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Notice the phrase ``Due to...''; it introduces the immediate cause of an action in a narrative. This helps avoid confusing the trigger event with subsequent activities.

Step 1: Understanding the Question:


This question consists of an Assertion (A) and a Reason (R) concerning the history of Indian English Literature.

We need to evaluate the historical accuracy of both statements independently and then determine if there is a causal relationship.



Step 2: Detailed Explanation:


Evaluating Assertion (A): Indian English literature indeed has a long history that predates India's independence in 1947. The earliest writings by Indians in English date back to the late 18th and early 19th centuries. For example, Sake Dean Mahomet published ``The Travels of Dean Mahomet'' in 1794, which is widely recognized as the first book written by an Indian in English. Thus, Assertion (A) is correct.

Evaluating Reason (R): The statement claims there were no Indian writers in English before 1947. This is factually incorrect. Many famous Indian writers wrote extensively in English before independence, including Toru Dutt, Sarojini Naidu, Rabindranath Tagore, Mulk Raj Anand, R.K. Narayan, and Raja Rao.

For instance, R.K. Narayan published his debut novel ``Swami and Friends'' in 1935, Mulk Raj Anand published ``Untouchable'' in 1935, and Raja Rao published ``Kanthapura'' in 1938. These works are foundational pillars of Indian English fiction and were all published well before 1947.

Since Assertion (A) is true but Reason (R) is false, the correct combination is represented by Option (C).



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Remember that the pre-independence era (especially the 1930s) was highly productive for the founding trio of Indian English fiction: Mulk Raj Anand, R.K. Narayan, and Raja Rao.

Step 1: Understanding the Question:


This question involves an Assertion and a Reason regarding the physical properties and electrical conductivity of metallic elements.

We must evaluate the accuracy of both statements based on physical principles of metallic bonding and charge transport.



Step 2: Detailed Explanation:


Evaluating Assertion (A): Metals are chemically characterized by their ability to readily lose valence electrons. In the solid state, metallic atoms form a crystalline lattice where positive ions are surrounded by a shared ``sea of mobile valence electrons.'' This structural arrangement makes metals excellent conductors of electricity and heat. Thus, Assertion (A) is scientifically correct.

Evaluating Reason (R): Electric current is defined as the net rate of flow of electric charge through a conductor. In metals, the charge carriers are the free, delocalized electrons that exist in the conduction band. When an electric potential difference (voltage) is applied across a metal wire, these free electrons experience an electrostatic force and drift toward the positive terminal, creating an electric current. Thus, Reason (R) is scientifically correct.

Causal Connection: The microscopic presence of free electrons (R) directly explains the macroscopic phenomenon of electrical conductivity in metals (A). Therefore, Reason (R) is the correct and complete explanation of Assertion (A).

Consequently, the correct choice is Option (A).



Step 3: Final Answer:

The correct option is (A).
Quick Tip: Electrical conductivity in solid conductors requires mobile charge carriers. In metals, these carriers are free electrons, whereas in liquid electrolytes, they are mobile ions.

Step 1: Understanding the Question:


This question analyzes a literary theory concept (Postcolonialism) using an Assertion-Reason format.

We need to determine if postcolonial literature focuses on questioning colonial power and whether this is achieved by highlighting themes of identity, conflict, and resistance.



Step 2: Detailed Explanation:


Evaluating Assertion (A): Postcolonial literature refers to body of writings produced in countries that were formerly colonized by European powers. The primary objective of postcolonial writers is to interrogate, challenge, and dismantle the lingering cultural, political, and social hegemonies of colonial rule. Thus, Assertion (A) is correct.

Evaluating Reason (R): To question and deconstruct colonial power, postcolonial writers focus on the lived experiences of the colonized. This includes exploring the fragmentation of identity, hybridity, conflicts between native traditions and colonial modernities, and direct or passive resistance against imperial oppression. Thus, Reason (R) is correct.

Causal Connection: Postcolonial literature is able to question and critique colonial power structures (A) precisely because/by showcasing issues of identity crisis, cultural clash, and anti-colonial resistance (R). The thematic content described in (R) serves as the primary mechanism to achieve the goals of (A).

Therefore, both (A) and (R) are correct, and (R) is the correct explanation of (A). This corresponds to Option (A).



Step 3: Final Answer:

The correct option is (A).
Quick Tip: In literary criticism questions, connect the major theoretical definition (e.g., Postcolonialism) with its common narrative themes (e.g., identity, cultural hybridity, and resistance) to evaluate logical links.

Step 1: Understanding the Question:


This vocabulary question requires us to identify the exact antonym (opposite in meaning) of the adjective ``Intimidating.''

We must analyze the definition of the target word and select the option that describes an opposing state or attitude.



Step 2: Detailed Explanation:


Definition of Intimidating: The word ``intimidating'' describes something or someone that makes others feel frightened, nervous, overwhelmed, or lacking in confidence. It represents an overbearing, menacing, or unapproachable demeanor.

Let us evaluate each option to find the correct opposite:

Option (A) ``Authoritative'' means commanding, powerful, or self-confident. This is a near-synonym or closely associated trait to intimidating, not an antonym.

Option (B) ``Casual'' means relaxed, informal, or unconcerned, which does not directly oppose the fear-inducing quality of intimidating.

Option (C) ``Non-serious'' describes a lack of depth or solemnity, which is semantically unrelated to intimidation.

Option (D) ``Friendly'' describes someone who is warm, approachable, kind, and supportive. A friendly person makes others feel comfortable and welcomed, which is the direct behavioral and emotional opposite of an intimidating person.

Therefore, ``Friendly'' is the most suitable antonym.



Step 3: Final Answer:

The correct option is (D).
Quick Tip: If a word creates a feeling of fear or distance (like ``intimidating''), its perfect antonym should promote feelings of comfort and closeness (like ``friendly'').

Step 1: Understanding the Question:


This is a sentence rearrangement (parajumble) question where we need to organize five sentences into a coherent, logical paragraph.

We must find introductory clues, transitional phrases, and concluding sentences to build the correct sequence.



Step 2: Detailed Explanation:


Sentence A introduces the general, overarching topic of the passage: ``People have always been fascinated by dreams.'' It makes a broad statement and serves as the perfect opening sentence.

Sentence D introduces a contrast to general dream fascination by focusing on nightmares: ``But the study of nightmares has been curiously neglected.'' The word ``But'' connects the fascination with dreams (A) to the neglect of nightmares (D). Thus, D must follow A.

Sentence C shows a transition in the historical neglect mentioned in D: ``Now that is changing.'' The pronoun ``that'' refers directly to the ``neglect'' mentioned in D. This makes the sequence A-D-C.

Sentence B explains how the change (C) is occurring by mentioning empirical research: ``In fact, only recently have there been serious studies...'' The phrase ``In fact'' elaborates on the change. This extends our sequence to A-D-C-B.

Sentence E discusses the outcomes/results of these serious studies: ``While results so far are inconclusive, it seems fair to say...'' This naturally serves as the concluding sentence because it references the results of the studies introduced in B.

Putting it all together, we get the logical flow: A \(\rightarrow\) D \(\rightarrow\) C \(\rightarrow\) B \(\rightarrow\) E.

This matches Option (B).



Step 3: Final Answer:

The correct option is (B).
Quick Tip: Identify pronoun connections. The word ``that'' in sentence C directly refers back to the ``neglect'' of the study of nightmares mentioned in sentence D, establishing a mandatory D-C pair.

Step 1: Understanding the Question:


This is a one-word substitution question from medical terminology.

We need to identify the exact term that matches the removal and testing of cells from a living body.



Step 2: Detailed Explanation:


Let us analyze each option based on its standard medical definition:

Biopsy (Option A) is a clinical procedure in which a doctor extracts a sample of cells or tissue from a living patient's diseased organ or lesion to examine it under a microscope for diagnostic purposes (e.g., checking for cancer cells). This perfectly matches the definition in the question.

Autopsy (Option B) is a highly specialized surgical procedure performed on a dead body (post-mortem) to determine the cause, manner, and mechanism of death. It is not performed on living, diseased organs.

Operation (Option C) is a broad term for any physical intervention or surgery on a patient, which may or may not involve cellular testing.

Amputation (Option D) is the surgical removal of a limb or extremity (like an arm or leg) due to trauma, infection, or severe vascular disease. It does not mean diagnostic cellular testing.

Therefore, Option (A) is the correct and precise answer.



Step 3: Final Answer:

The correct option is (A).
Quick Tip: Remember the prefixes: ``Bio-'' refers to life or living organisms (hence, biopsy is on a living body), while ``Auto-'' in autopsy historically refers to seeing with one's own eyes on a deceased subject.

Step 1: Understanding the Question:


This question requires us to match each vocabulary word in List-I with its correct antonym (opposite meaning) in List-II.

We need to establish the individual word meanings and find their opposites systematically.



Step 2: Detailed Explanation:


Let us define each word in List-I and identify its antonym in List-II:

A. Potent: Potent means powerful, strong, or highly effective. Its direct antonym is III. Weak, which denotes a lack of strength or influence. Thus, A matches with III.

B. Meagre: Meagre (or meager) means lacking in quantity, deficient, scarce, or thin. Its direct antonym is IV. Surplus, which indicates an excess or abundant supply. Thus, B matches with IV.

C. Chronic: Chronic refers to an illness, habit, or problem that is long-standing, persistent, or recurring. Its antonym is I. Temporary, which means lasting for only a short, limited period. Thus, C matches with I.

D. Evident: Evident means plain, clear, or obvious to see or understand. Its antonym is II. Hidden, which means concealed or obscure. Thus, D matches with II.

Combining these matches, we get: A-III, B-IV, C-I, D-II.

This matches option (D).



Step 3: Final Answer:

The correct option is (D).
Quick Tip: In matching questions, always start with the easiest or most familiar pair. For instance, pairing ``evident'' with its opposite ``hidden'' (D-II) quickly eliminates options (A), (B), and (C).

Step 1: Understanding the Question:


This question requires us to find the closest synonym (best expresses the meaning) of the noun ``Panacea.''

We must evaluate the options to identify the correct conceptual equivalent.



Step 2: Detailed Explanation:


Origin and Meaning of Panacea: The word ``panacea'' comes from the Greek roots \textit{pan (meaning ``all'') and \textit{akos (meaning ``cure''). In the English language, a panacea refers to a hypothetical remedy, medicine, or solution that can cure all diseases or resolve all problems and difficulties.

Let us evaluate the options:

Option (A) ``Flatter'' means to praise insincerely to gain favor. This is unrelated.

Option (B) ``Praise'' is an expression of warm approval or admiration. This is unrelated.

Option (C) ``Inactivity'' refers to a state of being passive or doing nothing. This is unrelated.

Option (D) ``Cure-all'' is a direct English equivalent that means a universal remedy for all illnesses or troubles.

Therefore, ``Cure-all'' is the perfect synonym for Panacea.



Step 3: Final Answer:

The correct option is (D).
Quick Tip: Etymology is highly helpful in vocabulary exams. The prefix ``pan-'' always means ``all'' or ``universal'' (as in panorama, pandemic, pantheon, and panacea).

Step 1: Understanding the Question:


This matching question requires us to pair each word in List-I with its correct definition or synonym in List-II.

We need to determine the semantic meanings of all four terms to find the correct combinations.



Step 2: Detailed Explanation:


Let us analyze each term in List-I and find its equivalent in List-II:

A. Chivalrous: Chivalrous behavior refers to the medieval knightly code of honor, which includes courtesy, courage, and protective behavior toward women. A highly appropriate synonym is III. Gallant, which also means brave, polite, and honorable. Thus, A matches with III.

B. Eternal: Eternal describes something that lasts forever without end, or is timeless. Its direct equivalent is I. Perpetual, which means never-ending or changing. Thus, B matches with I.

C. Dormant: Dormant means temporarily inactive, quiet, or in a state of suspended animation. It is figuratively and literally represented as being in a state of II. Sleeping (as in a dormant volcano or a dormant seed). Thus, C matches with II.

D. Irreverence: Irreverence denotes a lack of respect for people, ideas, or things that are generally taken seriously or held sacred. Its direct meaning is IV. Disrespect. Thus, D matches with IV.

Combining these matches: A-III, B-I, C-II, D-IV.

This matches option (C).



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Connect scientific and literary uses. For example, ``dormant'' is commonly associated with ``sleeping'' or ``inactive'' phases in biology and geology, helping to quickly lock in the C-II pair.

Step 1: Understanding the Question:


This question requires us to identify the correct figurative meaning of the common English idiom ``to flog a dead horse.''

We must avoid literal translations and focus on the metaphorical message of the phrase.



Step 2: Detailed Explanation:


Metaphorical Meaning: Flogging (whipping) a horse that is already dead is completely useless because no amount of whipping will make it run or perform work. Therefore, the phrase metaphorically refers to investing time, energy, or resources into a situation that is already a lost cause, unchangeable, or completely resolved.

Let us evaluate the options:

Option (A) is the literal translation of the words, which is incorrect because idioms should never be interpreted literally.

Option (B) ``attempt to do the possible'' is the exact opposite of the idiom's meaning, as the task is impossible.

Option (C) ``waste one's efforts'' perfectly captures the sense of futility and wasted energy associated with the phrase.

Option (D) ``to take advantage of a weakness'' is a completely different concept and does not fit the idiom.

Thus, Option (C) is the correct choice.



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Idiomatic expressions rely heavily on absurd or vivid physical metaphors. Visualizing the physical action (whipping a dead horse) helps reveal the underlying concept of futility and wasted effort.

Step 1: Understanding the Question:


This question requires us to identify which Article of the Constitution of India contains the provision prohibiting discrimination on the grounds of religion, race, caste, sex, or place of birth.

We need to match the given constitutional text with the correct Fundamental Right.



Step 2: Detailed Explanation:


The Indian Constitution guarantees Fundamental Rights in Part III (Articles 12 to 35).

Article 15(1) explicitly states: ``The State shall not discriminate against any citizen on grounds only of religion, race, caste, sex, place of birth or any of them.'' This is a crucial article under the Right to Equality (Articles 14-18). Thus, the quote belongs to Article 15.

Let us analyze the other options to understand why they are incorrect:

Article 21A (Option B) guarantees the Right to Education, mandating free and compulsory education for all children between the ages of six and fourteen.

Article 19 (Option C) protects the six democratic freedoms (Freedom of Speech and Expression, Assembly, Association, Movement, Residence, and Profession).

Article 35 (Option D) gives the Parliament of India the exclusive power to make laws to give effect to the provisions of Part III (Fundamental Rights).

Therefore, the correct constitutional article is Article 15, which corresponds to Option (A).



Step 3: Final Answer:

The correct option is (A).
Quick Tip: To easily remember the Right to Equality (Articles 14 to 18): Article 14 is Equality before Law; Article 15 is Prohibition of Discrimination; Article 16 is Equality of Opportunity in Public Employment; Article 17 is Abolition of Untouchability; and Article 18 is Abolition of Titles.

Step 1: Understanding the Question:


The question asks for the constitutional categorization of the mandate ``to develop the scientific temper, humanism and the spirit of inquiry and reform.''

We need to determine if this is a Fundamental Right, Fundamental Duty, Service Provision, or Directive Principle of State Policy (DPSP).



Step 2: Detailed Explanation:


The given quote is taken directly from the list of Fundamental Duties of Indian citizens.

The Fundamental Duties were not part of the original Constitution. They were incorporated into Part IV-A (Article 51A) by the 42nd Constitutional Amendment Act of 1976, following the recommendations of the Swaran Singh Committee.

Specifically, Article 51A(h) states that it shall be the duty of every citizen of India ``to develop the scientific temper, humanism and the spirit of inquiry and reform.''

Let us review the other categories:

Fundamental Rights (Option A) are enforceable individual rights located in Part III.

Services under the Union and States (Option C) are administrative provisions located in Part XIV.

Directive Principles of State Policy (Option D) are non-justiciable guidelines for the state to frame policies, located in Part IV.

Therefore, this citizen mandate is categorized under Fundamental Duties, which corresponds to Option (B).



Step 3: Final Answer:

The correct option is (B).
Quick Tip: Duties containing moral/intellectual guidelines for citizens, such as promoting scientific temper, protecting public property, or respecting the national flag, are always found under the Fundamental Duties in Article 51A.

Step 1: Understanding the Question:


This question is based on the characters and genealogy in the ancient Indian epic, the Mahabharata.

We need to identify the family lineage or clan of Yuyutsu, a figure known for choosing the side of righteousness (dharma) during the Kurukshetra war.



Step 2: Detailed Explanation:


In the epic Mahabharata, Yuyutsu was a son of King Dhritarashtra (the blind king of Hastinapur) and a Vaishya maid named Sughada. Since he was a biological son of Dhritarashtra, he belonged to the Kaurava family. He was a half-brother to Duryodhana and the other ninety-nine Kaurava brothers.

Despite being born in the Kaurava clan, Yuyutsu was deeply righteous and possessed a strong conscience.

On the eve of the Kurukshetra war, Yudhisthira (the eldest Pandava) made a final proclamation that anyone who believed in their cause of righteousness was welcome to cross over and join the Pandavas. Yuyutsu was the only person from the Kaurava camp who chose to join the Pandavas to fight for dharma.

He survived the devastating war and was later appointed by the Pandavas as the caretaker of Hastinapur when they embarked on their final journey to the Himalayas.

Therefore, Yuyutsu was biologically and genealogically a Kaurav, making Option (C) the correct choice.



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Do not confuse political alliance with biological lineage. Though Yuyutsu fought on the Pandavas' side, his biological heritage makes him a Kaurav.

Step 1: Understanding the Question:


This geography question requires us to identify the specific Himalayan range to which Kanchenjunga, the highest peak in India, belongs.

We need to evaluate the physical geography and structural classification of the Himalayas.



Step 2: Detailed Explanation:


Kanchenjunga is the third-highest mountain in the world, with an elevation of 8,586 meters (28,169 feet). It is situated on the border between Sikkim, India, and Nepal.

Structurally, the Himalayan mountain system consists of three parallel ranges from north to south:

1. The Greater Himalayas (Himadri): This is the northernmost, loftiest, and most continuous range, with an average height exceeding 6,000 meters. It contains all the highest peaks of the world, including Mount Everest and Kanchenjunga. Thus, Kanchenjunga belongs to the Greater Himalayas.

2. The Middle/Lesser Himalayas (Himachal): This range lies south of the Himadri, with heights ranging between 3,700 and 4,500 meters.

3. The Outer Himalayas (Shiwaliks): This is the southernmost range, with low-altitude hills.

The Pir Panjal Range (Option C) is a sub-range of the Lesser Himalayas, located mostly in Jammu and Kashmir and Himachal Pradesh.

The Mount Kailash Range (Option D) is part of the Trans-Himalayas, located in Tibet.

Thus, Kanchenjunga belongs to the Greater Himalayas Ranges, corresponding to Option (A).



Step 3: Final Answer:

The correct option is (A).
Quick Tip: The highest peaks of the world (exceeding 8,000 meters, such as Everest, Kanchenjunga, and Lhotse) are located in the Greater Himalayas (Himadri) due to its extreme tectonic elevation.

Step 1: Understanding the Question:


This chemistry question asks for the atomic number of the metal sodium, which is represented by the chemical symbol 'Na'.

We need to identify its position and number of protons in the periodic table.



Step 2: Detailed Explanation:


The atomic number of an element is defined as the total number of protons present in the nucleus of an atom of that element. It determines the element's position on the periodic table.

Sodium is a highly reactive alkali metal belonging to Group 1 and Period 3 of the periodic table. Its chemical symbol 'Na' comes from its Latin name, \textit{Natrium.

A neutral sodium atom has 11 protons and 11 electrons, giving it an atomic number of 11. Its electronic configuration is:
\[ 1s^2 2s^2 2p^6 3s^1 \]

Let us review the atomic numbers of neighboring elements:

Atomic number 11: Sodium (Na)

Atomic number 12: Magnesium (Mg) (Option A)

Atomic number 13: Aluminum (Al) (Option D)

Atomic number 14: Silicon (Si) (Option C)

Therefore, the atomic number of sodium is 11, which corresponds to Option (B).



Step 3: Final Answer:

The correct option is (B).
Quick Tip: Memorizing the first 20 elements of the periodic table (from Hydrogen with atomic number 1 to Calcium with atomic number 20) is essential for competitive science sections.

Step 1: Understanding the Question:


This question is about a social sector scheme launched by the Government of India, called PM-SHRI.

We need to identify the target beneficiaries or objective of this scheme from the given options.



Step 2: Detailed Explanation:


What is PM-SHRI? PM-SHRI stands for ``PM Schools for Rising India.'' It is a centrally sponsored scheme approved by the Union Cabinet of India in September 2022.

Core Objective: The scheme aims to upgrade and develop more than 14,500 existing schools across India (including those managed by the central government, state governments, Union Territories, and local bodies).

these upgraded schools will showcase all components of the National Education Policy (NEP) 2020. They will act as exemplar/model schools, offering mentorship to other schools in their respective neighborhoods.

These schools are designed with modern infrastructure, green school concepts, smart classrooms, ICT facilities, and student-centric pedagogy to improve the quality of education.

Thus, PM-SHRI is specifically designed for the development and upgradation of schools as model institutions. This corresponds to Option (D).



Step 3: Final Answer:

The correct option is (D).
Quick Tip: Expand the acronym to solve the question. PM-SHRI stands for ``PM Schools for Rising India,'' where the word ``Schools'' clearly points to educational institutions.

Step 1: Understanding the Question:


This current affairs question concerns the implementation of the National Education Policy (NEP) 2020 by different Indian states.

We need to identify which states rejected the central policy and decided to create their own State Education Policies.



Step 2: Detailed Explanation:


Under the Indian Constitution, Education falls in the Concurrent List (List III), which means both the Central Government and the State Governments have the power to make laws on it.

While the Central Government introduced NEP 2020, some state governments raised concerns regarding regional representation, linguistic autonomy, and administrative centralization.

The state governments of Karnataka and Tamil Nadu formally rejected the implementation of NEP 2020.

Both states set up high-level committees and commissions to draft their own customized ``State Education Policies'' (SEP) to protect local languages, address regional requirements, and maintain federal autonomy over education.

Therefore, the correct pair of states is Karnataka and Tamil Nadu, which corresponds to Option (D).



Step 3: Final Answer:

The correct option is (D).
Quick Tip: Federal conflicts in educational policies often occur in states with strong regional languages and identities, making Tamil Nadu and Karnataka key examples of states that prefer a localized State Education Policy (SEP).

Step 1: Understanding the Question:


This question consists of an Assertion (A) and a Reason (R) about the history, author, and public performance of India's national song, ``Vande Mataram.''

We need to evaluate the historical accuracy of both statements independently.



Step 2: Detailed Explanation:


Evaluating Assertion (A): The patriotic song ``Vande Mataram'' was sung publicly for the first time at the Kolkata session of the Indian National Congress in 1896. Rabindranath Tagore set the song to music and sang it himself before the assembly. Thus, Assertion (A) is correct.

Evaluating Reason (R): ``Vande Mataram'' is a Sanskrit poem composed by Bankim Chandra Chattopadhyay in the 1870s. He later included it in his famous Bengali novel Anandamath (published in 1882).

The statement claims that \textit{Anandamath was written by Swami Vivekananda, which is factually incorrect. It was written by Bankim Chandra Chattopadhyay. Swami Vivekananda was a spiritual leader and did not write this novel. Thus, Reason (R) is incorrect.

Since Assertion (A) is correct but Reason (R) is incorrect, the correct combination is represented by Option (C).



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Do not confuse authors of important national literature. Bankim Chandra Chattopadhyay wrote \textit{Anandamath (Vande Mataram), while Rabindranath Tagore wrote Gitanjali (Jana Gana Mana).

Step 1: Understanding the Question:


This question involves an Assertion and a Reason regarding India's public spending on education and policy recommendations.

We need to check if the government actually spends 6% of its GDP on education and if NEP 2020 recommends this target based on the Kothari Commission.



Step 2: Detailed Explanation:


Evaluating Assertion (A): While the Government of India has committed to increasing education funding, actual public spending on education (combined center and states) has remained around 3% to 4.5% of GDP over the last five years. It has not yet reached the 6% of GDP target. Thus, Assertion (A) is factually incorrect.

Evaluating Reason (R): The Kothari Commission (1964-66) was the first to recommend that public investment on education should be increased to at least 6% of GDP to ensure quality and equity in education. The National Education Policy (NEP) 2020 explicitly reiterates this recommendation, urging both the Center and States to work together to reach this 6% of GDP target. Thus, Reason (R) is correct.

Since Assertion (A) is incorrect but Reason (R) is correct, the correct choice is Option (D).



Step 3: Final Answer:

The correct option is (D).
Quick Tip: Although the 6% GDP target has been recommended by policy documents since 1968, actual public spending on education has historically hovered between 3% and 4%, making statements about achieving the 6% target factually incorrect.

Step 1: Understanding the Question:


This question requires us to arrange five major events of the Indian National Movement in their correct chronological order (from earliest to latest).

We need to assign historical years to each event to find the correct sequence.



Step 2: Detailed Explanation:


Let us look at the historical dates of each event:

A. Jallianwala Bagh Massacre: Occurred on April 13, 1919, when British troops fired on a peaceful gathering in Amritsar, Punjab.

C. Call for Purna Swaraj: Declared during the Lahore Session of the Indian National Congress in December 1929, under the presidency of Jawaharlal Nehru.

D. Dandi Yatra (Salt March): Led by Mahatma Gandhi from March 12 to April 6, 1930, initiating the Civil Disobedience Movement.

E. Execution of Bhagat Singh, Rajguru, and Sukhdev: Carried out by the colonial government on March 23, 1931, in Lahore Jail.

B. Quit India Movement: Launched by Mahatma Gandhi on August 8, 1942, demanding an immediate British exit from India.

Now, let us arrange the years in order:

1919 (A) \(\rightarrow\) 1929 (C) \(\rightarrow\) 1930 (D) \(\rightarrow\) 1931 (E) \(\rightarrow\) 1942 (B).

This gives the sequence: A, C, D, E, B.

This corresponds to Option (A).



Step 3: Final Answer:

The correct option is (A).
Quick Tip: Remember key landmarks: Jallianwala Bagh was shortly after WWI (1919), the Purna Swaraj declaration (1929) immediately preceded the Dandi Yatra (1930), and the execution of Bhagat Singh happened a year later (1931).

Step 1: Understanding the Question:


This question requires us to arrange five major post-independence events of India in chronological order.

We need to identify the years of these political, financial, scientific, and sporting milestones.



Step 2: Detailed Explanation:


Let us analyze the dates of each event:

B. Lal Bahadur Shastri becomes Prime Minister: Shastri took office as the second Prime Minister of India on June 9, 1964, following the death of Jawaharlal Nehru.

A. Banks get nationalised: Under the leadership of Prime Minister Indira Gandhi, 14 major commercial banks were nationalized on July 19, 1969.

C. India does first nuclear test: Codenamed ``Smiling Buddha,'' India conducted its first peaceful nuclear explosion at Pokhran on May 18, 1974.

D. India hosts Asiad with APPU as icon: The 9th Asian Games were hosted in New Delhi in November 1982. The mascot was a baby elephant named ``Appu.''

E. Manmohan Singh becomes Finance Minister: Dr. Manmohan Singh was appointed as Finance Minister by Prime Minister P.V. Narasimha Rao on June 21, 1991, initiating major economic reforms (LPG policy).

Arranging the years in order:

1964 (B) \(\rightarrow\) 1969 (A) \(\rightarrow\) 1974 (C) \(\rightarrow\) 1982 (D) \(\rightarrow\) 1991 (E).

This gives the sequence: B, A, C, D, E.

This matches Option (B).



Step 3: Final Answer:

The correct option is (B).
Quick Tip: Associate political shifts with major policies: Shastri's premiership (mid-1960s) preceded bank nationalization (late 1960s), which was followed by the 1974 Pokhran test, the 1982 Delhi Asian Games, and the 1991 economic reforms.

Step 1: Understanding the Question:


This question requires us to evaluate five statements about the ancient universities of Nalanda and Takshashila (Taxila).

We need to determine the accuracy of each statement regarding their location, patronage, and famous scholars.



Step 2: Detailed Explanation:


Let us analyze each statement individually:

Statement A: Nalanda was indeed a world-famous ancient Buddhist monastery (Mahavihara) and center of higher learning, established in Bihar during the Gupta Empire in the 5th century CE. This statement is correct.

Statement B: Chanakya (Kautilya) lived in the 4th century BCE during the Mauryan period. Since Nalanda University was founded much later (in the 5th century CE), Chanakya could not have studied or taught there. He was actually a student and teacher at Takshashila. This statement is incorrect.

Statement C: Takshashila (located in modern Pakistan) was an ancient center of learning deeply rooted in Vedic and Brahminical traditions, teaching scriptures, grammar, law, and medicine. This statement is correct.

Statement D: Nalanda is located near Rajgir in Bihar (Eastern India). The Narmada River flows through Central and Western India (Madhya Pradesh, Maharashtra, and Gujarat). Nalanda was not on the banks of the Narmada. This statement is incorrect.

Statement E: Ancient Takshashila is located in the Rawalpindi district of Punjab province in modern-day Pakistan, not in Nepal. This statement is incorrect.

Since only statements A and C are correct, the correct choice is Option (C).



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Keep timelines clear: Takshashila was an ancient university dating back to the 6th-5th centuries BCE (associated with Chanakya and Panini), while Nalanda was a later Buddhist university founded in the 5th century CE.

Step 1: Understanding the Question:


The goal of this question is to identify the correct pairing of North-Eastern Indian states and their respective capital cities.

We are given five pairs and must evaluate the correctness of each pair individually to choose the correct combination.



Step 2: Detailed Explanation:


Let us analyze the capital cities of all the given states in North-East India:

A. Arunachal Pradesh: The correct capital of Arunachal Pradesh is Itanagar. The given match (Aizawl) is incorrect. Aizawl is the capital of Mizoram.

B. Tripura: The correct capital of Tripura is Agartala. The given match (Itanagar) is incorrect.

C. Mizoram: The correct capital of Mizoram is Aizawl. The given match (Shillong) is incorrect. Shillong is the capital of Meghalaya.

D. Meghalaya: The correct capital of Meghalaya is Shillong. The given match is correct.

E. Nagaland: The correct capital of Nagaland is Kohima. The given match is correct.

Evaluating the choices shows that only statements D and E are accurate matches.

Therefore, the correct option is (D).



Step 3: Final Answer:

The correct option is (D).
Quick Tip: To easily remember the seven sister states and their capitals, use mnemonic associations: Arunachal Pradesh starts with 'A' and its capital Itanagar starts with 'I' (AI); Nagaland has Kohima (NK); Meghalaya has Shillong (MS).

Step 1: Understanding the Question:


This matching question requires us to align prominent historical theorists and scientists in List-I with their respective academic disciplines in List-II.

We need to analyze the contributions of each individual to determine the correct matches.



Step 2: Detailed Explanation:


Let us evaluate each theorist and match them with their respective fields:

A. Auguste Comte: Auguste Comte was an influential French philosopher who formulated the doctrine of positivism. He is widely regarded as the first philosopher of science and coined the term ``sociology'', making him the father of Sociology (IV). Thus, A matches with IV.

B. Charles Darwin: Charles Darwin was an English naturalist whose pioneering work on the theory of evolution by natural selection revolutionized the field of biological sciences. His work belongs to Biology (III). Thus, B matches with III.

C. Bertrand Russell: Bertrand Russell was an exceptionally influential British polymath, logician, mathematician, and historian who made fundamental contributions to analytic philosophy. His primary discipline is Philosophy (II). Thus, C matches with II.

D. Ernest Rutherford: Ernest Rutherford was a New Zealand-born physicist and chemist who came to be known as the father of nuclear physics. He won the Nobel Prize in Chemistry (I) in 1908 for his investigations into the disintegration of elements and the chemistry of radioactive substances. Thus, D matches with I.

Combining these individual matches gives: A-IV, B-III, C-II, D-I.

This combination corresponds directly to Option (B).



Step 3: Final Answer:

The correct option is (B).
Quick Tip: Auguste Comte is universally recognized as the founder of Sociology (A-IV) and Charles Darwin is synonymously linked with evolutionary biology (B-III). Identifying either pair narrows down the options significantly.

Step 1: Understanding the Question:


This matching question requires us to pair famous historical books written during the Indian independence movement with their respective authors.

We need to draw on historical knowledge of prominent national leaders and their literary works.



Step 2: Detailed Explanation:


Let us analyze each book and match it with its author:

A. Discovery of India: This highly celebrated book was written by India's first Prime Minister, Jawaharlal Nehru (III), during his imprisonment at the Ahmednagar Fort from 1942 to 1945. Thus, A matches with III.

B. India Wins Freedom: This is an autobiographical narrative written by Maulana Abul Kalam Azad (IV), a leading figure in the Indian independence movement and India's first Minister of Education. The book contains his personal view of partition and freedom. Thus, B matches with IV.

C. An Experiment with Truth (The Story of My Experiments with Truth): This is the highly influential autobiography of Mohandas Karamchand Gandhi, widely known as Mahatma Gandhi (I), covering his life from early childhood through to 1921. Thus, C matches with I.

D. Why I am an Atheist: This is a deeply philosophical essay written by the revolutionary freedom fighter Bhagat Singh (II) in 1930 while imprisoned in the Lahore Central Jail. Thus, D matches with II.

Putting these matches together: A-III, B-IV, C-I, D-II.

This matches Option (C).



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Bhagat Singh's famous jail essay is ``Why I am an Atheist'' (D-II), and Nehru's classic historical work is ``Discovery of India'' (A-III). Keeping these two highly celebrated works in mind will help resolve book matching questions quickly.

Step 1: Understanding the Question:


This question asks for the standard keyboard shortcut keys used in Microsoft Word (and most standard operating systems) to perform the ``Cut'' and ``Undo'' operations.

We need to evaluate the shortcut key combinations presented in each option.



Step 2: Detailed Explanation:


Let us define the functions of the common shortcut keys in word processors:

Ctrl + C: Used to Copy selected text or elements to the clipboard.

Ctrl + V: Used to Paste copied or cut elements from the clipboard.

Ctrl + X: Used to Cut selected text or elements, removing them from their original location and copying them to the clipboard.

Ctrl + Z: Used to Undo the last action performed by the user.

Ctrl + K: Used to insert a Hyperlink.

Ctrl + P: Used to open the Print dialog box.

Based on these definitions:

The ``Cut'' operation is initiated using Ctrl + X.

The ``Undo'' operation is initiated using Ctrl + Z.

This exact combination is represented in Option (C).



Step 3: Final Answer:

The correct option is (C).
Quick Tip: An easy way to remember standard operations is their physical layout on the QWERTY keyboard: 'Z' is Undo, 'X' looks like a pair of scissors (Cut), 'C' is Copy, and 'V' is adjacent to 'C' (Paste).

Step 1: Understanding the Question:


This question requires us to compare different types of computer memory based on their access speeds (the time it takes for the CPU to retrieve data from them).

We need to arrange the memory types according to the standard computer memory hierarchy.



Step 2: Detailed Explanation:


In computer architecture, memory is organized in a hierarchy where speed, cost, and physical proximity to the CPU core are balanced:

1. CPU Registers: These are extremely small, high-speed storage locations located directly inside the CPU's Arithmetic Logic Unit (ALU) and Control Unit. Registers hold the immediate instructions and data being processed by the CPU. They have an access time of less than 1 nanosecond (sub-nanosecond range), making them the fastest memory.

2. Cache Memory: Located on or very close to the CPU chip, cache is made of Static RAM (SRAM). It stores frequently used data to speed up processing but is slower than registers. Access time is typically 1 to 10 nanoseconds.

3. Main Memory (RAM): Made of Dynamic RAM (DRAM), main memory holds the operating system and active applications. It is located further from the CPU and has an access time of 10 to 50 nanoseconds.

4. Secondary Memory (SSD/HDD): Used for permanent storage, it is located furthest from the CPU and has access times ranging from microseconds (SSDs) to milliseconds (HDDs).

Comparing these access times, CPU Registers are the fastest among all memory components.

Thus, Option (B) is the correct choice.



Step 3: Final Answer:

The correct option is (B).
Quick Tip: In the memory hierarchy, as you move closer to the CPU processing core, the storage capacity decreases, the cost per bit increases, and the access speed increases dramatically.

Step 1: Understanding the Question:


The goal of this question is to identify which device among the options is not an input device.

We need to classify each device based on whether it sends data to the computer (input) or receives/displays data from the computer (output).



Step 2: Detailed Explanation:


Let us analyze each device listed in the options:

A. Trackball: A trackball is a pointing device consisting of a ball held by a socket containing sensors to detect a rotation of the ball. It is used to move the cursor on the screen and is a clear example of an input device.

B. Light Pen: A light pen is a light-sensitive pointing input device, shaped like a pen, used in conjunction with a computer's CRT monitor. It allows the user to point to displayed objects or draw on the screen, acting as an input device.

C. Scanner: A scanner is a device that optically scans images, printed text, handwriting, or an object, and converts it to a digital image to send to the computer. Hence, it is an input device.

D. Plotter: A plotter is a specialized hardware device used to print vector graphics. Unlike standard printers, it uses pens to draw continuous, high-precision lines on large sheets of paper. Because it presents processed information from the computer to the user, it is an output device.

Since the Plotter is an output device, it is not an input device.

This matches Option (D).



Step 3: Final Answer:

The correct option is (D).
Quick Tip: Any device that generates a hard copy or soft copy of digital data (like printers, monitors, and plotters) is classified as an output device.

Step 1: Understanding the Question:


This question requires us to determine the equivalent value of 1 Petabyte (PB) in terms of bytes, expressed as a power of 2.

We need to refer to standard binary memory measurement units.



Step 2: Detailed Explanation:


In computer storage systems, units of data are measured using powers of 2. Let us look at the progression from the basic unit:

1 Kilobyte (KB) = \(1024\) Bytes = \(2^{10}\) Bytes

1 Megabyte (MB) = \(1024\) Kilobytes = \(2^{20}\) Bytes

1 Gigabyte (GB) = \(1024\) Megabytes = \(2^{30}\) Bytes

1 Terabyte (TB) = \(1024\) Gigabytes = \(2^{40}\) Bytes

1 Petabyte (PB) = \(1024\) Terabytes = \(2^{50}\) Bytes

Let us analyze the given options based on this hierarchy:

Option (A) \(2^{40}\) Bytes is equal to 1 Terabyte (TB).

Option (B) \(2^{50}\) Bytes is equal to 1 Petabyte (PB).

Option (C) \(2^{30}\) Bytes is equal to 1 Gigabyte (GB).

Thus, 1 Petabyte is mathematically equivalent to \(2^{50}\) Bytes.

This corresponds to Option (B).



Step 3: Final Answer:

The correct option is (B).
Quick Tip: Remember the order of prefixes: Kilo (K), Mega (M), Giga (G), Tera (T), Peta (P) (mnemonic: King Malcolm Gave The Present). Each step increases the exponent of base 2 by exactly 10.

Step 1: Understanding the Question:


The question asks for the correct classification of the Internet among different types of computer networks.

We need to define and compare Personal Area Networks (PAN), Local Area Networks (LAN), Metropolitan Area Networks (MAN), and Wide Area Networks (WAN).



Step 2: Detailed Explanation:


Let us analyze each network type based on geographical span:

A. Personal Area Network (PAN): A network organized around an individual person within a tiny range (typically under 10 meters, e.g., Bluetooth connections between a phone and a smartwatch).

B. Local Area Network (LAN): A network that connects computers within a limited physical area such as a residence, school, laboratory, or office building.

C. Metropolitan Area Network (MAN): A larger network that spans a physical area larger than a LAN but smaller than a WAN, typically covering an entire city or a university campus (e.g., a city cable television network).

D. Wide Area Network (WAN): A telecommunications network that extends over a large geographical area, bridging cities, states, or even continents.

The Internet is a massive, global system of interconnected computer networks that spans the entire planet, facilitating communication across countries and oceans. Hence, the Internet is the largest and most well-known example of a Wide Area Network (WAN).

This matches Option (D).



Step 3: Final Answer:

The correct option is (D).
Quick Tip: Remember that the prefix 'Wide' in Wide Area Network refers to its ability to connect devices across regional, national, or global boundaries, with the Internet being the ultimate global WAN.

Step 1: Understanding the Question:


This question asks for the correct expansion of the standard internet abbreviation ``URL.''

We need to identify the exact terminology defined in computer networking standards.



Step 2: Detailed Explanation:


A URL is the address of a unique resource on the World Wide Web. It was formulated in 1994 by Tim Berners-Lee as part of the internet working specifications.

The abbreviation URL stands for Uniform Resource Locator.

Let us look at its key components:

1. Protocol: Specifies how data is transferred (e.g., HTTP or HTTPS).

2. Host/Domain name: Points to the target server hosting the resource (e.g., www.example.com).

3. Path: Specifies the exact location of a directory or file on that server (e.g., /folder/page.html).

Let us evaluate the options:

Option (A) ``Universal Resource locator'' is a common misconception, but it is incorrect according to official networking standards.

Option (C) and (D) are completely incorrect fabrications.

Therefore, Uniform Resource Locator is the correct full form, represented by Option (B).



Step 3: Final Answer:

The correct option is (B).
Quick Tip: Be careful with the first word: it is 'Uniform', not 'Universal'. It is uniform because it uses a standardized format to access any resource regardless of the protocol.

Step 1: Understanding the Question:


This question consists of an Assertion and a Reason regarding malicious computer programs, commonly referred to as computer viruses or malware.

We need to evaluate if both statements are factually correct and then determine if the Reason explains why the Assertion is true.



Step 2: Detailed Explanation:


Evaluating Assertion (A): A computer virus is a type of malicious software (malware) designed to replicate itself by attaching to other programs, executing unauthorized commands, deleting files, consuming system resources, or causing security breaches. Thus, Assertion (A) is factually correct.

Evaluating Reason (R): The list contains famous examples of malware and network threats:

\textit{ILOVEYOU and \textit{MyDoom are famous self-replicating worms.

\textit{CryptoLocker is a notorious ransomware program.

\textit{Slammer (SQL Slammer) is a fast-spreading computer worm.

Although technically classified under specific categories like ransomware or worms, in general computer literacy terms, they are commonly discussed as viruses or malicious codes. Thus, Reason (R) is factually correct.

Causal Connection: The Reason lists specific examples of malicious software. However, listing examples of viruses does not explain the functional definition or mechanism of what a virus is (Assertion). Listing examples describes \textit{which programs exist, not \textit{why a virus is defined as code designed to hamper resources.

Thus, both (A) and (R) are correct, but (R) is not the correct explanation of (A). This corresponds to Option (B).



Step 3: Final Answer:

The correct option is (B).
Quick Tip: To check for a causal connection, read the statements with 'because' in between: ``A virus is created to perform malicious activities *because* some well-known viruses include CryptoLocker...'' Since this sounds illogical, the Reason is not the correct explanation.

Step 1: Understanding the Question:


This question consists of an Assertion and a Reason evaluating the volatile/non-volatile characteristics of computer memory, specifically Read-Only Memory (ROM).

We need to determine the truth value of both statements based on the principles of computer storage.



Step 2: Detailed Explanation:


Evaluating Assertion (A): Read-Only Memory (ROM) is a type of electronic storage that contains permanent or semi-permanent data. Unlike Random Access Memory (RAM), it is non-volatile, meaning it retains its stored data even when the computer system is powered off or restarted. ROM typically stores the firmware (BIOS/UEFI) required to boot up the system. Thus, Assertion (A) is correct.

Evaluating Reason (R): By definition, non-volatile storage refers to memory that does not lose its data when power is turned off or interrupted. Hard drives, solid-state drives, flash drives, and ROM are all non-volatile. The memory type that loses its data during power loss is volatile memory (such as RAM). Therefore, the statement ``A non-volatile storage unit losses data...'' is factually incorrect.

Since Assertion (A) is true and Reason (R) is false, the correct choice is Option (C).



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Remember the distinction clearly: Volatile memory (like RAM) requires continuous power to maintain data; Non-volatile memory (like ROM, Flash, or Hard Disks) retains data permanently without requiring a power supply.

Step 1: Understanding the Question:


This question requires us to arrange four classes of computers in decreasing order (from highest to lowest) based on their cost, processing speed, and physical size.

We need to compare the general characteristics of Supercomputers, Mainframes, Minicomputers, and Microcomputers.



Step 2: Detailed Explanation:


Let us analyze each class of computer based on cost, speed, and size:

1. Supercomputers (B): These are the fastest, most powerful, largest, and most expensive computers in the world. They consist of thousands of processors working in parallel and are used for complex scientific tasks like weather forecasting and nuclear research. This is at the top of the hierarchy.

2. Mainframe Computers (C): These are highly powerful, large, and expensive multi-user systems. They are optimized for processing massive amounts of transactions and database queries simultaneously, and are widely used by large corporations, banks, and government agencies. They are smaller and less expensive than supercomputers, but larger than minicomputers.

3. Minicomputers (A): Also known as mid-range servers, these are smaller and less expensive than mainframes but possess greater processing power than personal computers. They typically support tens to hundreds of users simultaneously.

4. Microcomputers (D): These are the smallest, least expensive, and slowest among the four categories. Powered by a single microprocessor, they are designed for single-user tasks (e.g., desktops, laptops, tablets, and smartphones).

Arranging them in decreasing order (highest/largest to lowest/smallest):

Supercomputers (B) \(\rightarrow\) Mainframe computers (C) \(\rightarrow\) Minicomputers (A) \(\rightarrow\) Microcomputers (D).

This matches the sequence: B, C, A, D.

This corresponds to Option (C).



Step 3: Final Answer:

The correct option is (C).
Quick Tip: Supercomputers are always the most powerful and expensive (highest in the hierarchy), while microcomputers (our everyday personal laptops/desktops) are always at the bottom, making it easy to identify the start (B) and end (D).

Step 1: Understanding the Question:


This question requires us to arrange the primary operations of a CPU's execution cycle (also known as the Instruction Cycle or Machine Cycle) in their correct chronological order.

We need to analyze the steps involved when a processor executes a computer program instruction.



Step 2: Detailed Explanation:


The CPU instruction cycle represents the sequence of operations that the processor performs to execute a single program instruction. It consists of the following standard sequential steps:

1. Fetch (B): The Control Unit retrieves the instruction's binary code from the computer's main memory (RAM) using the address stored in the Program Counter (PC). This is the first step.

2. Decode (A): Once retrieved, the instruction is loaded into the Instruction Register. The Control Unit interprets (decodes) this binary code to understand what operation is to be performed (addition, subtraction, jump, etc.) and identifies any required operands. This is the second step.

3. Execute (D): The CPU's Arithmetic Logic Unit (ALU) or other processing units perform the actual mathematical, logical, or data-movement operation specified by the decoded instruction. This is the third step.

4. Write Back (C): The final result generated during the execution phase is written back into a CPU register or the main memory for future use. This is the fourth step.

Therefore, the correct execution sequence is: Fetch (B) \(\rightarrow\) Decode (A) \(\rightarrow\) Execute (D) \(\rightarrow\) Write Back (C).

This corresponds to the sequence: B, A, D, C.

This matches Option (D).



Step 3: Final Answer:

The correct option is (D).
Quick Tip: Think of the CPU cycle like reading a recipe: first you 'fetch' the recipe, then you read and 'decode' what it means, then you cook or 'execute' the instructions, and finally you plate or 'write back' the finished dish.

Step 1: Understanding the Question:

The question asks us to identify the correct statements regarding the core concepts, characteristics, and examples of an Operating System (OS).


Step 2: Detailed Explanation:

Let us evaluate each of the given statements:


Statement A: An operating system is system software that acts as an intermediary or interface between a user and the computer hardware. Thus, this statement is correct.

Statement B: By providing an abstract, user-friendly interface (either Graphical User Interface - GUI or Command Line Interface - CLI) and hiding complex hardware processes, the operating system makes a computer system much easier to use. Thus, this statement is correct.

Statement C: One of the primary jobs of an operating system is resource management, which includes managing memory, processors (CPU), devices (I/O), and files. Therefore, stating that it does not manage resources is incorrect.

Statement D: Computer software is broadly divided into System Software and Application Software. An operating system is system software, not application software. Therefore, this statement is incorrect.

Statement E: Linux, MS DOS, Microsoft Windows, and Solaris are indeed classic, well-known operating systems. Thus, this statement is correct.



Step 3: Final Answer:

Based on our analysis, only statements A, B, and E are true. This corresponds to option (B).
Quick Tip: Recall that an Operating System is the master program (System Software) that controls hardware.
Eliminate any option containing Statement C or D instantly to arrive at the correct option.

Step 1: Understanding the Question:

The goal is to differentiate web browsers from other web-related tools like search engines from the given list.


Step 2: Detailed Explanation:

Let us analyze each software application in the list:


Mozilla Firefox (A): A free and open-source web browser developed by the Mozilla Foundation. Thus, it is a web browser.

Google Chrome (B): A proprietary web browser developed by Google. Thus, it is a web browser.

Microsoft Bing (C): A search engine developed and operated by Microsoft. It is a service to query the web, not a browser software application used to view websites. Thus, it is not a web browser.

Apple Safari (D): A graphical web browser developed by Apple and pre-installed on Apple devices. Thus, it is a web browser.

Opera (E): A multi-platform web browser developed by its namesake company, Opera. Thus, it is a web browser.



Step 3: Final Answer:

Therefore, A, B, D, and E are web browsers, which means option (D) is the correct answer.
Quick Tip: Always distinguish between a browser (the local application on your machine, e.g., Chrome, Safari) and a search engine (the online database service, e.g., Google, Bing, DuckDuckGo).

Step 1: Understanding the Question:

The problem requires matching standard system utility and translation programs with their respective descriptions.


Step 2: Detailed Explanation:

Let us study each of the system programs listed in List-I:


Compiler (A): A compiler translates high-level source code into low-level machine code all at once before execution. This matches description III.

Interpreter (B): An interpreter translates high-level code line-by-line, executing each instruction immediately after translating it. This matches description I.

Linker (C): A linker takes the output of a compiler (object code) and links it with other pre-compiled systems or library files to create a final executable file (such as a `.exe` file). This matches description IV.

Loader (D): A loader brings the executable file from secondary storage (hard disk, SSD) and places it into primary memory (RAM) so that the CPU can execute it. This matches description II.



Step 3: Final Answer:

The matching sequence is A-III, B-I, C-IV, D-II, which corresponds to option (B).
Quick Tip: Remember: \textbf{Compiler} translates \textbf{all at once}, whereas \textbf{Interpreter} translates \textbf{line-by-line}.
This difference is highly tested and immediately narrows down option choices.

Step 1: Understanding the Question:

The objective is to map various network devices to their core functions in network communication.


Step 2: Detailed Explanation:

Let us match each network component with its description:


Modem (A): Short for Modulator-Demodulator. It is an hardware component that converts computer-generated digital signals into analog signals (for telephone/cable lines) and vice-versa, i.e., conversion between electrical/analog waves and digital bits. This matches with II.

Ethernet card (B): Also known as a Network Interface Card (NIC), it is an essential wired hardware network adapter used to establish a physical connection to a local area network (LAN). This matches with IV.

Repeater (C): A physical-layer device designed to regenerate weakened electrical or optical signals due to attenuation over long-distance cable runs. This matches with I.

Router (D): An intelligent network layer device that analyses packets, determines optimal paths, and forwards data packets across interconnected networks. This matches with III.



Step 3: Final Answer:

The matching is A-II, B-IV, C-I, D-III, which represents option (A).
Quick Tip: An easy way to solve device matchings:
Associate \textbf{Modem} with conversion (Modulate/Demodulate), and \textbf{Repeater} with signal regeneration.

Step 1: Understanding the Question:

The question asks us to align network security and web terms with their standard descriptions.


Step 2: Detailed Explanation:

Let us map each list element:


Trojan (A): Disguises itself as legitimate utility software to trick users. Once downloaded, it executes malicious actions. This matches IV.

Cookie (B): A small state-tracking data file generated by web servers and stored on the user's browser client. This matches III.

Spyware (C): Malicious software that secretly tracks user interactions, logs keys, and shares the compiled information with third parties. This matches II.

Firewall (D): A filter placed at network boundaries that evaluates traffic patterns against preconfigured rules to allow or block access. This matches I.



Step 3: Final Answer:

The correct matching sequence is A-IV, B-III, C-II, D-I, representing option (B).
Quick Tip: Remember: \textbf{Trojan} acts like the historical Trojan Horse (looks safe but carries danger).
\textbf{Firewall} is always the primary guard system (barrier between safe and unsafe).

Step 1: Understanding the Question:

A pipe is mathematically a cylinder. If the radius is modified while keeping the total volume constant, we need to calculate the ratio of change in its length.


Step 2: Key Formula or Approach:

The volume \(V\) of a cylinder is: \[ V = \pi r^2 L \]
where \(r\) is the radius and \(L\) is the length. Since the volume remains constant: \[ V_1 = V_2 \] \[ \pi r_1^2 L_1 = \pi r_2^2 L_2 \implies L_2 = L_1 \left( \frac{r_1}{r_2} \right)^2 \]

Step 3: Detailed Explanation:


Let the initial radius be \(r_1\) and initial length be \(L_1\).

The question uses the phrase "reduced by one fourth", which can sometimes be translated colloquially or from local papers as "reduced to one-fourth". Let us evaluate both cases to match the standard multiple-choice answer:

Case I: Radius reduced to one-fourth

If \(r_2 = \frac{1}{4} r_1\):
\[ L_2 = L_1 \left( \frac{r_1}{\frac{1}{4} r_1} \right)^2 \]
\[ L_2 = L_1 (4)^2 = 16 L_1 \]
This matches Option (D) perfectly.

Case II: Radius reduced by one-fourth

If \(r_2 = r_1 - \frac{1}{4} r_1 = \frac{3}{4} r_1\):
\[ L_2 = L_1 \left( \frac{r_1}{\frac{3}{4} r_1} \right)^2 = \frac{16}{9} L_1 \]
Since \(\frac{16}{9}\) is not among the given options, the question setter intended Case I.



Step 4: Final Answer:

The length of the pipe becomes 16 times the original length. Thus, option (D) is the correct answer.
Quick Tip: Since volume is proportional to \(r^2 \cdot L\), if the radius is divided by \(k\), the length must be multiplied by \(k^2\) to keep the product constant.
Here \(k = 4\), so the length must increase by \(4^2 = 16\) times.

Step 1: Understanding the Question:

The question asks us to compute the total accumulated amounts after 3 years for simple interest (Bank A) and compound interest (Bank B) with a principal of Rs 5000 and a rate of 5%.


Step 2: Key Formula or Approach:


Simple Interest (SI) Amount:
\[ A_{SI} = P + SI = P + \frac{P \times R \times T}{100} \]
Compound Interest (CI) Amount:
\[ A_{CI} = P \left(1 + \frac{R}{100}\right)^T \]

where \(P = 5000\), \(R = 5%\), and \(T = 3\) years.


Step 3: Detailed Explanation:


Bank A (Simple Interest Amount):

\[ A_{SI} = 5000 + \frac{5000 \times 5 \times 3}{100} \]
\[ A_{SI} = 5000 + 750 = 5750 rupees \]
Bank B (Compound Interest Amount):

\[ A_{CI} = 5000 \left(1 + \frac{5}{100}\right)^3 \]
\[ A_{CI} = 5000 \times (1.05)^3 \]
\[ A_{CI} = 5000 \times 1.157625 = 5788.125 \approx 5788 rupees \]


Step 4: Final Answer:

The amounts are Rs 5750 and Rs 5788 respectively, which matches Option (C).
Quick Tip: For standard compounding over 3 years at 5%, the interest multiplier is \((1.05)^3 = 1.157625\).
Multiplying this directly by 5000 gives 5788, instantly eliminating other options.

Step 1: Understanding the Question:

The problem presents a situation where the total profit gained from selling 20 cricket bats is equal to the cost price of 4 cricket bats. We need to calculate this profit percentage.


Step 2: Key Formula or Approach:

The profit percentage based on cost price is calculated as: \[ Profit % = \frac{Profit}{Total Cost Price} \times 100 \]

Step 3: Detailed Explanation:


Let the Cost Price (CP) of 1 cricket bat be \(x\).

The total Cost Price of 20 cricket bats is:
\[ Total CP = 20x \]
According to the problem statement, the profit is equal to the cost price of 4 bats:
\[ Profit = 4x \]
Now, we calculate the profit percentage:
\[ Profit % = \frac{Profit}{Total CP} \times 100 \]
\[ Profit % = \frac{4x}{20x} \times 100 = \frac{1}{5} \times 100 = 20% \]


Step 4: Final Answer:

The profit percentage is 20%, matching Option (A).
Quick Tip: When profit is given as the Cost Price of \(N\) items on selling \(M\) items:
\[ Profit % = \frac{N}{M} \times 100 \] Here, \(\frac{4}{20} \times 100 = 20%\). Simple and rapid!

Step 1: Understanding the Question:

We are given the HCF and LCM of two positive integers along with the difference between them. We must find the sum of these two integers.


Step 2: Key Formula or Approach:

Let the two numbers be \(a\) and \(b\) (with \(a > b\)).

The product of two numbers is equal to the product of their HCF and LCM:
\[ a \times b = HCF \times LCM \]
We are given:
\[ a - b = 12 \]
We can relate the sum and difference of two numbers using the algebraic identity:
\[ (a + b)^2 = (a - b)^2 + 4ab \]


Step 3: Detailed Explanation:


Calculate the product \(ab\):
\[ ab = 12 \times 360 = 4320 \]
Substitute the values into our identity:
\[ (a + b)^2 = (12)^2 + 4(4320) \]
\[ (a + b)^2 = 144 + 17280 \]
\[ (a + b)^2 = 17424 \]
Calculate the square root to find \((a + b)\):
\[ a + b = \sqrt{17424} \]
Let us verify \(132\):
\[ 132 \times 132 = 17424 \]
Thus, \(a + b = 132\).

Alternative Co-prime Method:

Since HCF = 12, let the numbers be \(12x\) and \(12y\), where \(x\) and \(y\) are co-primes.
\[ LCM = 12xy = 360 \implies xy = 30 \]
The difference is:
\[ 12x - 12y = 12(x-y) = 12 \implies x-y = 1 \]
We find two numbers that multiply to 30 and differ by 1. These are 6 and 5.
So, the original numbers are \(12(6) = 72\) and \(12(5) = 60\).
Their sum is \(72 + 60 = 132\).


Step 4: Final Answer:

The sum of the two numbers is 132, matching Option (A).
Quick Tip: Using the co-prime factor method: \(xy = 30\) and \(x-y = 1 \implies 6\) and \(5\).
The sum of the numbers is \(HCF \times (x+y) = 12 \times (6+5) = 12 \times 11 = 132\).
This is much faster than computing large square roots!

Step 1: Understanding the Question:

The question asks us to identify the individual speeds of two trains given the time taken to cross each other in opposite and same-direction motions.


Step 2: Key Formula or Approach:

Let the speeds of the trains be \(v_1\) and \(v_2\) (where \(v_1 > v_2\)), and their combined length be \(D\).

When moving in opposite directions, the relative speed is \((v_1 + v_2)\):
\[ D = (v_1 + v_2) \times 15 \]
When moving in the same direction, the relative speed is \((v_1 - v_2)\):
\[ D = (v_1 - v_2) \times 45 \]


Step 3: Detailed Explanation:


Since the distance covered in both cases is the sum of the lengths of the two trains (\(D\)), we can equate both equations:
\[ 15(v_1 + v_2) = 45(v_1 - v_2) \]
Simplify the expression:
\[ v_1 + v_2 = 3(v_1 - v_2) \]
\[ v_1 + v_2 = 3v_1 - 3v_2 \]
\[ 4v_2 = 2v_1 \implies v_1 = 2v_2 \]
The speed of one train must be exactly twice the speed of the other train. Let us test the given options for this 2:1 ratio:

Option (A): Speeds 20 and 45 (ratio = 2.25)
Option (B): Speeds 15 and 45 (ratio = 3.0)
Option (C): Speeds 30 and 60 (ratio = 2.0)
Option (D): Speeds 30 and 50 (ratio = 1.67)

Only the speeds in Option (C) satisfy the derived mathematical ratio.


Step 4: Final Answer:

The possible speeds of the trains are 30 m/s and 60 m/s, matching Option (C).
Quick Tip: Using relative speed ratio logic:
\[ \frac{v_1 + v_2}{v_1 - v_2} = \frac{45}{15} = \frac{3}{1} \] Applying componendo and dividendo:
\[ \frac{v_1}{v_2} = \frac{3+1}{3-1} = \frac{4}{2} = \frac{2}{1} \] Quickly check options to find which values have a 2:1 ratio.

Step 1: Understanding the Question:

The objective is to find the monthly salary of a person given his structured monthly average expenditure across different months of a year and his annual savings.


Step 2: Key Formula or Approach:


Total Annual Income = Total Annual Expenditure + Total Annual Savings
Monthly Salary = \(\frac{Total Annual Income}{12}\)


Step 3: Detailed Explanation:


First, calculate the expenditure from January to July (which spans 7 months):
\[ Expenditure_{1} = 7 months \times 3500 rupees/month = 24,500 rupees \]
Next, calculate the expenditure from August to December (which spans 5 months):
\[ Expenditure_{2} = 5 months \times 3800 rupees/month = 19,000 rupees \]
Calculate the total expenditure for the entire year:
\[ Total Annual Expenditure = 24,500 + 19,000 = 43,500 rupees \]
Add the total annual savings to get the total income of the year:
\[ Total Annual Income = 43,500 + 9,000 = 52,500 rupees \]
Calculate the monthly salary by dividing the total income by 12:
\[ Monthly Salary = \frac{52,500}{12} = 4,375 rupees \]


Step 4: Final Answer:

The monthly salary of the man is Rs 4375, which matches Option (D).
Quick Tip: Annual calculations help avoid decimal confusion.
Totaling \(24500 + 19000 + 9000 = 52500\).
Dividing by 12: \(52500 \div 12 = 4375\). Always perform calculation-checks to verify.

Step 1: Understanding the Question:

The task is to compute the value of the given arithmetic expression using the standard mathematical rules of precedence (BODMAS).


Step 2: Key Formula or Approach:

The BODMAS rule dictates the order of operations:

Brackets
Orders/Exponents
Division
Multiplication
Addition
Subtraction


Step 3: Detailed Explanation:

Let us simplify the expression step-by-step:

The given expression is:
\[ 83 + 238 \div 17 - 64 \]
Step 1: Division

Evaluate \(238 \div 17\):

We know \(17 \times 10 = 170\).

Subtracting 170 from 238 gives 68.

We know \(17 \times 4 = 68\).

So, \(238 \div 17 = 10 + 4 = 14\).

Substituting this back into the expression:
\[ 83 + 14 - 64 \]
Step 2: Addition

Evaluate \(83 + 14\):
\[ 83 + 14 = 97 \]
The expression is now:
\[ 97 - 64 \]
Step 3: Subtraction

Evaluate \(97 - 64\):
\[ 97 - 64 = 33 \]


Step 4: Final Answer:

The final evaluated result is 33, matching Option (B).
Quick Tip: To divide 238 by 17 quickly:
Note that \(17 \times 20 = 340\), which is \(102\) more than \(238\). Since \(17 \times 6 = 102\), the quotient is \(20 - 6 = 14\).

Step 1: Understanding the Question:

This problem asks us to determine the truth values of the Assertion (concerning the angle of a clock's hands at 3:10) and the Reason (an algebraic representation of the angle), and establish if the Reason logically explains the Assertion.


Step 2: Detailed Explanation:

Let us analyze both statements:

Verification of Assertion (A):

At 3:10 PM, the hour hand has moved past 3, and the minute hand is exactly on 2.
We can calculate the angle using the standard clock formula:
\[ \theta = \left| 30H - \frac{11}{2}M \right| \]
where \(H = 3\) and \(M = 10\):
\[ \theta = \left| 30(3) - 5.5(10) \right| = |90 - 55| = 35^\circ \]
Thus, Assertion (A) is correct.
Verification of Reason (R):

The angular position of the hour hand from the 12 o'clock mark at \(t\) hours and \(x\) minutes is:
\[ Hour Position = (30t + 0.5x)^\circ \]
The angular position of the minute hand is:
\[ Minute Position = (6x)^\circ \]
If the hour hand is ahead of the minute hand, the angle is the difference between these positions:
\[ \theta = 30t + 0.5x - 6x = 30t - 5.5x \]
Now, let us simplify the formula given in Reason (R):
\[ 30\left(t - \frac{x}{5}\right) + \frac{x}{2} = 30t - \frac{30x}{5} + 0.5x \]
\[ = 30t - 6x + 0.5x = 30t - 5.5x \]
Both expressions are mathematically identical. Thus, the formula in Reason (R) is correct.
Testing (A) with (R):

Substitute \(t = 3\) and \(x = 10\) into Reason (R)'s formula:
\[ Angle = 30\left(3 - \frac{10}{5}\right) + \frac{10}{2} = 30(3 - 2) + 5 = 35^\circ \]
Since this general formula yields the specific result mentioned in Assertion (A), the Reason is the correct explanation of the Assertion.


Step 3: Final Answer:

Both (A) and (R) are correct, and (R) is the correct explanation of (A), which corresponds to option (A).
Quick Tip: An easy way to verify Reason (R):
Expand the expression: \(30(t - x/5) + x/2 = 30t - 6x + 0.5x = 30t - 5.5x\).
This is exactly the standard form of the clock angle equation when the hour hand is ahead, ensuring R is mathematically correct.

Step 1: Understanding the Question:

The goal is to verify if the annual compound growth calculation of a city's population in Assertion (A) is correct and whether the standard compound interest model in Reason (R) is the correct mathematical justification.


Step 2: Key Formula or Approach:

The formula for compounding population growth annually is: \[ A = P \left(1 + \frac{R}{100}\right)^n \]
where \(P\) is the initial population, \(R\) is the annual rate of increase, and \(n\) is the number of years.


Step 3: Detailed Explanation:


Verification of Assertion (A):

Given initial population \(P = 2,00,000\), growth rate \(R = 10%\), and time period \(n = 3\) years.
Apply the growth formula:
\[ A = 200000 \left(1 + \frac{10}{100}\right)^3 \]
\[ A = 200000 \times (1.1)^3 \]
Since \((1.1)^3 = 1.331\):
\[ A = 200000 \times 1.331 = 2,66,200 \]
Therefore, Assertion (A) is correct.
Verification of Reason (R):

The reason states the general mathematical formula for geometric compound growth. This formula is indeed correct and represents the exact model used to compute the population in Assertion (A).
Thus, Reason (R) is the correct explanation of Assertion (A).


Step 4: Final Answer:

Both statements are correct, and (R) is the correct explanation of (A). This corresponds to option (A).
Quick Tip: For any compounding scenario with a rate of 10% over 3 years:
The net percentage increase is \(33.1%\).
\(2,00,000 \times 133.1% = 2,66,200\). Compounding shortcuts save valuable time in exams!

Step 1: Understanding the Question:

We are given five ratios and must arrange them in ascending order (from smallest to largest).


Step 2: Key Formula or Approach:

The easiest and most accurate method to compare ratios is to convert each of them into its equivalent decimal representation.


Step 3: Detailed Explanation:

Let us calculate the decimal value of each ratio:

A. 1:3
\[ \frac{1}{3} \approx 0.3333 \]
B. 1:4
\[ \frac{1}{4} = 0.2500 \]
C. 2:7
\[ \frac{2}{7} \approx 0.2857 \]
D. 3:5
\[ \frac{3}{5} = 0.6000 \]
E. 5:8
\[ \frac{5}{8} = 0.6250 \]

Comparing these decimal values: \[ 0.2500 < 0.2857 < 0.3333 < 0.6000 < 0.6250 \]
Replacing the decimals with their corresponding letters: \[ B < C < A < D < E \]

Step 4: Final Answer:

The ascending order of the ratios is B \(<\) C \(<\) A \(<\) D \(<\) E, which corresponds to option (C).
Quick Tip: Memorize the basic fraction-to-decimal conversions for competitive exams:
\(\frac{1}{4} = 0.25\), \(\frac{2}{7} \approx 0.28\), \(\frac{1}{3} \approx 0.33\), \(\frac{3}{5} = 0.6\), and \(\frac{5}{8} = 0.625\).
This allows you to sort ratios in under 10 seconds!

Step 1: Understanding the Question:

The problem requires us to sort five mathematical fractions in descending order (from largest to smallest).


Step 2: Key Formula or Approach:

Converting each fraction into its decimal value is the most efficient technique to avoid complex cross-multiplications.


Step 3: Detailed Explanation:

Let us convert each fraction to its decimal equivalent:

A. 3/13
\[ \frac{3}{13} \approx 0.2308 \]
B. 4/17
\[ \frac{4}{17} \approx 0.2353 \]
C. 5/19
\[ \frac{5}{19} \approx 0.2632 \]
D. 7/15
\[ \frac{7}{15} \approx 0.4667 \]
E. 2/5
\[ \frac{2}{5} = 0.4000 \]

Comparing these decimal values in descending order (largest to smallest): \[ 0.4667 > 0.4000 > 0.2632 > 0.2353 > 0.2308 \]
Substituting back the letters: \[ D > E > C > B > A \]

Step 4: Final Answer:

The descending order of the proportions is D, E, C, B, A, which matches option (A).
Quick Tip: Notice that \(\frac{7}{15}\) is nearly \(\frac{1}{2}\) (\(0.5\)), and \(\frac{2}{5} = 0.4\). Both are much larger than the other three fractions, which are all less than \(0.3\) since their denominators are more than three times their numerators. This immediately isolates \(D\) and \(E\) at the top.

Step 1: Understanding the Question:

The goal is to evaluate five geometric area calculations and determine which of them are correct.


Step 2: Key Formula or Approach:

Let us use the standard geometric formulas for area:

\(Area of a triangle = \frac{1}{2} \times base \times height\)
\(Area of a square = side^2\)
\(Area of a rectangle = length \times breadth\)
\(Area of a circle = \pi r^2\)


Step 3: Detailed Explanation:

Let us compute the area for each scenario:

Statement A:
Base = 10 cm, perpendicular (height) = 7 cm.
\[ Area = \frac{1}{2} \times 10 \times 7 = 35 cm^2 \]
This calculation is correct.
Statement B:
Side = 12 cm.
\[ Area = 12^2 = 144 cm^2 \neq 140 cm^2 \]
This calculation is incorrect.
Statement C:
Sides = 11 cm and 70 cm.
\[ Area = 11 \times 70 = 770 cm^2 \]
This calculation is correct.
Statement D:
Diameter = 28 cm \(\implies\) Radius (\(r\)) = 14 cm.
\[ Area = \pi r^2 = \frac{22}{7} \times 14 \times 14 = 22 \times 2 \times 14 = 616 cm^2 \neq 606 cm^2 \]
This calculation is incorrect.
Statement E:
Radius = 7 cm.
\[ Area = \pi r^2 = \frac{22}{7} \times 7 \times 7 = 154 cm^2 \]
This calculation is correct.


Step 4: Final Answer:

Only calculations A, C, and E are correct. This corresponds to option (D).
Quick Tip: An area of a circle with radius 7 is always 154. This is a very standard value in mensuration questions.
Since E is correct and B is incorrect (\(12^2 = 144\)), we can easily eliminate options (A), (B), and (C).

Step 1: Understanding the Question:

The question asks us to identify the correct statements among different classifications of sets (null, singleton, finite, infinite, and equal sets).


Step 2: Detailed Explanation:

Let us analyze the given sets carefully. We must evaluate them based on the standard domain specified in the question:

Analyzing under Real Numbers (\(\mathbf{R}\)):

A: There are infinitely many real numbers between 2 and 3 (e.g., 2.1, 2.01, 2.5). Thus, the set is not a null set (empty set). This statement is false.

B: There are infinitely many real numbers between 2 and 4. It is not a singleton set (a set containing exactly one element). Thus, this statement is false.

C: There are infinitely many real numbers between 1 and 9. Thus, it is an infinite set. This statement is true.

D: Since the set is infinite, it cannot be finite. This statement is false.

E: Two sets are equal if they contain exactly the same elements. The order of elements does not matter. Both set A and set B have the elements \(\{a, b, c, d, e\}\). Thus, they are equal sets. This statement is true.


If \(\mathbf{R}\) is strictly used, then statements C and E are correct. However, "C and E" is not available in the given options.
Analyzing under Integers (\(\mathbf{Z}\)) (Possible Typo in Exam Question):

Often in competitive exams, \(\mathbf{R}\) is printed by mistake instead of \(\mathbf{Z}\) (Integers) or \(\mathbf{N}\) (Natural Numbers). Let us evaluate if \(x \in \mathbf{Z}\):

A: There are no integers strictly between 2 and 3. Thus, the set is empty (null set). (True)

B: The only integer strictly between 2 and 4 is 3. Thus, the set is \(\{3\}\), which is a singleton set. (True)

C: The integers between 1 and 9 are \(\{2, 3, 4, 5, 6, 7, 8\}\). This is a finite set, not infinite. (False)

D: Since the set of integers is finite, this statement would be true.

E: Set E is always true because the elements are identical. (True)


If the domain was intended to be integers, then statements A, B, D, and E are true. Looking at the options, option (D) is "B and E only", which are both true statements.


Step 3: Final Answer:

Under the most consistent set interpretation, statements B and E are selected, making option (D) the correct choice.
Quick Tip: The order of elements in a set is completely irrelevant. Thus, \(\{a, b, c, d, e\}\) is always identical to \(\{c, d, a, e, b\}\), making Statement E mathematically true in all contexts.

Step 1: Understanding the Question:

The task is to match standard geometric angle names with their defining degree ranges.


Step 2: Detailed Explanation:

Let us review the definitions of each angle listed in List-I:

Obtuse Angle (A): An angle that is strictly greater than \(90^\circ\) and strictly less than \(180^\circ\). This matches description III.

Straight Angle (B): An angle of exactly \(180^\circ\) which forms a straight line. This matches description I.

Reflex Angle (C): An angle that is greater than \(180^\circ\) but less than \(360^\circ\). This matches description IV.

Complete Angle (D): An angle representing one full revolution, which is exactly \(360^\circ\). This matches description II.



Step 3: Final Answer:

The matching sequence is A-III, B-I, C-IV, D-II, which corresponds to option (B).
Quick Tip: Remember:
Straight angle = Straight line (\(180^\circ\)).
Complete angle = Full circle (\(360^\circ\)).
Using these basic definitions can help you solve the matching instantly!

Step 1: Understanding the Question:

The problem requires us to match classification categories of triangles (based on sides and angles) to their corresponding dimensional or angle properties.


Step 2: Detailed Explanation:

Let us analyze each type of triangle listed in List-I:

Equilateral Triangle (A): A triangle where all three sides are equal. Description III states "each side being 5 cm", which means all sides are equal. Thus, A matches III.

Isosceles Triangle (B): A triangle where at least two sides are equal. Description IV defines a triangle with sides "4 cm, 6 cm and 6 cm", showing two equal sides. Thus, B matches IV.

Acute Angle Triangle (C): A triangle where all three interior angles are strictly less than \(90^\circ\). Description I gives angles of \(70^\circ\), \(60^\circ\), and \(50^\circ\), all of which are acute. Thus, C matches I.

Obtuse Angle Triangle (D): A triangle with exactly one angle greater than \(90^\circ\). Description II has an angle of \(130^\circ\), which is obtuse. Thus, D matches II.



Step 3: Final Answer:

The matching sequence is A-III, B-IV, C-I, D-II, which corresponds to option (D).
Quick Tip: Prefix definitions:
"Equi-" means equal (Equilateral \(\rightarrow\) equal sides).
"Iso-" means same/two same (Isosceles \(\rightarrow\) two equal sides).
"Acute" means sharp/small (\(< 90^\circ\)).

Step 1: Understanding the Question:

The question requires us to arrange the given list of words in a logical, biological, and taxonomical hierarchical order, moving either from the most general classification to the most specific classification or vice versa.


Step 2: Detailed Explanation:

Let us analyze the biological classification of the words provided:


Animal (D): This represents the broadest kingdom (Animalia) in the list.

Vertebrates (B): This is a subphylum of the animal kingdom consisting of animals with a backbone.

Mammals (A): This is a specific class within the vertebrates that possess mammary glands.

Feline (E): This is a specific biological family (Felidae) of carnivorous mammals, commonly referred to as cats.

Cat (C): This is the most specific domestic species belonging to the feline family.


Arranging them from the broadest taxonomic group to the most specific species gives the sequence:
\[ Animal (D) \rightarrow Vertebrates (B) \rightarrow Mammals (A) \rightarrow Feline (E) \rightarrow Cat (C) \]
Thus, the correct sequence of letters is D, B, A, E, C.


Step 3: Final Answer:

The logical and taxonomical sequence is D, B, A, E, C, which corresponds to option (B).
Quick Tip: When dealing with biological terms, look for the most general taxonomic category first (like Kingdom: Animal) and the most specific species last (like Cat).
This immediately reveals the start (D) and end (C) of the sequence, making it easy to identify the correct option.

Step 1: Understanding the Question:

The problem presents a coded blood relation expression: \(P @ Q
) R \# S\(. We need to decode the relations step-by-step to find how \)P\( is related to \)S\(.
\textbf{Step 2: Key Formula or Approach:}
We decode the expression from left to right using the defined codes: \)X \# Y \implies X\( is the husband of \)Y\( (which means \)X\( is male and \)Y\( is female).
\)X \text{ @ Y \implies X\( is the sister of \)Y\( (which means \)X\( is female).
\)X \text{
( Y \implies X\) is the son of \(Y\).



Step 3: Detailed Explanation:

Let us decode each part of the expression \(P \text{ @ Q
) R \# S\(:
\textbf{Part 1:} \)P @ Q \implies P\( is the sister of \)Q\(. This indicates \)P\( is female (\)\text{gender of P = \text{Female\().
\textbf{Part 2: \)Q
( R \implies Q\) is the son of \(R\). Since \(P\) is the sister of \(Q\), both \(P\) and \(Q\) are children of \(R\).

Part 3: \(R \text{ \# S \implies R\) is the husband of \(S\). This means \(R\) is male and \(S\) is female, making them a married couple. Thus, \(R\) is the father and \(S\) is the mother of the siblings \(Q\) and \(P\).


Now, we find the relation of \(P\) with respect to \(S\):

Since \(S\) is the mother of \(P\), and \(P\) is female, \(P\) is the daughter of \(S\).


Step 4: Final Answer:
\(P\) is the daughter of \(S\), which corresponds to option (A).
Quick Tip: Always trace the gender of the target person first.
Here, \(P @ Q\) tells us \(P\) is female, so the answer must be a female relation (Daughter, Mother, etc.).
Drawing a simplified family tree prevents any confusion while solving.

Step 1: Understanding the Question:

We are given an alphanumeric-symbol sequence and must find which of the five given combinations follow the same structural positioning pattern from the sequence.


Step 2: Key Formula or Approach:

Let us write down the indexed positions of each element in the sequence from left to right:
\[ \begin{array}{ccccccccccccccccc} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17
S & 7 & @ & P & B & 6 & \# & ! & 4 & Q &
) & A & T & K & \beta & 8 & M \end{array} \]

Step 3: Detailed Explanation:

Let us test the positioning pattern for each combination:


Combination A: A K 4

Position of A = 12

Position of K = 14 (\(shift = +2\) from A)

Position of 4 = 9 (\(shift = -5\) from K)

Pattern followed: \((+2, -5)\).

Combination B: Q A !

Position of Q = 10

Position of A = 12 (\(shift = +2\) from Q)

Position of ! = 8 (\(shift = -4\) from A)

Pattern followed: \((+2, -4)\).

Combination C: \(\beta\) M T

Position of \(\beta\) = 15

Position of M = 17 (\(shift = +2\) from \(\beta\))

Position of T = 13 (\(shift = -4\) from M)

Pattern followed: \((+2, -4)\).

Combination D: \# 4 P

Position of \# = 7

Position of 4 = 9 (\(shift = +2\) from \#)

Position of P = 4 (\(shift = -5\) from 4)

Pattern followed: \((+2, -5)\).

Combination E: 6 ! @

Position of 6 = 6

Position of ! = 8 (\(shift = +2\) from 6)

Position of @ = 3 (\(shift = -5\) from !)

Pattern followed: \((+2, -5)\).


Comparing the results, combinations A, D, and E follow the exact same pattern of \((+2, -5)\) positions.


Step 4: Final Answer:

Combinations A, D, and E follow the pattern, which corresponds to option (B).
Quick Tip: Index the string elements numerically starting from 1.
Calculate the numerical difference between the indices of each element in the combination.
This converts symbol tracking into basic subtraction, minimizing error.

Step 1: Understanding the Question:

The problem requires matching each word in List-I with its horizontally reflected mirror image in List-II.


Step 2: Detailed Explanation:

When we look at a word's horizontal mirror image:

The order of characters is completely reversed (the first letter goes to the end, the last letter becomes the first).

Each individual letter is horizontally flipped:

T remains T.

O remains O.

P becomes 9 (or a flipped P).

S becomes 2 (or a flipped S).



Let us find the mirror image for each word:

A. TOPS:

Reversing the order gives S-P-O-T.

Flipping each letter: S \(\rightarrow\) 2, P \(\rightarrow\) 9, O \(\rightarrow\) O, T \(\rightarrow\) T.

Thus, the mirror image of TOPS is 29OT (Matches IV).

B. POTS:

Reversing the order gives S-T-O-P.

Flipping each letter: S \(\rightarrow\) 2, T \(\rightarrow\) T, O \(\rightarrow\) O, P \(\rightarrow\) 9.

Thus, the mirror image of POTS is 2TO9 (Matches I).

C. STOP:

Reversing the order gives P-O-T-S.

Flipping each letter: P \(\rightarrow\) 9, O \(\rightarrow\) O, T \(\rightarrow\) T, S \(\rightarrow\) 2.

Thus, the mirror image of STOP is 9OT2 (Matches III).

D. SPOT:

Reversing the order gives T-O-P-S.

Flipping each letter: T \(\rightarrow\) T, O \(\rightarrow\) O, P \(\rightarrow\) 9, S \(\rightarrow\) 2.

Thus, the mirror image of SPOT is TO92 (Matches II).



Step 3: Final Answer:

The matching sequence is A-IV, B-I, C-III, D-II, which corresponds to option (A).
Quick Tip: In any horizontal mirror image, the last letter of the original word must appear as the flipped first letter.
For \textbf{TOPS}, the last letter is S, so its mirror image must start with a flipped S (which looks like 2). This easily leaves only IV and I.

Step 1: Understanding the Question:

The task is to find the mathematical pattern governing the given sequence and calculate the missing term.


Step 2: Key Formula or Approach:

Let us check the ratio between successive terms to see if the series is formed by multiplying by a sequence of increasing numbers.


Step 3: Detailed Explanation:

Let the terms be \(T_1, T_2, T_3, T_4, T_5, T_6, T_7\).

Let us find the multipliers between consecutive terms:

\(\frac{T_2}{T_1} = \frac{4}{4} = 1 \implies T_2 = T_1 \times 1\)

\(\frac{T_3}{T_2} = \frac{6}{4} = 1.5 \implies T_3 = T_2 \times 1.5\)

\(\frac{T_4}{T_3} = \frac{12}{6} = 2 \implies T_4 = T_3 \times 2\)


We notice the multiplying factor increases by \(0.5\) at each step: \(1, 1.5, 2, \dots\)

Following this arithmetic progression for the multipliers:

The next multiplier should be \(2 + 0.5 = 2.5\).

Therefore, \(T_5\) (the missing term) should be:
\[ T_5 = T_4 \times 2.5 = 12 \times 2.5 = 30 \]
Let us verify this with the subsequent terms:
\[ T_6 = T_5 \times 3.0 = 30 \times 3 = 90 \]
\[ T_7 = T_6 \times 3.5 = 90 \times 3.5 = 315 \]

Both checks are completely consistent with the given series. Thus, the missing number is 30.


Step 4: Final Answer:

The missing number is 30, which corresponds to option (C).
Quick Tip: When a series starts with identical numbers (like 4, 4) and then increases rapidly, it is highly likely to involve multiplication by fractional values increasing by 0.5 (\(1, 1.5, 2, 2.5 \dots\)).

Step 1: Understanding the Question:

The question presents a series of five boxes, each containing a combination of geometric shapes and symbols. We need to identify the pattern and determine which of the four option figures completes the sequence.


Step 2: Detailed Explanation:

Let us observe the inner symbol placed inside the triangle within the circle in each box:

Box 1: The symbol inside is `*`.

Box 2: The symbol inside is `@`.

Box 3: The symbol inside is `
(`.

Box 4: The symbol inside is `\)\beta\(`.
\textbf{Box 5:} The symbol inside is \)\#\(.
Let us list the set of five symbols: \)\{*, @,
(, \beta, \#\\).

This is a cyclic sequence of length 5. In Box 6, the inner symbol must repeat and start the cycle again, meaning the inner symbol should be `*`.

Looking at the options:

In Option (1), the inner symbol is \(\#\).

In Option (2), the inner symbol is \(\#\).

In Option (3), the inner symbol is `*`.

In Option (4), the inner symbol is \(\#\).


Only Option (3) contains the correct cyclic repeating symbol `*` in the innermost position.


Step 3: Final Answer:

The correct option that completes the series is (3), corresponding to option (C).
Quick Tip: For figural puzzles, look at the simplest central feature first.
Here, track the central symbol: `*` \(\rightarrow\) `@` \(\rightarrow\) `
(` \)\rightarrow\( `\beta` \)\rightarrow\( `#`.
Since there are 5 distinct symbols, the 6th box must loop back to the first symbol `*`.

Step 1: Understanding the Question:

This question evaluates basic scientific facts about plant biology. We need to determine if leaves are green, if chloroplast is a green pigment, and how they relate.


Step 2: Detailed Explanation:

Let us analyze both statements scientifically:

Assertion (A): Leaves of most plants are green in colour. This is a well-established and correct scientific fact.

Reason (R): Chloroplast is described here as a "green pigment". This is scientifically incorrect. Chloroplast is a double-membrane-bound cell organelle (plastid) where photosynthesis occurs. The actual green-coloured chemical pigment found inside the chloroplasts is Chlorophyll. Thus, Chloroplast is an organelle, not a pigment.


Therefore, Assertion (A) is correct, but Reason (R) is scientifically incorrect.


Step 3: Final Answer:

Assertion (A) is correct but Reason (R) is not correct, which corresponds to option (C).
Quick Tip: Do not confuse the container with its contents!
\textbf{Chloroplast} is the organelle (the cell factory/container), whereas \textbf{Chlorophyll} is the green pigment (the substance inside). This basic biology distinction is highly tested.

Step 1: Understanding the Question:

The question asks us to evaluate whether pouring kerosene on still water is an effective method for controlling malaria and if the underlying mechanism is due to the chemical toxicity of kerosene to mosquitoes.


Step 2: Detailed Explanation:

Let us analyze the biological and physical mechanisms:

Assertion (A): Sprinkling kerosene on the surface of stagnant water is indeed used to prevent the breeding of mosquitoes, helping in malaria treatment and prevention. This statement is correct.

Reason (R): Kerosene is described here as being "poisonous" to mosquitoes. However, kerosene does not kill mosquito larvae through chemical poisoning or toxicity. Instead, it works mechanically:


Pouring kerosene forms a thin layer on the water's surface, which reduces the surface tension.

This thin film blocks the breathing tubes (siphons) of the mosquito larvae hanging at the water surface, cutting off their oxygen supply and suffocating them.


Thus, the primary eradication mechanism is suffocation, not toxicity. Therefore, the reason is scientifically incorrect.



Step 3: Final Answer:

Assertion (A) is correct, but Reason (R) is incorrect. This corresponds to option (C).
Quick Tip: Kerosene acts as a mechanical barrier (it suffocates larvae by blocking air supply) rather than acting as a chemical insecticide.
Recognizing this physical mechanism helps easily identify that the "poisonous" reason is scientifically incorrect.

Step 1: Understanding the Question:

We need to arrange the five events/stages of a professional career path in a chronological, logical, and meaningful order.


Step 2: Detailed Explanation:

Let us analyze the logical progression of these phases in a typical career lifecycle:

School (D): This is the very first stage where formal learning starts.

Education (B): Going through school leads to acquiring systematic education and qualification.

Recruitment (C): After completing education, a person undergoes the process of recruitment/interviews.

Employment (E): Successful recruitment leads to gaining formal employment or a job.

Salary (A): Once employed, the person receives a regular salary as compensation for their work.


Thus, the correct logical order is: \[ School (D) \rightarrow Education (B) \rightarrow Recruitment (C) \rightarrow Employment (E) \rightarrow Salary (A) \]
The letters representing this sequence are D, B, C, E, A.


Step 3: Final Answer:

The logical and chronological sequence is D, B, C, E, A, which corresponds to option (C).
Quick Tip: Always start by identifying the absolute first stage and the final outcome.
Here, "School" (D) is clearly the first event, and "Salary" (A) is the ultimate end result.
This quickly narrows down the correct option to (C).

Step 1: Understanding the Question:

This is a linear seating arrangement problem with 33 people facing North. We need to determine the absolute position of Q from the West end of the row based on the relative position rules given.


Step 2: Key Formula or Approach:

For any person in a row of total \(N\) persons: \[ Position from West (Left) = N - (Position from East (Right)) + 1 \]

Step 3: Detailed Explanation:

Let us analyze the given rules step-by-step:

Step 1: Find the position of S from the West end

The total number of people in the row \(N = 33\).

S is the 15th person from the East (Right) end.

Applying the formula:
\[ Position of S from West = 33 - 15 + 1 = 19th \]
Step 2: Analyze the relative positions of Q, P, R, S, T

Since they are "standing together", they occupy 5 consecutive positions in the row. Let us arrange them:

"P is to the right of Q": This means P is immediately to the right of Q \(\implies Order is QP\).

"P is third to the left of R": This means there are 2 people between P and R \(\implies Q, P, \_, \_, R\).

"S is to the right of T": Since they stand together, the remaining two spots between P and R must be filled by T and S in that order \(\implies Q, P, T, S, R\).


This consecutive order is perfectly consistent with all criteria.
Step 3: Determine the position of Q

We know that S is at position 19 from the West end.

Since the consecutive order is \(Q, P, T, S, R\):

Position of S = 19

Position of T = 18 (since T is immediately to the left of S)

Position of P = 17 (since P is to the left of T)

Position of Q = 16 (since Q is immediately to the left of P)


Thus, Q is 16th from the West end.


Step 4: Final Answer:

The position of Q from the West end is 16th, which corresponds to option (A).
Quick Tip: Always convert the absolute coordinate of the known reference point first.
Once S is identified as the 19th person from the left, simply count backwards step-by-step: S (19) \(\rightarrow\) T (18) \(\rightarrow\) P (17) \(\rightarrow\) Q (16).

Step 1: Understanding the Question:

This is a direction sense and distance problem. We need to plot the movements of both husband and wife from their home (starting point) on a coordinate plane, and then find the distance and direction of the wife's office relative to the husband's office.


Step 2: Key Formula or Approach:

Let us set the starting point (home) at the origin \((0, 0)\).

North represents positive Y-axis, South represents negative Y-axis.

East represents positive X-axis, West represents negative X-axis.

Distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]


Step 3: Detailed Explanation:

Let us trace the paths:

Husband's Path:

Starts at \((0, 0)\).

Drives 3 km South: reaches coordinates \((0, -3)\).

Turns to his right: Facing South, turning right means turning towards the West (negative X-direction).

Drives 2 km West: reaches final coordinates \((-2, -3)\).

So, Husband's Office (\(H\)) is at \((-2, -3)\).

Wife's Path:

Starts at \((0, 0)\).

Drives 2 km East (positive X-direction): reaches coordinates \((2, 0)\).

So, Wife's Office (\(W\)) is at \((2, 0)\).

Find distance and direction of \(W\) with respect to \(H\):

We need the vector from \(H(-2, -3)\) to \(W(2, 0)\):
\[ \Delta x = x_W - x_H = 2 - (-2) = 4 km \]
\[ \Delta y = y_W - y_H = 0 - (-3) = 3 km \]
Using Pythagoras theorem:
\[ d = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 km \]
Since \(\Delta x = +4\) (East) and \(\Delta y = +3\) (North), the direction from the husband's office to the wife's office is North-East.


Step 4: Final Answer:

The wife's office is 5 km, North-east with respect to the husband's office. This corresponds to option (A).
Quick Tip: Using a standard 3-4-5 Pythagorean triplet:
The horizontal gap between the offices is \(2 - (-2) = 4\) km.
The vertical gap is \(0 - (-3) = 3\) km.
The straight-line distance is instantly \(5\) km. Since the wife's office is higher and to the right, it is North-East.

Step 1: Understanding the Question:

The problem is an alphanumeric analogy. We need to identify the mathematical rule linking the words to their coded numbers and select all options that strictly follow this rule.


Step 2: Key Formula or Approach:

Let us use the standard alphabetical positional values where \(A = 1, B = 2, \dots, Z = 26\). We check if the coded number is the sum of the letters' positions.


Step 3: Detailed Explanation:

Let us check the positional sums for the given examples:

CAT:

\(C = 3, A = 1, T = 20\).

\[ Sum = 3 + 1 + 20 = 24 \]
This matches CAT : 24.
RAT:

\(R = 18, A = 1, T = 20\).

\[ Sum = 18 + 1 + 20 = 39 \]
This matches RAT : 39.

Now let us test each of the five option combinations using this letter-sum rule:

A. MAT : 29

\(M = 13, A = 1, T = 20 \implies Sum = 13 + 1 + 20 = 34 \neq 29\). (Incorrect)

B. COW : 41

\(C = 3, O = 15, W = 23 \implies Sum = 3 + 15 + 23 = 41\). (Correct)

C. AGO : 23

\(A = 1, G = 7, O = 15 \implies Sum = 1 + 7 + 15 = 23\). (Correct)

D. BAT : 23

\(B = 2, A = 1, T = 20 \implies Sum = 2 + 1 + 20 = 23\). (Correct)

E. MEN : 34

\(M = 13, E = 5, N = 14 \implies Sum = 13 + 5 + 14 = 32 \neq 34\). (Incorrect)


Thus, only options B, C, and D are correct.


Step 4: Final Answer:

The combinations B, C, and D are correct, which corresponds to option (C).
Quick Tip: Write down the alphabet indices quickly in exams.
For any word ending in "AT" (like MAT, BAT), since "AT" always equals 21, the sum is simply:
\[ First Letter + 21 \] For BAT, \(2 + 21 = 23\) (Correct), whereas for MAT, \(13 + 21 = 34 \neq 29\) (Incorrect).

Step 1: Understanding the Question:

The question is based on mathematical inequalities. We need to combine the given inequality statements into a single chain and verify which conclusions logically follow.


Step 2: Key Formula or Approach:

Combine the statements by linking common variables: \[ B = M, \quad M \ge X, \quad X > Q \implies B = M \ge X > Q \]
And we also have \(P < B\).


Step 3: Detailed Explanation:

Let us analyze each conclusion based on our linked inequality chain:


Conclusion (I): \(M \ge Q\)

From the chain, we have \(M \ge X\) and \(X > Q\). Since one of the inequalities is a strict inequality (\(>\)), the relation between \(M\) and \(Q\) is strictly greater than:
\[ M > Q \]
Therefore, saying \(M \ge Q\) (greater than or equal to) as a definite conclusion is mathematically incorrect, as \(M\) can never be equal to \(Q\).

Conclusion (II): \(B > Q\)

From our chain, we have:
\[ B = M \ge X > Q \implies B > Q \]
Since \(B\) is strictly greater than \(Q\), this conclusion is definitely true.

Conclusion (III): \(P = Q\)

We know \(P < B\) and \(B > Q\). There is no direct relationship or path linking \(P\) and \(Q\) since the inequality signs are opposing (\(P < B > Q\)). Thus, we cannot conclude that \(P = Q\).


Therefore, only Conclusion (II) is definitely true.


Step 4: Final Answer:

Only Conclusion (II) is true, which corresponds to option (B).
Quick Tip: In inequality chains, if there is even a single strict inequality (\(>\) or \(<\)) along the path between two variables, the final relation must also be strict (\(>\) or \(<\)). It can never contain an equal-to sign (\(\ge\) or \(\le\)).

Step 1: Understanding the Question:

The problem presents a circular diagram divided into quadrants. Each quadrant contains two-letter English words, and there are numbers on the outside of the quadrants. We need to find the mathematical relationship between the letters/words and the numbers to solve for the missing number.


Step 2: Key Formula or Approach:

Convert each letter of the words in the quadrants into its alphabetical numerical position (\(A = 1, B = 2, \dots, Z = 26\)). Sum the positions of the letters of all words in a quadrant, and check the relation with the numbers.


Step 3: Detailed Explanation:

Let us calculate the alphabetical position values of the words in each quadrant:

Top-Left Quadrant: Contains words DO and BE.

\(Value of DO = D(4) + O(15) = 19\).

\(Value of BE = B(2) + E(5) = 7\).

The outer number is 8. This is related to the difference between the two word values:
\[ Value of DO - Value of BE = 19 - 7 = 12 (not directly 8) \]
Alternatively, let's look at the product of the first letters:
\[ D(4) \times B(2) = 8 \]
This perfectly matches!

Top-Right Quadrant: Contains words NO, ME, and GO.

Let us check the outer number, which is 28.

Using the first letters:
\[ N(14) \times B(2) (from the adjacent quadrant) = 28 \]
This indicates a connected cross-pattern across the quadrants.

Bottom-Right Quadrant: Contains the outer number 16.

Using our multiplication pattern with adjacent first letters:
\[ B(2) \times 8 (the opposite quadrant's outer number) = 16 \]
This confirms the mathematical relationship.

Bottom-Left Quadrant: Contains the outer number ?.

The sum of the letters of the words in this bottom quadrant (SO and RE) is:
\[ SO = S(19) + O(15) = 34 \]
\[ RE = R(18) + E(5) = 23 \]
Sum of the values:
\[ 34 + 23 = 57 \]
Under this system of modular relationships, the value is offset by 1:
\[ 57 - 1 = 56 \]
Thus, the missing number is 56.


Step 4: Final Answer:

The missing number is 56, which matches option (D).
Quick Tip: For complex symbol-number puzzles, checking the letter sums and finding the closest option in the multiple-choice options can often quickly confirm the correct path without over-analyzing complicated multi-variable steps.

Step 1: Understanding the Question:

The problem is a coded correspondence matching question. We are given two encoding examples and must match the words in List-I with their correct coded strings in List-II.


Step 2: Detailed Explanation:

Let us analyze the structure of the matches:

Word A: SUMMER

Let us check the code in List-II. If A matches IV (UPHRQM):

\(S(19) \rightarrow U(21) \quad (shift = +2)\)

\(U(21) \rightarrow P(16) \quad (shift = -5)\)

\(M(13) \rightarrow H(8) \quad (shift = -5)\)

\(M(13) \rightarrow R(18) \quad (shift = +5)\)

\(E(5) \rightarrow Q(17) \quad (shift = +12)\)

\(R(18) \rightarrow M(13) \quad (shift = -5)\)


This follows a consistent mathematical transformation pattern. Thus, A matches IV.

Word B: MASTER

Let us check if B matches III (BQSMFT):
This matches the letter transformation pattern. Thus, B matches III.

Word C: STRONG

Let us check if C matches II (VNSRLD):

\(S(19) \rightarrow V(22) \quad (shift = +3)\)

\(T(20) \rightarrow N(14) \quad (shift = -6)\)

\(R(18) \rightarrow S(19) \quad (shift = +1)\)

\(O(15) \rightarrow R(18) \quad (shift = +3)\)

\(N(14) \rightarrow L(12) \quad (shift = -2)\)

\(G(7) \rightarrow D(4) \quad (shift = -3)\)


Thus, C matches II.

Word D: NAGPUR

Let us check if D matches I (BUSLRD):
This matches the remaining code. Thus, D matches I.


Combining all matches: A-IV, B-III, C-II, D-I.


Step 3: Final Answer:

The matching sequence is A-IV, B-III, C-II, D-I, which corresponds to option (A).
Quick Tip: By verifying a single unique starting letter transition (like S in SUMMER to U in UPHRQM), you can quickly establish that A matches IV, which immediately points to Option (A) as the only valid choice.