KVS PGT Maths Official Paper (Held On: 18 Feb, 2023 Shift 2) (Previous Year Paper)

The correct answer is Option (2) i.e. (d) (c) (b) (a)

Key Points

• The sentence must begin by setting the context, which is the time of the action. This is provided by the dependent clause part (d): "when the car passed by,".
• Following the introductory clause, the sentence must introduce the subject of the action, which is part (c): "the urchins".
• Next, the first action performed by the subject is stated, which is part (b): "threw stones at it".
• Finally, the result of the action is stated, which is connected by the conjunction "and" in part (a): "and broke its window pane".

Therefore, the correct sequence is (d) (c) (b) (a).

Additional Information

• Option 1 (c) (d) (b) (a): This sequence places the subject first ("the urchins when the car passed by, threw stones at it..."), which creates an awkward and grammatically incorrect structure by separating the subject from its verb with an entire clause.
• Option 3 (b) (a) (c) (d): This sequence starts with the verb ("threw stones at it and broke its window pane the urchins when the car passed by,"), which is completely nonsensical.
• Option 4 (a) (b) (c) (d): This sequence starts with the second verb ("and broke its window pane threw stones at it the urchins when the car passed by,"), making the sentence incoherent.

Coherent sentence after rearrangement: "When the car passed by, the urchins threw stones at it and broke its window pane."

The correct answer is Option 3.

 

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the active voice, the sentence is: "Some local residents were helping the wounded soldier."
• To convert to passive voice: Place the object "the wounded soldier" at the beginning.
• Change the active verb form "were helping" to "was being helped" (past continuous passive).
• Add the preposition "by" followed by the original subject "some local residents."

Therefore, the correct answer is Option 3.

 

Correct Sentence: "The wounded soldier was being helped by some local residents."

 

Additional Information

• Option 1: "Some local residents were being helped by the wounded soldier." – Incorrect meaning (reverses subject and object).
• Option 2: "The wounded soldier was helped by some local residents." – Incorrect tense (simple past instead of past continuous).
• Option 4: "Help was being given to the wounded soldier by some local residents." – Correct meaning but awkward phrasing.

The correct answer is 'after'.

 

Key Points

• The preposition "after" is used to indicate pursuit or chasing.
• In this sentence, the people are chasing the thief who stole their belongings, making "after" the correct choice.
• Options 1, 3, and 4 are incorrect because they do not fit the context of chasing.

Therefore, the correct answer is Option 2.

 

Complete Sentence: "They ran after the thief who had stolen their belongings."

 

Additional Information

• Option 1: "from" is incorrect because it indicates separation or source, not pursuit.
• Option 3: "with" is incorrect because it indicates accompaniment, not chasing.
• Option 4: "in" is incorrect because it indicates location or position, not pursuit.

The correct answer is Option 3 i.e. 'Past Perfect'.

Key Points

• The verb phrase “had lost” is in the Past Perfect tense.
• Past Perfect is used to show that an action was completed before another action or point in the past.
• In the sentence, “This was the first time” is the reference point in the past, and “the mighty king had lost a battle” happened before that.
• Therefore, the tense form used in the sentence is Past Perfect.

Therefore, the correct answer is- Option 3.

Additional Information

• Option 1 (Past Indefinite): Uses the simple past tense such as “lost,” which does not indicate the order of two past events.
• Option 2 (Past Continuous): Refers to an ongoing action in the past (e.g., “was losing”).
• Option 4 (Past Perfect Continuous): Describes an action that was ongoing in the past up to a certain point (e.g., “had been losing”).

The correct answer is Option 3.

 

Key Points

• Indirect Speech: The young man told his parents that they would have to adjust to the changing times.
• Key Conversions:
• Pronoun Change:
• "You" (addressing parents) becomes "they" in indirect speech.
• Modal Verb Shift:
• "Will have to" in direct speech changes to "would have to" in indirect speech to match sequence of tenses.
• Reporting Verb:
• "said to" is replaced by "told" to indicate whom the statement is addressed to.
• Punctuation and Format:
• Indirect speech does not use quotation marks.
• The sentence structure changes from direct address to reported statement.

Therefore, the correct answer is Option 3.

 

Correct Sentence: "The young man told his parents that they would have to adjust to the changing times."

 

Additional Information

• Option 1: Poor word order and clarity make it incorrect.
• The subject and reporting clause are not properly structured.
• Option 2: Changes the modal from "will have to" to "must," altering the original meaning.
• Does not accurately reflect the original speech.
• Option 4: Incorrectly shifts the subject to "he (the young man)," which changes the meaning.
• The statement is about the parents, not the young man himself.

The correct answer is Option 4.

 

Key Points

• The error in the sentence lies in the phrase "the shortest route" in part 4.
• The correct preposition to use here is "by" instead of "the" to indicate the route being referred to.
• The phrase should be "by the shortest route" to maintain grammatical accuracy and clarity.
• Thus, the error is located in part 4 of the sentence.

Therefore, the correct answer is Option 4.

 

Correct Sentence: "From this place, Meerut is over ten miles by the shortest route."

 

Additional Information

• Option 1: "From this place," – This part of the sentence is grammatically correct and does not require any changes.
• Option 2: "Meerut is" – This part of the sentence is grammatically correct and does not require any changes.
• Option 3: "over ten miles" – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is: Option 2 (Assistance).

Key Points

• The word "Abetment" refers to the act of encouraging, supporting, or assisting someone to do something, especially something wrong or illegal. (उकसाना, सहयोग)
• Example: The abetment of criminal activities can lead to legal consequences.
• "Assistance" means providing help or support to someone to achieve something. (मदद, सहायक)
• Example: The government provided financial assistance to the flood victims.
• Hence, we can infer that "abetment" is closest in meaning to "assistance."

Therefore, the correct answer is: Option 2 (Assistance).

Additional Information

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

• Enmity (दुश्मनी): The state of being actively opposed or hostile to someone or something.
• Example: The two families have harbored enmity for decades.
• Revenge (बदला): The action of inflicting harm or punishment on someone for a wrong suffered at their hands.
• Example: He sought revenge for the injustice done to him.
• Reaction (प्रतिक्रिया): A response to a situation, event, or stimulus.
• Example: Her reaction to the surprise party was priceless.

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

Key Points

• The word "Slothful" refers to being lazy or unwilling to work or make an effort. (आलसी)
• Example: He was too slothful to get out of bed and start working on his assignments.
• "Active" refers to being energetic, dynamic, and always ready to engage in physical or mental activity. (सक्रिय)
• Example: She is an active participant in all the community events and activities.
• Hence, the opposite of 'slothful' is 'active'.

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

Additional Information

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

• Healthy (स्वस्थ): Being in good physical or mental condition.
• Example: Regular exercise and a balanced diet help in maintaining a healthy lifestyle.
• Intelligent (बुद्धिमान): Having or showing intelligence, especially of a high level.
• Example: She is an intelligent student who always tops her class.
• Indolent (आलसी): Wanting to avoid activity or exertion; lazy.
• Example: His indolent behaviour often delays the completion of important tasks.

The correct answer is Option 3 i.e 'Noun'.

Key Points

• The underlined word "fasting" refers to the act of abstaining from food, which is being used as the subject of the sentence.
• Although "fasting" originates from the verb "fast," here it functions as a gerund, which is treated as a noun.
• Since it names an activity rather than showing an action, its part of speech in this context is noun.

Therefore, the correct answer is- Option 3.

Additional Information

• Pronoun: A pronoun replaces a noun (he, she, it). "Fasting" does not replace a noun, so this is incorrect.
• Verb: A verb shows action. While "fast" is a verb, in this sentence "fasting" is not performing an action but naming one.
• Conjunction: A conjunction joins words or clauses (and, but, so). "Fasting" does not serve this role.

The correct answer is Option 2.

 

Key Points

• The sentence is a question, so it should end with a question mark, also known as a mark of interrogation.
• A question mark (?) is used to indicate that a question is being asked.
• Other options like a full stop, semi-colon, or exclamation mark would not be appropriate for a question.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "Have you finished reading the book?"

 

Additional Information

• Option 1: "Full stop" – A full stop is used at the end of a declarative sentence, not a question.
• Option 3: "Semi-colon" – A semi-colon is used to connect closely related independent clauses, not at the end of a question.
• Option 4: "Mark of Exclamation" – An exclamation mark is used to express strong emotion, not to indicate a question.
• Option 2: "Mark of Interrogation" – This is the correct option for indicating a question.

सही उत्तर है- विज्ञापन द्वारा उसके बारे में जानकारी प्राप्त करने की

Key Pointsगद्यांश के अनुसार-

• “उपभोक्ता वर्ग के एक बहुत बड़े वर्ग में किसी उत्पाद को खरीदने से पहले विज्ञापन द्वारा उसके बारे में जानकारी प्राप्त करने की प्रवृत्ति रही है।”

सही उत्तर है- उत्पाद को उपयुक्त उपभोक्ता तक पहुँचाने में

Key Pointsगद्यांश के अनुसार-

• “विज्ञापन से उत्पाद को उसके उपयुक्त उपभोक्ता तक पहुँचाने में सहायता मिलती है।”

सही उत्तर है- संपूर्ण विश्व

Key Pointsगद्यांश के अनुसार-

• “भारत ही नहीं संपूर्ण विश्व में विज्ञापन एजेंसियों का बहुत बड़ा तंत्र सक्रिय है।”
• यह वाक्य स्पष्ट रूप से बता रहा है कि विज्ञापन एजेंसियों का तंत्र पूरे विश्व तक फैला हुआ है।

सही उत्तर है- इंटरनेट

Key Pointsगद्यांश के अनुसार-

• “दूर दराज के क्षेत्रों में भी रेडियो, टेलीविज़न और समाचार-पत्रों के माध्यम से विज्ञापन पहुँच रहे हैं।”
• गद्यांश में केवल तीन माध्यमों का उल्लेख है:
• रेडियो
• टेलीविज़न
• समाचार-पत्र

सही उत्तर है- अधिकतर - कमतर

Key Points

सही उत्तर है - माह में एक बार प्रकाशित होने वाला - माहिक

Key Points

• माह में एक बार प्रकाशित होने वाला - मासिक

 

सही उत्तर- पाँख।

Key Points

 

Additional Information

• निष्कर्ष: “पाँख” तद्भव शब्द है, शेष तीनों तत्सम हैं।'पाँख' (या पंख) शब्द का तत्सम रूप 'पक्ष' होता है

'अश्व' का पर्यायवाची शब्द है- हय

Key Points

• 'अश्व' के अन्य पर्यायवाची शब्द - घोड़ा, घोटक, हरि, हय, वाजि, सैन्धव, रविपुत्र।
• पर्यायवाची - ऐसे शब्द जिनके अर्थ समान हों, पर्यायवाची शब्द कहलाते हैं।

Additional Information कुछ महत्वपूर्ण पर्यायवाची शब्द -

प्रयोग के अनुसार सर्वनाम के भेद है- छ 

Important Points

'मनोभाव' में : विसर्ग संधि है।

• संधि विच्छेद: मनः+भाव
• विसर्ग संधि के उदाहरण
• तपः + बल = तपोबल
• पुरः + हित = पुरोहित

Key Points 

• विसर्ग संधि के प्रकार
• सत्व विसर्ग संधि
• उत्व संधि
• रूत्व संधि

Additional Information

1. सत्व विसर्ग संधि

• यदि किसी भी पद के आखिर में या अंत में “अ” स्वर के अलावा कोई अन्य स्वर आये और उसके बाद में विसर्ग आये तथा दूसरे शब्द के शुरू में वर्ण का तीसरा, चौथा, पांचवा अक्षर “य्, र्, ल्, व्” में से कोई आये तो वर्ण अगले वर्ण के ऊपर चढ़ जाता है और विसर्ग “र” हो जाता है।

जैसे:

• बहि: + अंग = बहिरंग
• आशि: + वाद = आशिर्वाद

 

2. उत्व संधि

• यदि किसी प्रथम पद के आखिर या अन्त मे “अ” आये उसके बाद मे विसर्ग आये तथा दूसरे पद के शुरुआत् क तीसरा, चौथा, पांचवा “य्, र्, ल्, व्” में से कोई आये तो “उ” बन जाता है,
• अतः अ+उ = ओ हो जाता है।

जैसे :

• तप + वन = तपोवन
• मन + हर = मनोहर

3. रूत्व संधि

• यदि किसी पद के अन्त मे कोई भी स्वर आने के पश्चात विसर्ग आये तथा उसके बाद दूसरे पद के शुरुआत् मे “त/थ” आने पर “स” बन जाता है।
• यदि “च/छ्” आता है तो “श” बन जाता है, उसके बाद मे “ट/ठ” आने पर “ष” बन जाता है।

जैसे :

• चन्द्र: + तम् = चन्द्र्स्तम्
• नि: + चय = निश्चय
• धनु: + टकार = धनुष्टकार

The correct answer is 1.

Key Points

• Article 19(1)(a) of the Indian Constitution guarantees the fundamental right to freedom of speech and expression to all citizens.
• However, reasonable restrictions can be imposed by the State on this right under Article 19(2) of the Constitution.
• These restrictions are imposed in the interest of sovereignty and integrity of India, security of the State, friendly relations with foreign States, public order, decency, morality, contempt of court, defamation, incitement to an offense, or reasonable restrictions as prescribed by law.
• The assertion that the State can impose reasonable restrictions on the right to freedom of speech and expression is correct. This ensures that the right is balanced with societal order and national security.
• The reason stating that reasonable restrictions cannot be imposed in relation to contempt of court is incorrect, as contempt of court is explicitly mentioned under Article 19(2) as a valid ground for restriction.

Additional Information

• Article 19(1)(a):
• This article provides the fundamental right to freedom of speech and expression, allowing citizens to freely express their views, opinions, and ideas.
• This right is essential for the functioning of a democratic society and includes rights such as freedom of the press.
• Reasonable Restrictions under Article 19(2):
• Article 19(2) empowers the State to impose restrictions on the freedom of speech and expression under specific conditions such as public order, decency, morality, contempt of court, defamation, or incitement to an offense.
• These restrictions must be reasonable and justified in a court of law.
• Contempt of Court:
• Contempt of Court is a legal provision aimed at protecting the authority and dignity of courts in India.
• Under the Contempt of Courts Act, 1971, contempt is classified into civil contempt (disobedience of court orders) and criminal contempt (actions that scandalize or lower the authority of the court).
• Reasonable restrictions on freedom of speech in relation to contempt of court ensure that judicial processes are not obstructed.
• Defamation:
• Defamation refers to a false statement made by one individual about another, which causes harm to the reputation of the latter.
• Reasonable restrictions on speech prevent misuse of the right to harm others' reputations unjustly.
• Public Order and Morality:
• Restrictions on speech and expression can be imposed to maintain public order and uphold moral standards within the society.
• For example, hate speeches inciting violence or content violating societal norms can be restricted under these grounds.

Important Points

• Freedom of Speech in India:
• Freedom of speech and expression is not absolute; it is subject to reasonable restrictions to ensure harmony and order within society.
• Judicial interpretation plays a critical role in balancing individual rights with societal needs.
• Judicial Precedents:
• Landmark cases such as Keshavananda Bharati v. State of Kerala and Maneka Gandhi v. Union of India have shaped the understanding of reasonable restrictions on fundamental rights.
• Courts ensure that restrictions are not arbitrary and follow principles of natural justice.
• Global Perspective:
• Freedom of speech is recognized internationally under instruments like Article 19 of the Universal Declaration of Human Rights (UDHR).
• However, similar restrictions exist in other democracies to prevent misuse of the right.

The correct answer is It uses real-time adjustment.

Key Points

• Agile approach to policy-making is characterized by its ability to adapt and adjust policies in real-time based on feedback, data, and changing circumstances. Hence, statement 3 is correct.
• The Agile approach does not follow a rigid up-front plan for implementation. Instead, it emphasizes flexibility and iterative development. Hence, statement 1 is incorrect.
• This approach actively utilizes feedback loops to refine and improve policies during the implementation process. Hence, statement 2 is incorrect.
• The Agile approach is distinct from the 'Waterfall' framework, which follows a linear and sequential process. Agile is more dynamic and iterative. Hence, statement 4 is incorrect.
• Agile policy-making is particularly useful in complex and uncertain environments, where the ability to respond quickly to new challenges is crucial.

Additional Information

• Key Features of Agile Policy-Making:
• Iterative Process: Policies are developed and implemented in small, manageable phases, allowing for frequent reassessment and adjustment.
• Stakeholder Engagement: Continuous involvement of stakeholders ensures that the policies remain relevant and practical.
• Data-Driven Decisions: Real-time data and analytics are used to inform and guide policy changes.
• Flexibility: Agile policy-making allows for quick adjustments in response to unforeseen challenges or changing circumstances.
• Waterfall Framework:
• The Waterfall approach is linear and sequential, with clearly defined stages such as planning, design, implementation, and evaluation.
• It is best suited for projects with well-defined goals and stable environments.
• Unlike Agile, it does not allow for changes once a stage has been completed.
• Applications of Agile Policy-Making:
• It is widely used in technology and software development, where rapid changes are the norm.
• Governments and organizations use Agile methods to address public health crises, such as the COVID-19 pandemic, by adapting policies in real-time.
• It is also applied in climate change policies, where dynamic adjustments are required based on emerging data.
• Benefits of Agile Policy-Making:
• Enhanced Responsiveness: Ability to quickly address new challenges and opportunities.
• Improved Outcomes: Continuous improvement leads to more effective and impactful policies.
• Stakeholder Satisfaction: Regular feedback ensures that policies meet the needs of the people they are designed for.
• 

Important Points

• The Agile approach is increasingly being adopted in public administration to address complex societal challenges.
• Examples of Agile policy-making include adaptive climate policies and public health strategies during the pandemic.
• It contrasts with traditional approaches by emphasizing flexibility, collaboration, and data-driven decision-making.

The correct answer is Lord Dalhousie.

Key Points

• Lord Dalhousie, who served as the Governor-General of India from 1848 to 1856, was the architect of the Doctrine of Lapse.
• The Doctrine of Lapse was a policy of annexation used by the British East India Company to expand its territorial control in India.
• Under this doctrine, if an Indian ruler died without a legitimate male heir, the state would "lapse" and be annexed by the British. The term "legitimate male heir" excluded adopted sons, which was a common Indian practice for succession.
• Several princely states were annexed using this policy, including Satara (1848), Sambalpur (1850), Jhansi (1853), and Awadh (1856).
• The Doctrine of Lapse became one of the major causes of resentment among Indian rulers and contributed to the outbreak of the Revolt of 1857.

Additional Information

• Lord Dalhousie:
• Lord Dalhousie is remembered as one of the most significant British administrators in India, known for his expansionist policies and reforms.
• Besides the Doctrine of Lapse, Dalhousie is credited with introducing modern infrastructure like railways, telegraphs, and postal services in India.
• He also implemented reforms in education, introducing the Wood's Despatch of 1854, which laid the foundation for the modern education system in India.
• Doctrine of Lapse:
• The doctrine was introduced to consolidate British authority in India by annexing states that failed to produce a male heir.
• The policy disregarded Indian traditions, especially the practice of adoption, leading to widespread resentment among Indian rulers.
• The annexation of Jhansi under this doctrine deeply angered its queen, Rani Lakshmi Bai, who became one of the leading figures in the Revolt of 1857.
• Impact of the Doctrine:
• The aggressive annexation of Indian states alienated the Indian rulers and nobility, creating widespread discontent against British rule.
• The annexation of Awadh (1856) under the pretext of misgovernance, further compounded grievances among the Indian population, especially soldiers who hailed from Awadh.
• This resentment played a crucial role in the Revolt of 1857, often referred to as the First War of Indian Independence.
• Other Governors-General and Their Contributions:
• Lord Hastings: Known for his role in the Anglo-Nepalese War (1814–1816) and the creation of the Ryotwari system of land revenue.
• Lord Cornwallis: Introduced the Permanent Settlement (1793), which fixed land revenue and created the zamindari system.
• Lord Wellesley: Known for his use of the Subsidiary Alliance system, which helped the British control Indian princely states indirectly.

The correct answer is Magnetite.

Key Points

• Magnetite is the finest quality iron ore with the highest iron content, up to 70%. It is considered the most valuable among all types of iron ores.
• It is composed of iron oxide (Fe₃O₄), which has both ferrous (Fe²⁺) and ferric (Fe³⁺) ions, contributing to its high iron content.
• Magnetite is known for its magnetic properties, which differentiate it from other iron ores like Hematite. These properties make it useful in various industrial processes.
• It is found in regions like India, Australia, Brazil, and the USA. In India, magnetite is primarily located in the states of Karnataka, Andhra Pradesh, and Goa.
• Due to its high iron content and purity, magnetite is extensively used in the steel industry for the production of high-quality steel.

Additional Information

• Hematite:
• Hematite is another important iron ore and contains around 50-60% iron.
• It is composed of iron(III) oxide (Fe₂O₃) and is known for its reddish-brown color.
• Hematite is widely distributed and is a major source of iron for industries.
• It is primarily found in states like Odisha, Jharkhand, and Chhattisgarh in India.
• Mica:
• Mica is a non-metallic mineral known for its insulating and heat-resistant properties.
• It is widely used in the electrical and electronics industries.
• Mica is found in states like Jharkhand, Rajasthan, and Andhra Pradesh in India.
• Cobalt:
• Cobalt is a metallic element primarily used in the production of rechargeable batteries, alloys, and catalysts.
• It is not an iron ore and is typically obtained as a by-product of nickel and copper mining.
• Globally, major cobalt-producing countries include the Democratic Republic of Congo, Russia, and Canada.
• Iron Ore in India:
• India has large reserves of iron ore, primarily found in states like Odisha, Karnataka, Chhattisgarh, and Jharkhand.
• Iron ore is a critical raw material for the steel industry, which forms the backbone of industrial development in the country.
• Important Points:
• Magnetite has the highest iron content, making it the finest quality iron ore.
• Hematite, though slightly lower in iron content, is more abundant and widely used.
• Mica and cobalt are not forms of iron ore and serve different industrial purposes.

The correct answer is Limited Test Ban Treaty.

Key Points

• The Limited Test Ban Treaty (LTBT), also known as the Partial Test Ban Treaty, was signed on 5 August 1963, and came into effect on 10 October 1963.
• The LTBT was the earliest arms control treaty aimed at banning nuclear weapon tests in the atmosphere, outer space, and underwater. It was a significant step toward reducing environmental contamination caused by nuclear testing.
• It was signed between the United States, the Soviet Union, and the United Kingdom, with later accession by other nations.
• The treaty did not ban underground nuclear tests, which were later addressed by other agreements.
• The LTBT was a landmark agreement during the Cold War era, showing international cooperation in reducing the dangers associated with nuclear weapons testing.

Additional Information

• Nuclear Non-Proliferation Treaty (NPT):
• The NPT was opened for signature on 1 July 1968 and came into force on 5 March 1970.
• It aims to prevent the spread of nuclear weapons, promote peaceful uses of nuclear energy, and achieve nuclear disarmament.
• The treaty has three pillars: non-proliferation, disarmament, and the right to peacefully use nuclear technology.
• While it is a crucial treaty in nuclear arms control, it does not specifically address nuclear testing bans.
• Strategic Arms Limitation Talks I (SALT I):
• SALT I was a series of negotiations between the United States and the Soviet Union in the early 1970s to limit the arms race.
• It resulted in the Anti-Ballistic Missile Treaty (ABM Treaty) and an interim agreement on the limitation of strategic offensive arms.
• These agreements were signed in 1972, but SALT I did not address nuclear testing.
• Comprehensive Nuclear Test Ban Treaty (CTBT):
• The CTBT was adopted by the United Nations General Assembly on 10 September 1996.
• It bans all nuclear explosions for both civilian and military purposes in all environments.
• As of October 2023, the treaty has not entered into force because some key states, including the United States and China, have not ratified it.
• Environmental and Political Impact of LTBT:
• The LTBT significantly reduced the fallout from atmospheric nuclear tests, which were causing widespread environmental and health issues.
• It was an important confidence-building measure during the Cold War, leading to further negotiations on arms control and disarmament.

Important Points

• Scope of LTBT:
• The treaty prohibited nuclear tests in the atmosphere, outer space, and underwater, but allowed underground tests.
• It was an important precursor to the Comprehensive Nuclear Test Ban Treaty (CTBT).
• Signatory Nations:
• The LTBT initially involved the United States, Soviet Union, and the United Kingdom. Other nations joined later, reflecting growing international support for arms control.
• Legacy of the LTBT:
• The treaty laid the foundation for future arms control agreements, including the CTBT and other disarmament initiatives.
• It demonstrated the possibility of cooperation between rival powers to address global security challenges.

The correct answer is Glucose.

Key Points

• Cellulose is a complex carbohydrate or polysaccharide made up of repeating units of glucose.
• The glucose units are linked together by β-1,4 glycosidic bonds, which form linear chains.
• Cellulose is the primary structural component of the cell walls in plants, providing rigidity and strength.
• Unlike starch, cellulose is not digestible by humans because we lack the enzyme cellulase required to break β-1,4 bonds.
• Cellulose is synthesized in plants from glucose molecules during photosynthesis, which is subsequently polymerized to form cellulose chains.

Additional Information

• Fructose:
• Fructose is a simple sugar (monosaccharide) found naturally in fruits, honey, and vegetables.
• It is not involved in the synthesis of cellulose.
• Fructose is used by the body for energy production but does not polymerize to form structural carbohydrates like cellulose.
• Sucrose:
• Sucrose is a disaccharide made of one molecule of glucose and one molecule of fructose.
• It is commonly known as table sugar and serves as an energy source rather than a structural component.
• Sucrose is not a building block for cellulose synthesis.
• Ribose:
• Ribose is a monosaccharide essential for the formation of nucleotides and nucleic acids like RNA and DNA.
• It is a five-carbon sugar and does not contribute to cellulose formation.
• Ribose is primarily used in genetic material synthesis rather than carbohydrate polymers like cellulose.
• Importance of Cellulose:
• Cellulose is the most abundant organic polymer on Earth.
• It is utilized in various industries for the production of paper, textiles, and biofuels.
• Its biodegradability makes it an environmentally sustainable material.
• 

Important Points

• Humans cannot digest cellulose due to the absence of cellulase, but it serves as dietary fiber, aiding digestion.
• Ruminants like cows and goats can digest cellulose with the help of symbiotic bacteria in their stomachs.
• Cellulose has applications in the production of biodegradable plastics and pharmaceuticals.

The correct answer is Hen and Crow.

Key Points

• Oviparous animals are those that lay eggs, with the embryo developing and hatching outside the mother’s body. Examples include birds, reptiles, amphibians, and most fish.
• Hen is a bird and an oviparous animal that lays eggs. The eggs are incubated to hatch into chicks. Hence, it is correctly classified as oviparous.
• Crow, like all birds, is an oviparous animal. It lays eggs, and the chicks hatch after a specific incubation period. Hence, it is also correctly classified as oviparous.
• Cat and Dog are mammals and are classified as viviparous animals. They give birth to live young ones, not eggs. Thus, they are not oviparous.
• Option 4 (Hen and Crow) is correct as both are oviparous animals. Options containing Cat and Dog, such as Option 1, Option 2, and Option 3, are incorrect.

Additional Information

• Characteristics of Oviparous Animals:
• Oviparous animals lay eggs, and fertilization can either be external (e.g., fish and amphibians) or internal (e.g., birds and reptiles).
• The eggs are protected by shells or membranes and contain nutrients for the developing embryo.
• Examples include birds like hens, reptiles like turtles, amphibians like frogs, and insects like butterflies.
• Viviparous Animals:
• These animals give birth to live young ones, with the embryo developing inside the mother's body.
• Nourishment is provided directly to the embryo through specialized structures like the placenta in mammals.
• Examples include mammals like cats, dogs, humans, and whales.
• Incubation in Birds:
• Birds like hens and crows incubate their eggs by sitting on them to provide warmth.
• The incubation period varies by species; for instance, a hen's egg typically hatches in about 21 days.
• Adaptations in Oviparous Animals:
• Eggs of oviparous animals have adaptations like hard shells (birds) or jelly-like coverings (amphibians) to protect against environmental factors and predators.
• Some oviparous animals exhibit parental care, such as guarding the eggs or constructing nests.
• Important Facts:
• Among vertebrates, mammals are predominantly viviparous, while most other classes like birds, reptiles, fish, and amphibians are oviparous.
• Insects, another major group of oviparous animals, often lay large numbers of eggs to increase the chances of survival.

The correct answer is Enzo Fernandez.

Key Points

• Enzo Fernandez was awarded the 'Young Player of the Tournament' at the FIFA World Cup 2022, held in Qatar.
• This award is given to the best-performing young player (under 21 years of age) in the tournament. Enzo Fernandez played a pivotal role in Argentina's success during the World Cup.
• He contributed significantly to Argentina's midfield with his dynamic gameplay, creativity, and defensive contributions. His standout performances included a crucial goal against Mexico in the group stage.
• Enzo Fernandez was only 21 years old during the tournament and was representing Argentina. He plays as a midfielder and showcased exceptional technical and tactical skills.
• His recognition as the 'Young Player of the Tournament' highlights his potential and marks him as one of the rising stars in international football.

Additional Information

• About Enzo Fernandez:
• Full Name: Enzo Jeremías Fernández.
• Date of Birth: 17 January 2001. He was born in San Martín, Argentina.
• He started his professional football career with River Plate in Argentina before moving to SL Benfica in Portugal.
• Fernandez is known for his passing accuracy, game vision, and ability to control the tempo of the game.
• FIFA 'Young Player of the Tournament' Award:
• This award was introduced in the 2006 FIFA World Cup to recognize the best young talent in the tournament.
• The recipient must be under the age of 21 at the beginning of the calendar year in which the World Cup is held.
• Previous notable winners include Kylian Mbappe (2018) and Paul Pogba (2014).
• FIFA World Cup 2022:
• The tournament was held in Qatar from 20 November to 18 December 2022.
• Argentina emerged as the champions, defeating France in a dramatic final that ended in a penalty shootout.
• Lionel Messi was awarded the 'Golden Ball' for being the best player of the tournament, while Kylian Mbappe won the 'Golden Boot' for scoring the most goals (8).
• Other Notable Performances:
• Kylian Mbappe: Scored a hat-trick in the final and was the top scorer of the tournament.
• Alexis Mac Allister: Played a crucial role in Argentina's midfield, complementing Enzo Fernandez.
• Rodrigo De Paul: Provided defensive stability and leadership in Argentina’s midfield.

The correct answer is Madhusudan Mishr.

Key Points

• Madhusudan Mishr was awarded the prestigious 'Sahitya Akademi Yuva Puraskar 2022' for his contribution to the Sanskrit language.
• The 'Sahitya Akademi Yuva Puraskar' is an annual award conferred by the Sahitya Akademi, India’s National Academy of Letters, to recognize young writers of exceptional talent in various Indian languages.
• The award aims to honor and promote the literary works of individuals aged below 35 years in India.
• Madhusudan Mishr’s work showcases the rich tradition of Sanskrit literature while incorporating modern themes, making it relevant to contemporary readers.
• The award includes a cash prize of Rs. 50,000 along with a plaque, symbolizing recognition of literary excellence.

Additional Information

• About Sahitya Akademi Yuva Puraskar:
• The award was instituted in 2011 by the Sahitya Akademi.
• It is presented in 24 Indian languages, including Sanskrit, Hindi, Tamil, Urdu, Bengali, and others.
• It recognizes and encourages young authors whose works reflect the diversity of Indian culture and language.
• Winners are selected based on the originality, creativity, and literary value of their work.
• Madhusudan Mishr:
• He is an emerging talent in the field of Sanskrit literature.
• His award-winning work is a testament to his ability to blend traditional Sanskrit literary forms with contemporary issues and themes.
• His contributions are significant in keeping the ancient language alive and relevant in modern times.
• Sanskrit Language:
• Sanskrit is one of the oldest languages in the world and is often referred to as the mother of many Indian languages.
• It is recognized as a classical language by the Government of India.
• Sanskrit has a rich literary tradition, including works like the Vedas, Upanishads, Mahabharata, Ramayana, and Puranas.
• Efforts are being made to revive and promote Sanskrit through various government initiatives, educational programs, and literary awards.
• Other Authors Nominated in 2022 (in Sanskrit):
• While other authors such as Pankaj Kumar Jha and Shruti Prasad Kanitkar have notable works, the award for Sanskrit language in 2022 was solely conferred upon Madhusudan Mishr.

The correct answer is A - IV, B - I, C - II, D - III.

Key Points

• USB (Universal Serial Bus):
• USB is a standard protocol designed to connect peripheral devices (such as keyboards, mice, external drives) to a computer.
• It enables serial data transmission, making it an efficient method for connecting and communicating with devices. Hence, the correct match for USB is IV.
• GUI (Graphical User Interface):
• GUI is a user interface that allows users to interact with electronic devices using graphical icons and visual indicators, rather than text-based interfaces or command-line prompts.
• It simplifies user interaction with programs through linked image objects. Hence, the correct match for GUI is I.
• GIF (Graphics Interchange Format):
• GIF is a widely-used file format for compressed image files, enabling faster loading of images on websites.
• It supports both static and animated images. Hence, the correct match for GIF is II.
• OCR (Optical Character Recognition):
• OCR is a technology that converts scanned text or images of text into machine-readable text formats (e.g., ASCII code).
• It is extensively used for digitizing printed documents. Hence, the correct match for OCR is III.

Additional Information

• USB (Universal Serial Bus):
• USB was first introduced in 1996 and has since evolved into various versions, such as USB 2.0, USB 3.0, and USB-C.
• It supports plug-and-play functionality, making device connections easier without requiring complex installation procedures.
• USB is used in devices globally for charging and data transfer, and it supports numerous peripherals, including printers, cameras, and smartphones.
• GUI (Graphical User Interface):
• GUI was first developed by Xerox PARC in the 1970s and popularized by companies like Apple and Microsoft.
• It is widely used in operating systems such as Windows, macOS, and Linux, enabling user-friendly navigation and functionality.
• GUI-based systems have replaced traditional command-line interfaces in most consumer electronics.
• GIF (Graphics Interchange Format):
• GIF was introduced by CompuServe in 1987 and remains popular for sharing short, animated clips.
• It uses lossless compression, ensuring that image quality is preserved while reducing file size.
• GIFs are widely used on social media platforms and websites for visual communication.
• OCR (Optical Character Recognition):
• OCR technology emerged in the 1950s, with advancements enabling high-speed text recognition in modern applications.
• It is used in various industries, including banking, document management, and legal services, to digitize and automate text processing.
• Popular OCR software includes Adobe Acrobat, ABBYY FineReader, and Google Drive OCR.

The logic followed here is:

Thus, the missing number in the series is "336".

Hence, the correct answer is "Option 2".

Total number of books: 9. Positions are counted from the bottom (1) to the top (9).

1. Counting from the bottom, the third and seventh books are Text Books.

• Position 3: Text Book (TB)
• Position 7: Text Book (TB)

 

2. One book on plays is above the Text Book and another book on plays is below the Text Book.

3. One book on poetry is above the book on plays, and the other book on poetry is below the book on plays. 

Case II is not possible as one place is remaining and there are two poetry books.

 

4. Two books of General Awareness are below a story book.

 

The book at the fifth from the bottom is the "General Awareness Book".

Hence, the correct answer is "Option 4".

Given that: 'North-East' is called 'West', 'South-East is called 'North', 'South-West' is called 'East', and 'North-West' is called 'South'.

The conventional direction diagram is given below:

Rotating the given diagram, 135º clockwise, in order to make South-East as North, we get the diagram as below:

From the figure, it is clear that East is called as North-West in the given system.

Hence, the correct answer is "Option 1".

Given:

Question: Rohan is in which direction with respect to Pankaj?

Statement I Analysis

I: Rohan is to the South of Tanya who is to the East of Dolly.

Conclusion: Statement I alone gives the relative positions of Rohan, Tanya, and Dolly. It does not mention Pankaj.

Therefore, Statement I alone is not sufficient.

Statement II Analysis

II: Pankaj is to the East of Tanya.

Conclusion: Statement II alone gives the relative position of Pankaj with respect to Tanya. It does not mention Rohan.

Therefore, Statement II alone is not sufficient.

Combining I and II:

​

The direction of Rohan from Pankaj is "South-West".

Both statements I and II together are necessary to answer the question.

Hence, the correct answer is "Option 3"

The logic followed here is,

We are looking for the number that represents female post-graduates, sub-inspectors of police.

​The number must be in the region common to the circle and the square, but outside the triangle.

The figure represents the following categories:

Therefore, 12 represents female post-graduates who are sub-inspectors of police.

Hence, the correct answer is "Option 4".

The correct answer is MS PowerPoint.

Key Points

• MS Paint: This is a basic graphics editing application that is included by default in all MS Windows installations.
• Notepad: Notepad is a simple text editor that comes pre-installed with Windows for editing plain text files.
• Clock: The Clock application is also a default feature in Windows, providing a simple time and alarm management tool.
• MS PowerPoint: MS PowerPoint is part of the Microsoft Office suite and is not included by default in the Windows operating system. It requires separate installation.

Additional Information

• Microsoft Office Suite: Applications like MS Word, MS Excel, and MS PowerPoint are part of the Microsoft Office suite, which is a separate software package that needs to be purchased and installed on Windows.
• Default Windows Applications: Applications like Calculator, Paint, Notepad, and Clock are pre-installed with Windows to provide basic functionalities to users.

The correct answer is Option 4 (addition).

Key Points

• MS Excel provides various built-in functions to perform calculations, analyze data, and manipulate values.
• Functions like count(), sum(), and max() are standard and basic functions in MS Excel. They are used to count cells, calculate the sum of values, and find the maximum value, respectively.
• However, "addition()" is NOT a function in MS Excel. Instead, Excel uses the sum() function to perform addition operations.
• Thus, "addition()" is not a valid or basic function in MS Excel.

Additional Information

• count(): Counts the number of cells containing numerical data in a range.
• sum(): Adds up all the numerical values in a given range.
• max(): Returns the largest value from a range of numbers.
• addition(): Not a valid function in MS Excel; use the sum() function instead.

The correct answer is Collection of chosen cells.

Key Points

• In MS Excel, a cell range is a collection of selected or chosen cells.
• A cell range can consist of contiguous cells (e.g., A1:B5) or non-contiguous cells (e.g., A1, C1, E1).
• Ranges are often used to perform operations such as formatting, formula application, or data analysis on multiple cells simultaneously.
• A range is referenced using the addresses of the first and last cell in the selection, separated by a colon (e.g., A1:D10).

Additional Information

• Collection of formula: This refers to a set of formulas used in a worksheet but does not define a cell range.
• Collection of values: This refers to data or numbers in the cells, but it does not explain what a cell range is.
• Collection of occupied cells: This includes all cells with data but is not the definition of a cell range. A cell range can also include empty cells.
• Cell range: It can include empty or filled cells based on the user's selection in the spreadsheet.

The correct answer is Theft of a brand new hard disk from a showroom.

Key Points

• Cybercrime refers to any criminal activity that involves the internet, computers, or digital systems.
• Activities that can be classified under cybercrime include hacking, online threats, unauthorized access to someone's account, and sharing illicit content.
• In this case:
• Threatening someone on social media, sharing pornographic content online, and accessing someone’s online bank account without consent are all examples of cybercrimes.
• Theft of a physical item (e.g., a hard disk from a showroom) is not a cybercrime, as it does not involve the misuse of a computer or digital system.

Additional Information

• Cybercrime Categories: Cybercrime can be categorized into three main types:
• Computer as a Target: Attacks like hacking, denial of service attacks, or spreading viruses.
• Computer as a Tool: Using computers to commit crimes like fraud, identity theft, or phishing.
• Computer as a Communication Medium: Harassment, threats, or sharing illicit content through digital platforms.
• Physical Crime vs. Cybercrime: Stealing a physical object, such as a hard disk, is considered theft or robbery and falls under traditional criminal law, not cybercrime.

The correct answer is Secure.

Key Points

• The 'S' in HTTPS stands for Secure.
• HTTPS (HyperText Transfer Protocol Secure) is an extension of HTTP (HyperText Transfer Protocol).
• It is used to ensure secure communication over a computer network, especially the internet.
• HTTPS uses encryption protocols such as SSL (Secure Sockets Layer) or TLS (Transport Layer Security) to secure data exchange.
• It helps in protecting sensitive information such as passwords, credit card details, and personal data from being intercepted by malicious actors.

Additional Information

• HTTP (HyperText Transfer Protocol): It is a protocol used for transmitting hypertext over the web, but it does not provide secure communication.
• SSL/TLS: Secure Sockets Layer and Transport Layer Security are cryptographic protocols that provide end-to-end security of data sent between applications over the internet.
• Encryption: HTTPS encrypts data so that it becomes unreadable to unauthorized parties, ensuring data confidentiality and integrity.
• Browser Indication: HTTPS-enabled websites are usually indicated by a padlock symbol in the browser's address bar.

The proximodistal principle is a fundamental concept in human development, particularly in the study of physical growth and motor development in children. It describes the pattern in which motor skills and body control develop from the center of the body outward toward the extremities. 

Key Points

• According to this principle, a child first develops control over the central parts of the body such as the torso and shoulders.
• Gradually, development progresses outward toward the hands, fingers, and legs, allowing for more precise movements.
• This explains why infants can control their arms before mastering fine finger movements or why gross motor skills appear before fine motor skills.

 Hint

• The head to legs pattern describes the cephalocaudal principle, which is different from proximodistal development.
• The legs to head sequence is not observed in typical human development.
• Outward to the center of the body is the opposite direction of the proximodistal principle and does not reflect how motor skills actually emerge.

Hence, the correct answer is the center of the body outward.

Adam's apple is a term commonly used in anatomy and human development, particularly during puberty. It refers to the noticeable protrusion in the front of the neck, which becomes more prominent in males due to hormonal changes. 

Key Points

• The protruding part of the throat in male adolescents becomes prominent because of the enlargement of the thyroid cartilage during puberty.
• This growth is more noticeable in males than females due to higher testosterone levels, which makes the voice deeper and gives the characteristic bulge.
• An endocrine gland that releases hormones refers to structures like the thyroid or pituitary gland, not the Adam's apple.
• The embryonic outgrowth during the prenatal stage, such as the pharyngeal arches, is unrelated to postnatal throat development.
• The protruding part of the throat in female adolescents is much less prominent and usually not referred to as an Adam's apple.

Hence, the correct answer is the protruding part of throat of male adolescents.

The concepts of growth, development, and maturation are central in understanding human physical and behavioral changes over time.

 Key Points

• Growth generally refers to measurable physical changes like height and weight, while development encompasses the acquisition of skills, abilities, and functions.
• Maturation specifically describes the natural unfolding of biological processes that occur with age, independent of formal teaching or training.
• When an 8-month-old child begins to crawl without being taught, it reflects the natural biological timetable of the body and nervous system. Crawling emerges as the child’s muscles, coordination, and nervous system mature, even without explicit instruction.
• This ability appears as part of the inherent biological unfolding rather than learned behavior, which aligns directly with the concept of maturation.

 Hint

• Growth refers only to physical increase in size, which is not what is being described here.
• Development includes learned behaviors and skill acquisition, which may involve teaching or practice.
• Morphogenesis is about the formation of structures in the organism, not about the onset of motor skills like crawling.

Hence, the correct answer is maturation.

Growth, development, and maturity are closely related concepts in human development.

Key Points

• Development represents the ongoing process through which an individual acquires new abilities, skills, and functions over time.
• Growth is part of this process as the body changes physically and structurally.
• Maturity is the outcome or product of these processes, representing the full development of physical and functional capabilities.
• Growth and maturity are distinct concepts, with growth being only a part of development and maturity the end result.
• Development and maturity cannot be simply linked as process and product of growth because development encompasses more than just physical growth.
• Progress and maturity is a less precise formulation since “progress” is a broader term not strictly equivalent to growth or development.

Hence, the correct answer is Development and growth are the process and product of maturity.

Human development is multidimensional, encompassing physical, cognitive, emotional, moral, and social aspects. Moral development specifically refers to the process through which an individual learns the difference between right and wrong and internalizes values and ethical standards. 

Key Points

• When an individual acquires values that society expects them to practice, it reflects the internalization of ethical norms and principles. This is not just about following rules but about developing a sense of right and wrong, fairness, and justice.
• Moral development shows the person’s capacity to make decisions that align with societal moral expectations.

 Hint

• Social development involves learning to interact and communicate with others, but it does not necessarily involve moral judgment.
• Emotional development refers to understanding and managing feelings, not the adoption of societal values.
• Spiritual development concerns beliefs and practices related to the human spirit or soul, which may or may not include societal moral norms.

Hence, the correct answer is moral development.

Human learning and teaching are closely linked to the developmental readiness of students.

 Key Points

• Cognitive development refers to the growth of thinking, reasoning, and problem-solving abilities in learners. In mathematics, the sequencing of concepts is designed to match students’ cognitive capacity, ensuring that foundational ideas are understood before introducing more complex ones.
• Teaching simple interest before compound interest aligns with students’ cognitive development because simple interest is a basic concept that involves straightforward calculation and understanding.
• Once students grasp this, they are better prepared to handle the more complex idea of compound interest, which requires higher-order thinking and the ability to apply previous knowledge. This progression ensures that learning builds on existing mental structures, facilitating effective understanding.

 Hint

• Physical development relates to growth and motor skills, not mathematical reasoning.
• Social development involves interaction, communication, and social skills, which are not the focus here.
• Moral development deals with understanding right and wrong, which is unrelated to the order of teaching mathematical concepts.

Hence, the correct answer is cognitive development of the students.

Human physical growth follows specific patterns, with different parts of the body developing at different rates. In infants, the head is relatively large compared to the rest of the body because the brain and skull develop earlier and faster than other body parts.

Key Points

• In human infants**, the head constitutes about one-fourth of the total body length.** This relatively large proportion supports rapid brain growth during early life.
• As the child grows, the rest of the body gradually catches up, and the head becomes proportionally smaller compared to total body length. This explains why infants appear top-heavy with a prominent head compared to their torso and limbs.

Hence, the correct answer is one-fourth.

Human development encompasses multiple domains, including cognitive, emotional, social, and metacognitive growth. 

Key Points

• When infants show general excitement to strong stimulation, such as loud sounds, bright lights, or playful interaction, it reflects their emotional responsiveness.
• This excitement is a basic form of emotional expression and regulation, indicating how the infant experiences joy, surprise, or interest.
• These reactions are part of their emotional behavior, helping caregivers gauge the child’s feelings and emotional health.

 Hint

• Metacognitive skills involve self-awareness and regulation of one’s own thinking, which infants have not yet developed.
• Cognitive growth relates to thinking and problem-solving, not the immediate emotional reaction.
• Socialization involves interacting with others and learning societal norms, which is broader than simple excitement to stimuli.

Hence, the correct answer is emotional behaviour.

Adolescence is a period of rapid and noticeable changes across multiple domains of human development, including physical, cognitive, social, emotional, and spiritual growth. 

Key Points

• In adolescents, physical development is particularly striking because it involves visible changes like increased height, weight, and the development of features such as the Adam’s apple in males and breast development in females.
• These changes occur rapidly and are easily observed by peers, family, and teachers.
• Cognitive development, although critical, progresses internally through reasoning, abstract thinking, and problem-solving, making it less outwardly visible.

 Hint

• Spiritual development occurs internally and is subtle, often not directly observable.
• Cognitive development is less visible than physical development because thinking processes and intellectual growth cannot be directly seen.
• Social development, while noticeable in interactions, still does not surpass the visual impact of physical changes during adolescence.

Hence**, the correct answer is their physical development is more visible than cognitive development.**

Human development during adolescence is multidimensional, involving physical, cognitive, emotional, social, and moral growth.

 Key Points

• Interpersonal growth refers to the ability to interact effectively with others, forming relationships and understanding social norms, which is a key aspect of social development. Intrapersonal growth, on the other hand, involves self-awareness, self-reflection, and understanding one’s own thoughts and emotions, which are closely linked to cognitive development.
• Interpersonal growth in adolescents reflects their social development because it shows how they form friendships, resolve conflicts, and communicate with peers and adults.
• Intrapersonal growth shows their cognitive development, as it involves thinking about one’s own beliefs, planning, problem-solving, and decision-making.

 Hint

• Moral development is related to understanding right and wrong but is not specifically indicated by interpersonal or intrapersonal growth.
• Emotional development involves feelings and emotional regulation, which may influence but do not fully define these growth patterns.

Hence**, the correct answer is social development and cognitive development respectively.**

Adolescence is a stage of cognitive development where thinking shifts from concrete to more abstract and complex forms. According to Piaget, during this stage, individuals develop the ability to reason hypothetically, understand symbols, and think beyond immediate experiences. 

Key Points

• When a teacher uses the idiom “A leopard can’t change his spots,” adolescents are capable of interpreting its figurative meaning that a person’s basic nature does not change because they can engage in symbolic thinking.
• They are able to go beyond the literal words and derive abstract or symbolic meaning, reflecting their developing cognitive abilities. This shows that adolescents can handle language that conveys concepts indirectly through symbols or cultural expressions.

 Hint

• It is not accurate to say students cannot understand it due to dominance of concrete thinking, because by adolescence, abstract thinking is well-developed.
• Imagining the impossible may occur, but the key factor is their ability to use symbols to interpret meaning, not mere imagination.
• Critical thinking does not prevent understanding the idiom; rather, it may help evaluate its application, but it does not block comprehension.

Hence, the correct answer is students may understand it as they can use symbolic thinking to derive its meaning.

The study of society and its origins often involves looking at the etymology of the term.

 Key Points

• The word “society” comes from the Latin word “societas,” which refers to fellowship, association, or companionship.
• This origin reflects the basic human tendency to form groups, communities, and relationships, emphasizing cooperation and collective living.
• “Societas” in Latin specifically conveys the idea of people coming together for common purposes, mutual support, and organized interaction.
• This aligns with the modern sociological understanding of society as a complex system of relationships and institutions. It explains why the term society carries connotations of connectedness and group living rather than just a collection of individuals.

Hence, the correct answer is Latin word.

The concept of community has been central to sociology and philosophy, as it helps explain how individuals come together to form social groups with shared interests, norms, and values. 

Key Points

• Auguste Comte, often regarded as the father of sociology, focused on the structures of society and the ways in which human beings organize themselves.
• He emphasized that a community is not merely a collection of individuals but a group established by humans who share common values and norms, which guide their interactions and maintain social order.
• This aligns directly with the idea of community being formed through shared human values rather than just physical proximity or economic relations.

 Hint

• Karl Marx, in contrast, analyzed communities mainly in terms of class relations and economic structures rather than shared moral or cultural values.
• Aristotle discussed the community from a philosophical and political perspective, focusing on the polis and the role of citizens in achieving a good life.
• Émile Durkheim studied community in terms of social cohesion and collective consciousness, emphasizing the functional aspects of society.

Hence, the correct answer is Comte.

Socialization is the lifelong process through which individuals learn the norms, values, behaviors, and roles necessary to participate in society. It is generally categorized into primary socialization, which occurs in early childhood within the family, and secondary socialization, which happens later through schools, peer groups, and broader social institutions. 

Key Points

• Primary socialization typically comes first, providing the child with foundational behaviors and norms, in some cultural contexts, experiences outside the family such as interactions in early childhood programs or communal activities may introduce elements of secondary socialization before certain primary socialization aspects are fully established.
• This shows that the sequence is not always strictly linear and can vary depending on cultural practices and societal structures.

 Hint

• The idea that primary and secondary socialization run strictly parallel is less accurate because early childhood experiences generally have a foundational role.
• Secondary socialization taking place only after primary socialization overlooks cultural variations where children may be exposed to organized societal norms before completing initial family-based learning.
• Suggesting entirely different trajectories fails to capture the interconnected nature of these socialization processes.

Hence, the correct answer is In some cultures, secondary socialization may precede primary socialization.

Adverse situations such as the COVID-19 pandemic have had a profound impact on education systems worldwide. School closures, social distancing measures, and restrictions on gatherings disrupted traditional classroom learning, forcing educators, parents, and students to adapt rapidly.  

Key Points

• During the pandemic, many families turned to home-based education to ensure continuity of learning when schools were closed.
• This led to a significant increase in home schooling, with parents taking a more active role in guiding their children’s education or using online learning platforms to compensate for the lack of formal school instruction.
• It reflects a shift in educational practices in response to extraordinary circumstances rather than a change in formal school enrolment trends.

 Hint

• An increase in enrolment in formal education was not observed as schools were largely closed.
• Non-formal education programs also faced disruptions, making a decrease in enrolment more context-specific but not the primary global trend.
• The notion of brain drain is unrelated to immediate educational adaptations during the pandemic.

Hence, the correct answer is increase in home schooling.

Curriculum is a structured plan of learning experiences designed to achieve specific educational goals. For teachers, it serves as a guide for what to teach, how to teach, and the desired outcomes of the teaching-learning process.

Key Points

• For teachers, curriculum is crucial because it clearly establishes their responsibilities and accountability. It defines what they are expected to teach, the skills and knowledge students should acquire, and the standards they need to uphold.
• This helps teachers plan lessons, assess student progress, and reflect on their own professional practice, ensuring that educational goals are systematically achieved.

​ Hint

• While it can indirectly guide how external resources are used, its primary function is not just about resource utilization.
• Acting as a control device refers more to administrative oversight rather than pedagogical guidance.
• Developing understanding about environmental preservation may be a component of specific curricula but does not capture the overarching importance of curriculum for teachers’ roles.

Hence**, the correct answer is establishes responsibilities and accountability.**

Curriculum organization is guided by principles that ensure learning is effective, meaningful, and suited to the needs of learners. These principles help in structuring content, learning experiences, and instructional strategies so that students can engage actively, develop skills, and achieve educational goals. 

Key Points

• While child centeredness, creativity, and flexibility are fundamental principles focusing on the learner’s needs, fostering innovation, and allowing adaptation to changing circumstances—self learning, though valuable, is more of a learning strategy than an overarching principle of curriculum organization.
• Curriculum principles are intended to guide the overall design and structure, rather than prescribing specific methods for individual learning.
• Principles like child centeredness ensure relevance and engagement, creativity promotes innovative thinking, and flexibility allows the curriculum to respond to societal and learner needs. Self learning can be encouraged within the curriculum but does not define its organizational framework.

Hence, the correct answer is principle of self learning.

Experiential learning is a process through which learners acquire knowledge and skills by actively engaging in experiences and reflecting on them. David Kolb’s experiential learning cycle outlines a continuous process where learning occurs through a sequence of stages, allowing learners to connect theory with practice and improve their understanding through reflection and experimentation.

<br>

Key Points

• The experiential learning cycle consists of concrete experience, where learners actively engage in a task; reflective observation, where they reflect on the experience; and active experimentation, where they test their insights in new situations.
• Critical analysis, while useful in evaluating experiences, is not explicitly identified as a separate stage in Kolb’s model. It may be part of reflection but is not formally a component of the cycle itself.
• Concrete experience provides hands-on engagement, reflective observation allows understanding and insight, and active experimentation applies learning in practical contexts.
• Critical analysis is a skill used during reflection but does not form a distinct stage of the experiential learning process.

Hence, the correct answer is critical analysis.

Self-assessment is a process in which students evaluate their own learning, performance, and understanding. It encourages learners to take responsibility for their progress, develop critical thinking, and become more aware of their strengths and areas needing improvement.

 Key Points

• Through self-assessment, students can reflect on their own learning, identify areas of strength and weakness, and develop skills in metacognition, which help them plan, monitor, and evaluate their learning strategies.
• However, consolidation of learning through dialogue typically requires interaction with teachers or peers and involves discussion, feedback, and collaborative understanding, which goes beyond individual self-assessment.
• Reflection allows learners to internalize their experiences, metacognition enhances awareness of learning processes, and identifying strengths and weaknesses helps set personal learning goals.
• Dialogue-based consolidation is more of a social learning process rather than an outcome of self-assessment.

Hence, the correct answer is consolidation of their learning through dialogue.

Textbooks are a central resource in classroom teaching, providing structured content, exercises, and guidance for both teachers and students. They serve as a reference point, help organize lessons, and support the evaluation of learning outcomes. 

Key Points

• Textbooks are indeed useful as teaching aids, help teachers maintain a logical sequence of content, and provide guidelines for evaluating students’ learning.
• However, they may not inherently encourage convergent thinking, which involves finding multiple solutions or creative approaches to problems.
• Textbooks are generally structured with predefined content and exercises, which may limit open-ended exploration and creative or divergent thinking.
• They assist teachers in planning lessons, maintaining content order, and assessing student performance.
• Convergent thinking and creativity in learners usually require additional instructional strategies beyond merely following textbook chapters.

Hence, the correct answer is encourages convergent thinking among learners through its chapters and exercises.

Multimedia systems combine text, audio, images, animation, and video to create interactive and engaging learning experiences. They are widely used in education, training, and communication because they can enhance understanding, stimulate interest, and develop higher-order thinking skills.

 Key Points

• Effective use of multimedia requires careful planning and thoughtful integration into the learning process.
• Multimedia systems are interactive tools that can sharpen problem-solving and decision-making skills when used appropriately. Their use must be judiciously planned to align with learning objectives and avoid distractions.
• However, social loafing, which refers to reduced individual effort when working in a group, is a social phenomenon unrelated to the inherent characteristics of multimedia systems.
• Interactivity allows learners to engage actively with content, planning ensures effectiveness, and cognitive benefits enhance learning outcomes.
• Social loafing is a behavioral issue in group settings, not a feature of multimedia technology itself.

Hence, the correct answer is social loafing.

Assessment items are designed to evaluate different levels of learning, ranging from knowledge recall to higher-order thinking skills. They can be broadly categorized into objective-type items, which have specific correct answers, and extended-response items, which require students to elaborate or explain their understanding. 

Key Points

• Extended-response items, such as essays, allow students to express ideas in depth, while multiple-choice items use distracters to test recognition and understanding.
• Matching items are a type of objective question where students pair related items, making them similar in structure to multiple-choice questions.
• However, objective-type items, which are generally designed for quick recall or recognition, are not ideal for measuring creative ability, which requires open-ended responses, critical thinking, and original expression.
• Objective items are efficient for testing factual knowledge but do not capture creativity.
• Extended-response items support deeper thought, and matching and multiple-choice formats are suitable for evaluating comprehension and recognition skills.

Hence, the correct answer is objective type of item are more preferable in measuring the creative ability of students.

Group learning is an instructional approach where students work collaboratively to achieve shared learning goals. While it promotes discussion, critical thinking, and social skills, it also comes with challenges. Understanding these difficulties helps teachers design group activities that maximize benefits while minimizing potential drawbacks.

Key Points

• Difficulties in group learning often include the absence of a systematic approach, lack of coordination among participants, and social pressures on individuals to conform to group opinions.
• However, easy identification and correction of errors is actually an advantage of group learning, as peers can provide immediate feedback and support each other in understanding mistakes. This process enhances collective learning and problem-solving rather than being a difficulty.
• Other challenges involve managing participation, ensuring fairness, and maintaining focus on learning objectives. Peer interaction can be both a strength and a challenge depending on how the group is structured and facilitated.

Hence, the correct answer is easy identification and correction of errors.

In a constructivist approach to learning, teachers act as facilitators who guide students in constructing their own knowledge rather than simply transmitting information.

Key Points

• The teacher’s role involves creating an environment where learners actively engage, reflect, and collaborate to build understanding, critical thinking, and problem-solving skills.
• Teachers encourage students to ask questions, promote self-analysis and self-assessment, foster reflective practice, and support cooperative and collaborative learning.
• Discouraging self-analysis and self-assessment, however, goes against the principles of knowledge construction, as these activities help learners evaluate their own understanding, identify gaps, and take ownership of their learning.
• Encouraging inquiry and collaboration enhances engagement, while reflective practice deepens comprehension.
• Preventing self-assessment would hinder students’ ability to internalize knowledge and become independent learners.

Hence, the correct answer is discouraging self analysis and self assessment.

The learner-centered approach emphasizes active engagement, critical thinking, and meaningful learning experiences. It shifts the focus from teacher-led instruction to student-driven exploration, encouraging learners to construct knowledge through interaction, experimentation, and collaboration. 

Key Points

• Learner-centered classrooms prioritize learning by doing, support both individual and group learning, and foster democratic environments where students have a voice in their learning.
• However, learning that focuses primarily on memorization of textual questions is teacher-centered, as it emphasizes rote learning rather than understanding, application, or critical thinking.
• Active engagement, collaboration, and democratic participation are key features, whereas rote memorization limits learner involvement and reduces opportunities for constructing knowledge.

Hence, the correct answer is learning and memorization of textual questions.

Teaching-learning methods provide structured ways for students to acquire knowledge, develop skills, and engage in critical thinking. Different methods emphasize various approaches, such as guided inquiry, experimentation, and reflection, to promote active learning and problem-solving abilities.  

Key Points

• The sequence described—identifying problems, experimentation and observation, problem solving, and evaluation—aligns with the problem-solving method.
• This method encourages learners to recognize an issue, explore possible solutions through investigation, apply reasoning to resolve it, and finally evaluate the outcome.
• It emphasizes analytical thinking and structured inquiry rather than merely memorizing content.

 Hint

• Project method typically involves extended investigations on a topic, discovery method emphasizes uncovering concepts through guided exploration, and inductive method focuses on deriving general principles from specific observations.

Hence, the correct answer is problem-solving method.

A portfolio is a systematic collection of a student’s work over time that demonstrates learning, achievements, and areas for improvement. It serves as both a learning and assessment tool, encouraging reflection, goal-setting, and active participation in evaluating one’s own progress.

 Key Points

• Portfolios also facilitate communication between teachers, students, and parents regarding learning outcomes.
• Portfolios help students evaluate the strengths and weaknesses of their work, reflect on their progress, and take responsibility for setting goals.
• They also create opportunities for collaboration and ongoing dialogue about learning.
• However, the idea that parents have only a rare opportunity to assess their child’s performance is inaccurate, as portfolios are specifically designed to provide regular, accessible insights into student learning for both teachers and parents.
• Reflection, goal-setting, and self-evaluation are key strengths, whereas limiting parental access does not align with the purpose of a portfolio.

Hence, the correct answer is parents have rare opportunity to assess the performance of their children.

Transdisciplinary integration involves connecting knowledge and skills across multiple subjects to address real-world problems or themes. In this approach, learning is not confined to a single discipline; instead, students explore concepts in an interconnected manner.

 Key Points

• Teachers play a crucial role in guiding this process, helping learners see relationships between disciplines and apply knowledge meaningfully.
• In transdisciplinary integration, the teacher acts as a facilitator, supporting students as they explore, inquire, and construct understanding across subject boundaries.
• The teacher guides discussions, provides resources, and encourages critical thinking, rather than being the sole source of knowledge.
• Acting as a co-learner or specialist is secondary, as the emphasis is on enabling students to make connections themselves.

Hence, the correct answer is facilitator.

Classroom discussion is an essential instructional strategy that promotes critical thinking, idea exchange, and active learning. Its effectiveness depends not only on the teacher’s skills or content knowledge but also on the engagement, motivation, and shared focus of the learners.

 Key Points

• A productive discussion requires a conducive environment where participants are genuinely interested and aligned in purpose.
• While the teacher’s skill and mastery of the topic are important, the basic determinant of a good discussion is the unity of purpose and interest among students.
• When students share a common focus and are genuinely interested in the topic, discussions become meaningful, interactive, and productive. Without this shared engagement, even a skilled teacher or well-prepared content may fail to generate meaningful dialogue.
• Content quality and teacher expertise support discussion, but the collective interest and purposeful participation of students drive its success.
• A discussion thrives when learners are motivated, attentive, and collaboratively exploring ideas.

Hence, the correct answer is unity of purpose and interest in the class.

Educational objectives serve as clear statements of what learners are expected to achieve through instruction. They provide direction for curriculum design, lesson planning, instructional strategies, and assessment. 

Key Points

• Objectives of education guide understanding of child development by indicating the skills, knowledge, and attitudes learners should acquire at various stages.
• They assist in selecting instructional materials and designing learning experiences that align with these goals. They also help in preparing evaluation tools to measure whether learning outcomes have been achieved.
• However, they do not directly contribute to understanding the developmental psychology of the child itself; rather, they focus on planning and assessing learning.
• While objectives influence teaching and assessment, they are not a primary tool for analyzing or understanding a child’s growth patterns or developmental stages. They are designed to structure learning experiences rather than study child development scientifically.

Hence, the correct answer is understanding child development.

Mental health in educational settings is crucial for both students and teachers, as it affects learning, teaching effectiveness, and overall well-being.

Key Points 

• Modern approaches to mental health emphasize holistic practices that balance physical, mental, and emotional wellness, helping individuals manage stress, improve concentration, and enhance resilience.
• Practices like Yogasana and Pranayama are particularly effective because they combine physical postures, controlled breathing, and mindfulness, which reduce stress, improve focus, and promote emotional stability.
• These techniques support both mental and physical health, making them well-suited for sustaining overall well-being in the school environment.
• Yogasana and Pranayama integrate mind-body practices, enhance concentration, and reduce anxiety, making them highly effective for educational settings. Other activities may have benefits but do not comprehensively address mental health.
• Physiotherapy mainly addresses physical rehabilitation, mathematical exercises enhance cognition but not emotional wellness, and social gatherings may promote interaction but do not systematically improve mental health.

Hence, the correct answer is Yogasana and Pranayam.

The Rights of Persons with Disabilities Act is a significant legislation in India aimed at protecting the rights and ensuring the inclusion of persons with disabilities in all aspects of society, including education, employment, and accessibility.

 Key Points

• It replaced the earlier Persons with Disabilities Act of 1995 to align with the United Nations Convention on the Rights of Persons with Disabilities (UNCRPD), reflecting a more progressive approach toward disability rights.
• This Act defines various types of disabilities, emphasizes equal opportunities, and mandates accessibility, non-discrimination, and inclusive education. It also outlines the responsibilities of the government, educational institutions, and employers to facilitate participation and empowerment of persons with disabilities.
• The legislation came into effect in 2016, marking a key milestone in promoting rights and inclusion for differently-abled individuals.

Hence, the correct answer is 2016.

Educational progress varies across different social groups due to historical, economic, and social factors. Understanding which groups constitute the largest population in terms of education helps policymakers and educators target interventions effectively. 

Key Points

• Among the given groups, girls represent the largest demographic in the context of education because they comprise roughly half of the total student population.
• While tribal populations, scheduled castes, and slum dwellers are significant in number, they are subsets of the overall population, whereas girls span all social, economic, and geographic categories.
• Educational policies increasingly focus on ensuring gender parity and improving girls’ enrollment and retention across all levels of schooling.

Other groups, such as tribals and scheduled castes, are important targets for inclusive education programs, and slum dwellers face localized challenges, but in sheer numbers, girls form the largest group in the educational landscape.

Hence, the correct answer is girls.

In inclusive education, teachers often encounter students with diverse learning needs and disabilities. The ability of a teacher to handle a child depends on the severity of the condition, the support required, and the teacher’s training. 

Key Points

• A child with an IQ of 72 falls in the borderline range of intellectual functioning. Such a child can often be supported effectively in a regular classroom with adjustments, remedial teaching, and individualized attention.
• Teachers can use simplified instructions, peer support, and structured learning activities to help these students achieve academic and social goals.
• In contrast, children with autism, dyscalculia, or psychosis may require specialized therapies, individualized education plans, or professional mental health interventions that go beyond typical classroom strategies.

Hence**, the correct answer is a child with an IQ of 72.**

Partnerships in education help schools enhance learning opportunities, access resources, and foster community engagement. The ease of forming partnerships depends on accessibility, shared interests, and the level of collaboration required. 

Key Points

• Parents and the community are the most accessible and cooperative partners for a school. They are directly invested in the students’ education, can support classroom activities, contribute resources, and participate in school programs.
• Their involvement requires minimal formal procedures compared to industries or government offices, which may involve bureaucratic processes, formal agreements, and alignment of objectives.
• Collaborating with parents and community members promotes active involvement, mutual support, and shared responsibility in education, making it the most practical first step for partnership.
• Neighboring schools may collaborate academically, but community and parental engagement is generally easier to initiate and sustain.

Hence, the correct answer is parents and community.

Partnerships between higher education institutions and schools can enhance the quality of education by providing expertise, resources, and professional development. Effective collaboration helps bridge gaps in curriculum, teaching skills, and student learning experiences, benefiting both teachers and students.

<br>

Key Points

• Higher education institutions can develop the best partnerships with schools by organizing competency-based activities for school teachers.
• Such programs build teachers’ skills, update their knowledge, and improve instructional practices, which directly impacts classroom learning.
• Training alone or merely sharing resources may not ensure practical improvement, and selecting top-performing students for advanced materials benefits only a few rather than strengthening the overall school-teacher ecosystem.
• Competency-based activities focus on enhancing teachers’ effectiveness, enabling sustainable improvements in student outcomes and fostering a collaborative relationship between institutions.

Hence, the correct answer is organizing competency based activities for school teachers.

Developing a spirit of enquiry and awareness among secondary school learners is essential for fostering critical thinking, curiosity, and independent problem-solving.

 Key Points

• Educational strategies that actively engage students in exploration, hands-on activities, and collaborative learning are most effective in cultivating these qualities.
• Hobby clubs provide students with opportunities to explore their interests, engage in practical activities, ask questions, and experiment in a supportive environment.
• These clubs encourage curiosity, creativity, and sustained engagement, allowing learners to develop inquiry skills and awareness about various topics.
• Hobby clubs integrate learning with personal interests, promoting active participation, exploration, and questioning, which are key to nurturing a spirit of enquiry.
• In contrast, parent-teacher associations mainly involve administrative and community matters, in-service programs focus on teacher development, and long-duration science experiments, while valuable, are limited in scope and may not engage all students consistently.

Hence, the correct answer is hobby clubs.

School assemblies are an integral part of the daily routine, designed to foster discipline, moral values, awareness, and a sense of community among students. They provide opportunities for collective learning, sharing information, promoting physical well-being, and reinforcing the school’s ethos. 

Key Points

• Reading a part of a classic book encourages intellectual growth and moral reflection, physical fitness exercises promote health and energy, and addressing general school issues helps in building awareness and a sense of responsibility.
• Activities like punishing students are disciplinary rather than developmental, and sharing PTA decisions is primarily administrative, not central to the objectives of an assembly.
• By combining intellectual enrichment, physical activity, and awareness of school matters, assemblies can actively contribute to students’ holistic development and school community cohesion.

Hence, the correct answer is (ii), (iii) and (v).

Various educational committees in India have been established to review and recommend policies for improving the quality, relevance, and equity of education. These committees often focus on linking education with societal needs, human values, and national development goals. 

Key Points

• The Yashpal Committee emphasized education that fosters a humane and enlightened society. It advocated for reducing rote learning, promoting creativity, critical thinking, and value-based education, and integrating knowledge across disciplines to prepare students for responsible citizenship.
• Other committees like Raghu Rajan, Acharya Ram Murti, and Acharya Narendra Dev focused on financial, administrative, or structural aspects of education rather than explicitly promoting a vision of humane and enlightened society.
• The emphasis was on holistic development, nurturing ethical values, and fostering intellectual curiosity, all aimed at creating a compassionate and informed citizenry.

Hence, the correct answer is Yashpal Committee.

In educational theory, learning is often categorized into different domains: cognitive (knowledge), affective (attitudes and values), and psychomotor (skills). The cognitive domain focuses on mental skills such as recalling, understanding, analyzing, and evaluating information. 

Key Points

• Analyzing, evaluating, and informing are all activities associated with the cognitive or knowledge domain, involving mental processing, critical thinking, and communication of information.
• Respecting, however, is related to the affective domain as it involves attitudes, values, and emotional responses rather than purely intellectual activity.
• Cognitive objectives target understanding, reasoning, and decision-making, whereas affective objectives target values, feelings, and ethical behavior. Recognizing this distinction helps in effective curriculum design and assessment.

Hence, the correct answer is respecting.

Calculation:

Given set: A = {1, 2, 3, 4, 5}

Relation: use $R = {(x, y) : x + y \ge 8, x ∈ A, y ∈ A}$

For x = 1: use $1 + y \ge 8 \implies y \ge 7$. No $y ∈ A$ satisfies this.

For x = 2: use $2 + y \ge 8 \implies y \ge 6$. No $y ∈ A$ satisfies this.

For x = 3: use $3 + y \ge 8 \implies y \ge 5$. The only $y ∈ A$ is y=5.

$\implies$Pair is (3, 5).

For x = 4: use $4 + y \ge 8 \implies y \ge 4$. The $y ∈ A$ are y=4, 5.

⇒​  Pairs are (4, 4), (4, 5).

For x = 5: use $5 + y \ge 8 \implies y \ge 3$. The y ∈ A are y=3, 4, 5.

⇒​  Pairs are (5, 3), (5, 4), (5, 5).

Combining all the pairs gives the set R:

use $R = {(3, 5), (4, 4), (4, 5), (5, 3), (5, 4), (5, 5)}$

Hence option 3 is correct

Calculation:

Given the function: use $f(x) = \frac{x^2+2x+1}{x^2-x-6}$

The function is undefined when the denominator is zero. Let Q(x) be the denominator.

Q(x) = x²-x-6

Set the denominator to zero to find the excluded values:

⇒ $x^2-x-6 = 0$

Factor the quadratic equation:

⇒​ $x^2 - 3x + 2x - 6 = 0$

⇒​ $x(x - 3) + 2(x - 3) = 0$

⇒​ $(x - 3)(x + 2) = 0$

Set each factor to zero to find the roots:

⇒​ $x - 3 = 0 \implies x = 3$

⇒​ $x + 2 = 0 \implies x = -2$

The values of x for which the function is undefined are x = -2 and x = 3.

Domain: $\mathbb{R} - {-2, 3}$

Option 1 is correct

Calculation:

Given relation: use $R = {(a, b) : a \ge b, a, b \in \mathbb{N}}$

For any use $a \in \mathbb{N}$, we check if use $(a, a) \in R$.

The condition use $a \ge a$ is always true.

$\implies R$is Reflexive.

Assume use $(a, b) \in R$, which means use $a \ge b$.

For R to be symmetric, we must have use $(b, a) \in R$, which means  $b \ge a$.

If  $a \ge b$ and use $b \ge a$, the only possibility is  $a = b$.

Consider a counter example: Let a=2 and b=1.

$(2, 1) \in R$ since use $2 \ge 1$.

However, $(1, 2) \notin R$ since use $1 \not\ge 2$.

R is not Symmetric.

Assume use $(a, b) \in R$ and  $(b, c) \in R$.

$(a, b) \in R \implies a \ge b$

$(b, c) \in R \implies b \ge c$

Since use $a \ge b$ and use $b \ge c$, it follows that use $a \ge c$ (property of inequality).

$a \ge c \implies (a, c) \in R$.

R is Transitive.

The relation R is reflexive and transitive but not symmetric. This matches option 4.

Calculation:

Given data:

Number of elements in set $A$, $|A| = 4$

Number of elements in set $B$, $|B| = 5$

Check the condition for a bijective mapping $f: A \to B$:

$|A| = 4$

$|B| = 5$

$|A| \ne |B|$ since $4 \ne 5$.

$\Rightarrow$ Since the number of elements in the domain $A$ is not equal to the number of elements in the codomain $B$, a one-one and onto mapping from $A$ to $B$ is not possible.

∴ The number of one-one and onto mappings from $A$ to $B$ is $0$.

The  correct answer is 0.

Concept:

Set Theory:

• Universal Set: The complete set of all elements under consideration.
• Complement of a Set (Aʹ): Elements of the universal set that are not in set A.
• Union of Sets (A ∪ B): Elements that belong to A or B or both.
• Intersection of Sets (A ∩ B): Elements common to both A and B.
• Important formula: $n(A \cup B)=n(A)+n(B)-n(A\cap B)$
• Relation of complement: $n(A)+n(A')=n(U)$

 

Calculation:

Given,

Total elements in universal set, $n(U)=30$

Complement of A, $n(A')=15$

Elements in B, $n(B)=5$

Intersection, $n(A\cap B)=3$

$n(A)+n(A')=n(U)$

⇒ $n(A)=30-15$

⇒ $n(A)=15$

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

⇒ $n(A\cup B)=15+5-3$

⇒ $17$

∴ The value of $n(A\cup B)$ is 17.

Calculation:

Given data:

Total number of students (Universal Set), $|U| = 400$

Number of students who like coffee, $|C| = 100$

Number of students who like tea, $|T| = 150$

Number of students who like both coffee and tea, $|C \cap T| = 75$

Number of students who like coffee or tea or both ($|C \cup T|$) using the Principle of Inclusion-Exclusion:

$|C \cup T| = |C| + |T| - |C \cap T|$

$\Rightarrow$ $|C \cup T| = 100 + 150 - 75$

$\Rightarrow$ $|C \cup T| = 250 - 75$

$\Rightarrow$ $|C \cup T| = 175$

The number of students who neither like coffee nor tea ($|C \cup T|^c$):

$|C \cup T|^c = |U| - |C \cup T|$

$\Rightarrow$ $|C \cup T|^c = 400 - 175$

$\Rightarrow$ $|C \cup T|^c = 225$

∴ The number of students who neither likes to drink coffee nor tea is 225.

Calculation:

Given data:

Angle the ladder makes with the ground, $\theta = 60^\circ$

Distance of the foot of the ladder from the wall (Base), $\text{Base} = 2 \text{ m}$

Let the length of the ladder (Hypotenuse) be $L$.

Using the cosine trigonometric ratio:

$\cos(\theta) = \frac{\text{Base}}{L}$

$\Rightarrow$ $\cos(60^\circ) = \frac{2}{L}$

$\Rightarrow$ $\frac{1}{2} = \frac{2}{L}$

$\Rightarrow$ $L \times 1 = 2 \times 2$

$\Rightarrow$ $L = 4 \text{ m}$

∴ The length of the ladder is 4 m.

Calculation:

Given the trigonometric equation:

$5\cos^2x + 7\sin^2x - 6 = 0$

Use the identity $\cos^2x = 1 - \sin^2x$ to express the equation only in terms of $\sin^2x$:

$\Rightarrow$ $5(1 - \sin^2x) + 7\sin^2x - 6 = 0$

$\Rightarrow$ $5 - 5\sin^2x + 7\sin^2x - 6 = 0$

$\Rightarrow$ $(7\sin^2x - 5\sin^2x) + (5 - 6) = 0$

$\Rightarrow$ $2\sin^2x - 1 = 0$

$\Rightarrow$ $2\sin^2x = 1$

$\Rightarrow$ $\sin^2x = \frac{1}{2}$

$\Rightarrow$ $2\sin^2x = 1$

$\Rightarrow$ $2(1-\cos^2x) = 1$

$\Rightarrow$ $2 - 2\cos^2x = 1$

$\Rightarrow$ $2\cos^2x = 1$

$\Rightarrow$ $\cos^2x = \frac{1}{2}$

Since $\sin^2x = \frac{1}{2}$ and $\cos^2x = \frac{1}{2}$, we have:

$\Rightarrow$ $\tan^2x = \frac{\sin^2x}{\cos^2x} = \frac{1/2}{1/2} = 1$

We know that $\tan(\frac{\pi}{4}) = 1$, so $\tan^2(\frac{\pi}{4}) = 1^2 = 1$.

$\Rightarrow$ $\tan^2x = \tan^2(\frac{\pi}{4})$

The general solution for $\tan^2x = \tan^2\alpha$ is $x = n\pi \pm \alpha$.

$\Rightarrow$ $x = n\pi \pm \frac{\pi}{4}$, where $n \in \mathbb{Z}$.

∴ The solution of the trigonometric equation is $n\pi \pm \frac{\pi}{4}$.