UPPSC LT Grade Assistant Teacher (Science) Official Paper (Held On: 07 Dec, 2025 Shift 1) (Previous Year Paper)

The Correct answer is Bhuvankosha - Ksheer Swami.

Key Points

• Bhuvankosha is not authored by Ksheer Swami. It is a geographical and cosmographical work attributed to other scholars, not Ksheer Swami.
• Ksheer Swami is known for his commentary on the Amarakosha, which is an ancient Sanskrit thesaurus.
• The Amarakosha commentary by Ksheer Swami provides insights into the meanings and interpretations of Sanskrit words.
• The mismatch in attribution makes this option incorrect, making it the right answer to the question.

Additional Information

• Prabhavak Prashasti - Chandraprabha Suri
• Prabhavak Prashasti is a Jain work attributed to Chandraprabha Suri.
• This text is significant in Jain literature and provides insights into Jainism and its practices.
• It is considered a prashasti, or an encomium, detailing the achievements and virtues of Jain figures.
• Viddhashalabhanjika - Rajashekhara
• Viddhashalabhanjika is a famous play authored by Rajashekhara, a renowned Sanskrit dramatist and poet.
• Rajashekhara lived during the ninth and tenth centuries and is known for his contributions to Sanskrit drama and poetry.
• This play is an example of classical Sanskrit literature.
• Prithvirajavijaya - Jayanaka
• Prithvirajavijaya is a Sanskrit epic written by Jayanaka.
• It is a eulogy of the Chahamana king, Prithviraj Chauhan, detailing his life and achievements.
• This work is an important source for understanding the history of Northern India during Prithviraj Chauhan's reign.

The Correct answer is Both III and IV.

Key Points

• Milinda-Panha is associated with Buddhism. It is a Pali text that records a dialogue between the Indo-Greek King Menander I (Milinda) and the Buddhist monk Nagasena.
• The Bhagawati Sutra is a significant text in Jainism. It is part of the Jain Agamas and is written in the Prakrit language. It includes detailed discussions on Jain philosophy, ethics, and metaphysics.
• Tripitaka is a set of three sacred texts in Buddhism, not Jainism. It includes the Vinaya Pitaka, Sutta Pitaka, and Abhidhamma Pitaka, which cover monastic rules, discourses, and doctrinal teachings, respectively.
• Anguttara Nikaya is part of the Sutta Pitaka in Buddhism, not Jainism. It is a collection of discourses classified numerically, which helps in understanding and memorizing the teachings.

Additional Information

• Tripitaka
• Tripitaka is the sacred scripture of Buddhism, comprising three "baskets" or sections: Vinaya Pitaka (rules for monastic life), Sutta Pitaka (Buddha's discourses), and Abhidhamma Pitaka (philosophical analysis).
• It serves as the doctrinal foundation for Theravada Buddhism.
• Anguttara Nikaya
• This text is a part of the Sutta Pitaka, which forms the second basket of the Tripitaka.
• The discourses in the Anguttara Nikaya are categorized based on numerical enumeration, such as groups of ones, twos, threes, etc., making it a unique text for studying Buddha's teachings.
• Milinda-Panha
• The title Milinda-Panha translates to "Questions of Milinda," and it is notable for the dialogue between King Milinda and Nagasena.
• This text explores key Buddhist concepts such as anatta (non-self), rebirth, karma, and the nature of Nirvana.
• Bhagawati Sutra
• It is one of the 12 Angas of Jain literature and provides a detailed description of Jain doctrines and metaphysical concepts.
• The text is written in Ardhamagadhi Prakrit and contributes significantly to Jain canonical literature.

The Correct answer is II, III, IV, I.

Key Points

• Niryat Bandhu Yojana was launched in 2011 by the Directorate General of Foreign Trade (DGFT). It was aimed at mentoring first-generation entrepreneurs in the field of export and import.
• PM Kaushal Vikas Yojana (PMKVY) was introduced in 2015 under the Ministry of Skill Development and Entrepreneurship to provide skill development training to youth and improve their employability.
• Government e-Marketplace (GeM) was launched in 2016 for the procurement of goods and services by various government ministries and departments. It aims to ensure transparency, efficiency, and speed in public procurement.
• e-Satyapan Yojana was introduced later in 2022. This scheme is focused on verification of documents and ensuring transparency in government processes.

Additional Information

• Niryat Bandhu Yojana
• This scheme emphasizes capacity building and aims to promote entrepreneurship among exporters.
• It is aligned with India’s efforts to boost export competitiveness and improve the trade balance.
• PM Kaushal Vikas Yojana
• Under PMKVY, training is provided based on industry-relevant skills with certifications issued by National Skill Development Corporation (NSDC).
• The scheme has specific focus areas such as digital skills, hospitality, and construction sectors.
• Government e-Marketplace (GeM)
• GeM has facilitated over one crore transactions since its inception and has created value for government procurement.
• It is implemented by the Ministry of Commerce and Industry.
• e-Satyapan Yojana
• The scheme is designed to digitize verification processes and provide a secure mechanism for document authentication.
• It is part of India’s push for Digital Governance.

The Correct answer is Seasonal unemployment.

Key Points

• Seasonal unemployment refers to unemployment that occurs during specific seasons in a year due to the nature of work or the industry. For example, unemployment in agriculture during the non-cultivation periods.
• This type of unemployment is primarily prevalent in rural areas, particularly in sectors such as agriculture, where work is dependent on seasons like sowing and harvesting.
• In urban areas, industries and services tend to operate year-round, which minimizes the occurrence of seasonal unemployment.
• Seasonal unemployment is more common in sectors with cyclical demand, such as tourism and agriculture, but it has limited relevance in urban employment setups.

Additional Information

• Educated unemployment
• Educated unemployment occurs when individuals with formal education, such as graduates and postgraduates, are unable to find jobs matching their skills and qualifications.
• This type of unemployment is common in urban areas, where people often face a mismatch between the skills they possess and the requirements of available jobs.
• It is a major challenge in developing economies where the job market cannot absorb the growing number of educated individuals.
• The issue is often linked to a lack of industrial growth and insufficient opportunities in the services sector.
• Industrial unemployment
• Industrial unemployment refers to a situation where workers lose their jobs due to industrial closures, downsizing, or lack of demand for industrial products.
• This type of unemployment is prevalent in urban areas, where industries form the primary source of employment.
• Factors such as technological advancements, automation, and economic slowdowns can contribute to industrial unemployment.
• It highlights the need for policies aimed at industrial growth and diversification to create sustainable employment opportunities.

The Correct answer is Both (A) and (R) are true and (R) is the correct explanation of (A).

Key Points

• Leghaemoglobin is a pink-colored, oxygen-binding pigment found in the root nodules of leguminous plants.
• It plays a vital role in biological nitrogen fixation, where atmospheric nitrogen is converted into ammonia by symbiotic bacteria like Rhizobium.
• The process of nitrogen fixation is catalyzed by the enzyme nitrogenase, which is highly sensitive to oxygen and becomes inactive in its presence.
• Leghaemoglobin acts as an oxygen scavenger, maintaining a low oxygen concentration in the root nodules, which is essential for the proper functioning of nitrogenase.
• By protecting nitrogenase from oxygen, leghaemoglobin ensures efficient nitrogen fixation, which is crucial for the growth of plants in nitrogen-deficient soils.

Additional Information

• (A) is true, but (R) is false
• This option is incorrect because (R) is true. Leghaemoglobin indeed protects nitrogenase from oxygen, which validates the reason provided in the statement.
• Both (A) and (R) are true, but (R) is not the correct explanation of (A)
• This option is incorrect because (R) is directly related to and explains the role of leghaemoglobin in nitrogen fixation.
• (A) is false, but (R) is true
• This option is incorrect because both (A) and (R) are true. Leghaemoglobin indeed plays a critical role in biological nitrogen fixation.

The correct answer is Ice.

Key Points

• In solid substances, such as Ice, the forces of attraction between particles are the strongest. This is because the particles are tightly packed together in a fixed structure.
• The particles in Ice have a definite arrangement, and their movement is restricted to vibrations in fixed positions, leading to maximum intermolecular forces.
• Ice is a crystalline solid, and the hydrogen bonding in Ice is responsible for its strong intermolecular forces.
• Due to these strong attractive forces, Ice has a fixed shape and volume and is less compressible compared to liquids or gases.
• Ice is a form of water in its solid state, where the water molecules are arranged in a hexagonal lattice structure.
• The structure of Ice makes it unique, as its density is lower than that of liquid water, which is why Ice floats on water.

Additional Information

• Water
• Water is a liquid and has weaker forces of attraction between its molecules compared to Ice. This is because the particles in water are not as tightly packed and can move past each other freely.
• Water molecules are held together by hydrogen bonds, but these bonds are not as rigid as in Ice, resulting in fluidity.
• Water is an example of a fluid, meaning it takes the shape of its container.
• Kerosene Oil
• Kerosene oil is a liquid with even weaker intermolecular forces compared to water due to its molecular structure.
• Kerosene is a mixture of hydrocarbons, and its particles are less polar, leading to weaker attractive forces.
• It is widely used as a fuel for lamps and stoves.
• Oxygen
• Oxygen is a gas and has the weakest forces of attraction between its particles compared to Ice, water, or kerosene oil.
• In gases like oxygen, the particles are far apart and move freely, resulting in minimal intermolecular forces.
• Oxygen is essential for respiration and supports combustion.

The correct answer is Both I and II.

Key Points

• Tropical evergreen forests are predominantly found in regions near the equator, where the climate is characterized by high temperature and heavy rainfall throughout the year.
• These forests are known for their dense canopy, which allows minimal sunlight to reach the forest floor, thus maintaining a unique ecosystem.
• Statement I is correct as these regions experience hot and humid conditions with annual rainfall exceeding 200 cm.
• They are home to a variety of hardwood tree species, such as ebony, mahogany, rosewood, and rubber, which are highly valued for their durability and quality. Therefore, Statement II is also correct.
• The evergreen nature of these forests is due to the fact that trees shed their leaves at different times of the year, ensuring that they remain lush green throughout.
• Tropical evergreen forests are primarily found in regions like the Amazon Basin, Congo Basin, Southeast Asia, and parts of India, including states like Kerala, Karnataka, and Andaman & Nicobar Islands.
• These forests are crucial for maintaining global biodiversity and serve as a significant carbon sink, mitigating climate change.
• They are rich in wildlife and serve as the habitat for a wide variety of species including insects, birds, reptiles, and mammals.

Additional Information

• Ebony and Mahogany
• Ebony: A dense black wood found in tropical forests. It is highly durable, used for making furniture, carvings, and musical instruments.
• Mahogany: A reddish-brown hardwood valued for its strength and beauty. It is used in furniture-making, boat-building, and luxury items.
• Climate Characteristics
• Tropical evergreen forests are typically found in regions with high humidity and temperatures averaging 25-30°C.
• They receive rainfall exceeding 200 cm annually, which is vital for their lush vegetation.
• Location in India
• In India, tropical evergreen forests are found in regions like the Western Ghats, North-Eastern states (Assam, Arunachal Pradesh), and the Andaman & Nicobar Islands.
• These areas are rich in biodiversity and are home to several endemic species.

Given:

Check each pair using algebraic identities.

Formula used:

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ − b³ = (a − b)³ + 3ab(a − b)

(x)³ + (y)³ = 0 if x + y = 0

Calculations:

1st pair:

a + b = 15

(a − 10) + (b − 5) = a + b − 15 = 0

⇒ (a − 10)³ + (b − 5)³ = 0 ✔

2nd pair:

a − b = 4 , ab = 2

a³ − b³ = (a − b)³ + 3ab(a − b)

⇒ = 4³ + 3×2×4

⇒ = 64 + 24 = 88 ≠ 80 ✖

3rd pair:

a + b = 8 , ab = 10

a³ + b³ = 8³ − 3×10×8

⇒ = 512 − 240 = 272 ✔

4th pair:

a + b = 15 , ab = 14

(a − b)² = (a + b)² − 4ab

⇒ = 225 − 56 = 169

⇒ a − b = 13 ✔

∴ The 2nd pair is not correctly matched.

The Correct answer is (A) is false, but (R) is true.

Key Points

• Assertion (A): Cyclonic conditions are not formed when the atmospheric pressure is high and the air temperature is low. Cyclones are generally associated with low-pressure systems, not high-pressure systems.
• Reason (R): Winter rains, especially in North India, are influenced by western disturbances. These disturbances generally result in anticyclonic conditions, characterized by low temperatures and dry weather after the rains.
• Western disturbances are an example of an extratropical storm originating in the Mediterranean region, which brings winter rain to North and North-Western India.
• High atmospheric pressure is a characteristic of anticyclonic conditions, not cyclonic ones. In anticyclonic conditions, the air is descending, leading to clear skies and stable weather.
• Cyclones, on the other hand, are associated with low atmospheric pressure, rising air, and unstable weather conditions like storms and heavy rainfall.
• Since the assertion incorrectly links cyclonic conditions with high pressure, it is false. However, the reason correctly explains how winter rains are associated with anticyclonic conditions.

Additional Information

• Western Disturbances
• Western disturbances are moisture-laden cyclonic systems that originate in the Mediterranean region.
• They bring rain and snowfall to the northwestern parts of India during the winter months.
• These disturbances are important for Rabi crop cultivation, particularly wheat in North India.
• Anticyclones
• Anticyclones are associated with high atmospheric pressure, where the air descends and spreads outward.
• They typically result in clear skies, dry weather, and low wind speeds.
• After winter rains in North India, anticyclonic conditions often dominate, bringing cold and stable weather.
• Cyclones
• Cyclones are low-pressure systems that result in rising air and unstable atmospheric conditions.
• They are often associated with strong winds, heavy rainfall, and storms.
• Examples include tropical cyclones like Cyclone Fani and extratropical cyclones.

Given:

Ratio of radii of two cylinders = 2 : 3

Ratio of heights of two cylinders = 5 : 3

Formula used:

Curved surface area of cylinder = 2 × π × r × h

Calculations:

Ratio of curved surfaces

⇒ r₁ × h₁ : r₂ × h₂

⇒ (2 × 5) : (3 × 3)

⇒ 10 : 9

∴ The ratio of their curved surfaces is 10 : 9.

The Correct answer is Ahmedabad.

Key Points

• Ahmedabad, located in the state of Gujarat, is known for its rich history, culture, and modern infrastructure.
• The city has a strong focus on sports infrastructure and has hosted multiple national and international sporting events.
• Ahmedabad's Narendra Modi Stadium is the largest cricket stadium in the world, showcasing its capability to host large-scale events.
• Gujarat has been actively promoting sports under various initiatives, making Ahmedabad an ideal choice for hosting the Commonwealth Games 2030.
• The decision reflects India's growing prominence in the global sports arena and its ambition to organize mega international sporting events.
• Hosting the Commonwealth Games is expected to boost tourism, infrastructure, and economic development in Ahmedabad and surrounding regions.
• The event will also provide an opportunity to showcase India's cultural heritage to a global audience.

Additional Information

• Bhopal
• Bhopal is the capital city of Madhya Pradesh and is known as the City of Lakes due to its numerous natural and artificial lakes.
• The city has a strong cultural heritage but does not have the same level of international sports infrastructure as Ahmedabad.
• New Delhi
• New Delhi, the capital city of India, has previously hosted the 2010 Commonwealth Games, making it unlikely to host the 2030 edition.
• It is renowned for its historic landmarks and government institutions but is not being considered for this event.
• Mumbai
• Mumbai, the financial capital of India, has world-class infrastructure and has hosted several major events, but it is not the chosen city for the 2030 Commonwealth Games.
• The city's focus is more on commerce, entertainment, and business rather than large-scale international sports events.

The Correct answer is Gujarat, Kerala, and Punjab.

Key Points

• The State Energy and Climate Index (SECI) Round-I was released by NITI Aayog in 2022.
• The index aims to rank states and union territories based on their efforts in energy efficiency and climate resilience.
• Gujarat, Kerala, and Punjab emerged as the top three performers among the larger states category in the SECI Round-I.
• The index evaluates performance across six parameters: discom performance, energy efficiency, renewable energy, access to energy, environmental sustainability, and new initiatives.
• Gujarat has been leading in renewable energy adoption and efficient energy policies, contributing to its top ranking.
• Kerala has focused on achieving high energy access and sustainability, ensuring balanced development in the energy sector.
• Punjab excelled in discom performance and renewable energy integration, showcasing its commitment to energy transition.
• The SECI encourages states to work on improving their strategies in energy management and climate action.

Additional Information

• Madhya Pradesh, Rajasthan, and Himachal Pradesh
• These states were not among the top three performers in the SECI Round-I. However, Himachal Pradesh has made significant contributions to renewable energy, particularly in hydropower generation.
• Rajasthan is known for its vast solar energy potential, but it did not rank among the top three in the SECI Round-I.
• Madhya Pradesh has been working on improving its energy efficiency but needs more efforts to reach the top rankings.
• Uttar Pradesh, Uttarakhand, and Punjab
• While Punjab ranked among the top three performers, Uttar Pradesh and Uttarakhand did not perform as well in the SECI Round-I.
• Uttarakhand has potential in hydro energy, but its overall performance in energy efficiency and climate resilience needs improvement.
• Uttar Pradesh, Andhra Pradesh, and Gujarat
• Gujarat was indeed one of the top performers, but Uttar Pradesh and Andhra Pradesh did not rank in the top three in the SECI Round-I.
• Andhra Pradesh has made progress in renewable energy, especially in wind and solar sectors, but it still needs to improve its performance in other parameters.

The Correct answer is I, II, III, IV.

Key Points

• The A.K. Gopalan vs State of Madras Case (1950) is one of the earliest and landmark cases related to the interpretation of Article 21 of the Indian Constitution. In this case, the Supreme Court adopted a narrow interpretation of the rights guaranteed under Article 21.
• The Satwant Singh Sawhney vs Assistant Passport Officer, New Delhi Case (1967) dealt with the issuance of passports. The Supreme Court held that the "right to travel abroad" is a part of the personal liberty guaranteed under Article 21.
• The Maneka Gandhi vs Union of India Case (1978) redefined the interpretation of Article 21 by broadening its scope. The court emphasized the principle of "due process" and linked the provisions of Article 14, 19, and 21.
• The Hussainara Khatoon vs State of Bihar Case (1979) focused on the plight of undertrial prisoners. This case laid the foundation for the concept of speedy trial as a fundamental right under Article 21.
• The chronological order of these cases is significant in understanding the evolution of judicial interpretation of Article 21 and the expansion of fundamental rights in India.

Additional Information

• A.K. Gopalan vs State of Madras Case
• This case marked the beginning of judicial interpretations of Article 21.
• The Supreme Court adopted a narrow approach and ruled that each article in the Constitution is independent and cannot be interlinked.
• The case primarily dealt with preventive detention laws.
• Maneka Gandhi vs Union of India Case
• In this case, the Supreme Court expanded the scope of personal liberty under Article 21 and interlinked Articles 14, 19, and 21.
• The judgment emphasized that any law affecting life or liberty must satisfy the test of reasonableness.
• This decision marked a shift from the narrow interpretation of Article 21 to a broader and more inclusive perspective.

The Correct answer is Both I and II.

Key Points

• The Delimitation Commission is established by the Government of India under the provisions of the Delimitation Commission Act.
• It is responsible for redrawing the boundaries of the Lok Sabha and State Assembly constituencies based on the latest census.
• The orders issued by the Delimitation Commission are considered final and cannot be challenged in any court of law, ensuring its authority.
• Once the orders are placed before the Lok Sabha or State Legislative Assembly, no amendments or modifications can be made to them, ensuring their binding nature.
• The Commission is an independent body, and its decisions aim to ensure fairness in the representation of constituencies based on population.
• The Commission includes a chairperson, usually a retired judge of the Supreme Court, and other members such as the Chief Election Commissioner and representatives of the concerned states.
• The process is vital for maintaining the principle of equal representation as prescribed by the Constitution of India.

Additional Information

• Delimitation Commission Act
• This Act provides the legal framework for the functioning of the Delimitation Commission.
• The purpose is to ensure that constituencies are redrawn periodically to reflect changes in population and demographics based on the latest census data.
• It ensures that each constituency has equal representation to maintain the democratic process.
• Role of the Chief Election Commissioner
• The Chief Election Commissioner is an integral part of the Delimitation Commission.
• They provide expertise and ensure that the process aligns with the electoral guidelines.
• They help uphold the principles of free and fair elections.

The Correct answer is Election of the President - Article 53.

Key Points

• The Election of the President is governed by Article 54 of the Indian Constitution, not Article 53.
• Article 54 specifies the procedure for electing the President of India, which involves an electoral college comprising elected members of both Houses of Parliament and the elected members of the Legislative Assemblies of the States.
• Article 53, on the other hand, deals with the Executive power of the Union, stating that the executive authority of the Union shall be vested in the President.
• The President's election process is conducted under strict guidelines laid down by the Constitution to ensure a fair and transparent procedure.
• The President serves as the constitutional head of the country and represents the unity and integrity of the nation.

Additional Information

• Conditions of the President's office - Article 59
• Article 59 deals with the conditions under which the President holds office.
• It specifies that the President cannot be a member of Parliament or any State Legislature and should not hold any other office of profit.
• The President is entitled to an official residence and other allowances during the term of office.
• The President of India - Article 52
• Article 52 establishes the office of the President of India as the head of the State.
• The President serves as the chief executive authority and symbol of national unity.
• The article emphasizes that India shall have a President who exercises powers as per the Constitution.
• Term of office of the President - Article 56
• Article 56 outlines the President's term of office, which is five years from the date of entering office.
• The President may resign before the term or be removed through impeachment as per the constitutional provisions.
• The article also allows for re-election of the President after the completion of the term.

The correct answer is 3322.98 lakh metric tonnes.

Key Points

• India's total foodgrain production for the year 2023-24, as per the Final Estimates released by the Department of Agriculture and Farmers' Welfare, reached a record high of 3322.98 lakh metric tonnes (LMT).
• This figure reflects the continuous efforts of the Indian government to achieve self-sufficiency in foodgrain production through improved agricultural policies, modern farming techniques, and high-yielding crop varieties.
• The achievement is a significant contributor to food security in India, which is a critical priority for a country with a large and growing population.
• Key contributors to this record production include major crops like rice, wheat, and pulses, which form the backbone of India's agricultural sector.
• The record production is attributed to favorable weather conditions, timely sowing, and government initiatives like the Pradhan Mantri Fasal Bima Yojana (PMFBY) and the Soil Health Card Scheme.
• The Department of Agriculture and Farmers' Welfare consistently monitors the agricultural output to ensure accurate and reliable estimates of foodgrain production.

Additional Information

• Key Government Initiatives
• The Pradhan Mantri Fasal Bima Yojana (PMFBY) provides insurance coverage to farmers for crop failure due to natural calamities.
• The Soil Health Card Scheme helps farmers understand the nutrient status of their soil and take informed decisions on fertilizer usage.
• Government focus on Minimum Support Price (MSP) ensures farmers receive fair prices for their produce.
• Programs like Paramparagat Krishi Vikas Yojana promote organic farming, enhancing sustainability in agriculture.
• Modern Farming Techniques
• Precision agriculture involves the use of technology like drones and satellite imagery to optimize farming practices.
• High-yielding crop varieties have been developed to resist pests, diseases, and climate changes.
• Farmers are encouraged to adopt drip irrigation and micro-irrigation techniques for efficient water usage.

The correct answer is I, III, IV, II.

Key Points

• The First Five-Year Plan was launched in 1951 to focus on the agriculture sector and establish a foundation for economic development in India. It was a major step in post-independence economic planning.
• The concept of Social Banking in India started in the late 1960s and early 1970s with the nationalization of banks in 1969. The goal was to ensure financial inclusion and provide banking services to rural and underprivileged areas.
• NABARD (National Bank for Agriculture and Rural Development) was established in 1982 under the recommendations of the B. Sivaraman Committee. It focuses on rural development and financing agriculture and rural infrastructure.
• The Goods and Services Tax (GST) was implemented in India on 1st July 2017. It replaced multiple indirect taxes and created a unified tax structure in the country.

Additional Information

• First Five-Year Plan
• The plan was inspired by the Harrod-Domar model and emphasized agricultural development, irrigation, and energy production.
• It laid the foundation for long-term economic planning in independent India.
• The plan achieved its targets, especially in food grain production.
• Social Banking
• The nationalization of banks in 1969 marked a turning point in Indian banking history.
• Social banking aimed to ensure equitable distribution of credit to priority sectors like agriculture, small-scale industries, and weaker sections of society.
• NABARD
• NABARD plays a vital role in supporting rural infrastructure projects and financial institutions engaged in agriculture.
• It also provides refinance facilities and supports microfinance initiatives in rural areas.
• GST
• GST is an indirect tax that has simplified the Indian tax system by subsuming multiple taxes like VAT, service tax, and excise duty.
• It is a destination-based tax and promotes a unified national market.
• GST rates are categorized into 5%, 12%, 18%, and 28%, depending on the type of goods and services.

The Correct answer is 61st Constitutional Amendment Act.

Key Points

• The 61st Constitutional Amendment Act of 1988 reduced the minimum voting age in India from 21 years to 18 years.
• This amendment aimed to increase the participation of youth in the democratic process by granting them the right to vote at an earlier age.
• It amended Article 326 of the Indian Constitution, which deals with elections to the House of the People and the Legislative Assemblies of States.
• The rationale for this amendment was that individuals aged 18 years were considered mature enough to understand and participate in governance.
• The amendment was passed during the tenure of the Rajiv Gandhi government.
• This change was significant as it allowed a larger section of the population to participate in the electoral process, thereby strengthening the foundation of democracy in India.

Additional Information

• 66th Constitutional Amendment Act
• This amendment was passed in 1990 and dealt with the inclusion of certain land reforms laws in the Ninth Schedule of the Indian Constitution.
• The aim was to protect these laws from judicial review on the grounds of violation of fundamental rights.
• 79th Constitutional Amendment Act
• This amendment was enacted in 1999 and extended the reservation of seats for Scheduled Castes, Scheduled Tribes, and Anglo-Indians in the Lok Sabha and State Legislative Assemblies for another 10 years.
• 86th Constitutional Amendment Act
• This amendment, passed in 2002, made education a fundamental right for children aged 6 to 14 years under Article 21A of the Constitution.
• It also made the provision for early childhood care and education for children below the age of 6 years under Article 45.

The correct answer is Akbar.

Key Points

• Akbar, the third Mughal emperor, implemented the policy of Sulh-i-kul, which translates to "universal peace" or "peace with all."
• This policy was a part of Akbar's broader efforts to promote religious tolerance and harmony within his diverse empire, which included people of various religions, cultures, and ethnicities.
• Under Sulh-i-kul, Akbar sought to create an environment of mutual respect among different religious communities, emphasizing justice and equality for all subjects, regardless of their faith.
• He abolished discriminatory practices such as the jizya tax (a tax imposed on non-Muslims) and allowed Hindus, Jains, Christians, and other religious groups to freely practice their religion.
• Akbar also held discussions with scholars and religious leaders of various faiths at his court, fostering an era of intellectual and cultural exchange.
• The policy of Sulh-i-kul contributed significantly to the consolidation of the Mughal Empire by ensuring the loyalty of diverse communities.
• Akbar's approach to governance and religious tolerance earned him the title of “Akbar the Great.”

Additional Information

• Babur
• Babur was the founder of the Mughal Empire in India in 1526 after defeating Ibrahim Lodi in the First Battle of Panipat.
• He is known for introducing gunpowder and advanced military techniques to India.
• Babur wrote an autobiography called “Baburnama”, which provides insights into his life and the cultural and political history of his era.
• Alauddin Khilji
• Alauddin Khilji was the second ruler of the Khilji dynasty of the Delhi Sultanate.
• He implemented rigorous economic and administrative reforms, including market control policies and price regulation.
• Alauddin is also remembered for his military campaigns and his successful defense against the Mongol invasions.
• Jahangir
• Jahangir was the fourth Mughal emperor and the son of Akbar.
• He is known for his contributions to art and architecture and his patronage of painters like Ustad Mansur.
• Jahangir continued Akbar's policies of religious tolerance but was more focused on cultural and administrative achievements.

The Correct answer is ₹ 808736.06 Lakh Crore.

Key Points

• The Uttar Pradesh Government Budget for the year 2025-26 was ₹ 808736.06 Lakh Crore, marking a significant allocation of resources towards development and welfare schemes in the state.
• This budget is aimed at achieving the goals set forth in various sectors such as healthcare, education, infrastructure, agriculture, and industrial development.
• The budget reflects the state government’s focus on socio-economic development and creating opportunities for employment generation.
• There is an emphasis on sustainable development practices and addressing key challenges such as poverty, unemployment, and urban-rural disparity.
• Special provisions were made for the implementation of flagship schemes launched by the government.
• The allocation reflects the government's effort to improve public service delivery systems and strengthen governance at all levels.
• It also highlights the government’s commitment to promoting self-reliance and entrepreneurship in the state.
• With this budget, Uttar Pradesh aimed to maintain its pace of growth and contribute to the overall development of the Indian economy.

Additional Information

• Important Points for Examination:
• The budget’s focus on infrastructure development can be highlighted as a key area for growth in Uttar Pradesh.
• Flagship government schemes and their impact can be a significant discussion point.
• The allocation towards agriculture and rural development underscores the government’s push for balanced growth across urban and rural areas.
• The role of the budget in promoting employment generation and entrepreneurship is crucial.

The Correct answer is Potato.

Key Points

• The potato is a classic example of a stem tuber, which is a swollen underground storage structure of the plant.
• It is a part of the plant's stem, not a root, and it stores starch, which is a source of energy for the plant.
• Potatoes have eyes, which are nodes on the tuber that can sprout into new plants. These eyes are a distinguishing feature of stem tubers.
• The Solanum tuberosum, the scientific name of the potato, belongs to the Solanaceae family.
• Potatoes are widely cultivated for their nutritional value and are a staple food in many countries.
• They are rich in carbohydrates, potassium, and vitamin C, making them an important food crop globally.
• Stem tubers like potatoes play a significant role in asexual reproduction, as new plants can grow from the buds or eyes of a single tuber.

Additional Information

• Onion
• The onion is an example of a bulb, not a stem tuber.
• Bulbs are underground storage structures made up of layers of fleshy, modified leaves that surround a short stem.
• Onions are rich in antioxidants and are widely used in cuisines around the world.
• Ginger
• Ginger is a rhizome, a type of modified underground stem.
• Rhizomes grow horizontally under the soil and help in the vegetative reproduction of the plant.
• Ginger is valued for its medicinal properties and is used as a spice in many dishes.
• Garlic
• Garlic, like onions, is a bulb, not a stem tuber.
• It is composed of multiple segments called cloves, which are covered in a papery skin.
• Garlic is known for its antibacterial and antiviral properties and is used in traditional medicine.

The Correct answer is A-i, B-ii, C-iii, D-iv.

Key Points

• PM-KUSUM Yojana (Pradhan Mantri Kisan Urja Suraksha evam Utthaan Mahabhiyan) is an initiative aimed at providing energy security to farmers and promoting the use of renewable energy. In the Uttar Pradesh Budget 2025-26, ₹650 crore has been allocated for this scheme.
• Micro Irrigation Plan (Per Drop More Crop) is a flagship program under the PM Krishi Sinchayee Yojana that encourages the use of micro-irrigation techniques such as drip and sprinkler irrigation. The budget allocation for this initiative is ₹720 crore.
• The National Industrial/Horticulture Mission Yojana focuses on the development and promotion of horticulture crops. The budget has allocated ₹300 crore for this scheme to improve agricultural practices and enhance productivity.
• The Uttar Pradesh Food Processing Industry Policy, 2022 is aimed at promoting the food processing sector in Uttar Pradesh by providing incentives and encouraging private investment. ₹509 crore has been allocated for this policy in the 2025-26 budget.
• The matching of List I with List II is as follows:
• A (PM-KUSUM Yojana) - i (₹650 crore)
• B (Micro Irrigation Plan) - ii (₹720 crore)
• C (National Industrial/Horticulture Mission Yojana) - iii (₹300 crore)
• D (Uttar Pradesh Food Processing Industry Policy, 2022) - iv (₹509 crore)

Additional Information

• PM-KUSUM Yojana
• Launched by the Government of India in 2019.
• Aims to provide solar power pumps to farmers for irrigation and reduce dependence on grid electricity.
• Promotes the use of renewable energy in agriculture.
• Micro Irrigation Plan (Per Drop More Crop)
• Part of the Pradhan Mantri Krishi Sinchayee Yojana (PMKSY).
• Focuses on water use efficiency in agriculture.
• Supports the adoption of drip and sprinkler irrigation techniques.
• National Industrial/Horticulture Mission Yojana
• Focuses on the development of horticulture crops such as fruits, vegetables, and flowers.
• Aims to enhance farmers’ income and ensure food security.
• Uttar Pradesh Food Processing Industry Policy, 2022
• Encourages investment in the food processing sector.
• Provides financial incentives and support to entrepreneurs and investors.
• Aims to reduce post-harvest losses and promote value addition.

The correct answer is Match List I with List II.

Key Points

• National Bird - The zoological name Pavo cristatus corresponds to the Indian Peafowl, which is designated as the National Bird of India. It symbolizes grace, beauty, and pride.
• National Animal - The zoological name Panthera tigris represents the Bengal Tiger, which is the National Animal of India. It is a symbol of strength, power, and courage.
• National Flower - The botanical name Nelumbo nucifera refers to the Lotus flower, which is India's National Flower. It signifies purity and spirituality.
• National Tree - The botanical name Ficus benghalensis refers to the Banyan tree, recognized as the National Tree of India. It represents immortality and is deeply rooted in Indian culture.
• Therefore, the correct match for List I and List II is: A-iii, B-ii, C-iv, D-i.

Additional Information

• Indian Peafowl (Pavo cristatus)
• The Indian Peafowl is a native species found throughout the Indian subcontinent.
• It is known for its distinctive colorful plumage and majestic display during courtship.
• It is considered sacred in Indian culture and often associated with Lord Krishna and Saraswati.
• Bengal Tiger (Panthera tigris)
• The Bengal Tiger is one of the most iconic and endangered species found in India.
• It is primarily found in mangroves like Sundarbans, forests, and national parks.
• India is home to over 70% of the world's wild tiger population, as part of the Project Tiger conservation program.
• Lotus (Nelumbo nucifera)
• The Lotus is deeply rooted in Indian mythology, art, and culture and symbolizes purity and detachment.
• It grows in stagnant water bodies and is considered a sacred flower in Hinduism and Buddhism.
• Banyan Tree (Ficus benghalensis)
• The Banyan tree is considered sacred and holds a place of importance in Indian tradition.
• It is known for its large canopy and aerial roots, which symbolize longevity and support.

The correct answer is Base metal - Cobalt.

Key Points

• Cobalt is not classified as a base metal. It is primarily categorized as a strategic metal or sometimes as a minor metal due to its specific uses and rarity.
• Base metals include metals like copper, zinc, nickel, and lead, which are commonly used and are not precious metals.
• Cobalt is widely used in the manufacturing of batteries, especially lithium-ion batteries, and in superalloys for aerospace applications.
• It is a critical material for renewable energy technologies such as electric vehicles and is considered a strategic resource.
• Cobalt is primarily mined in countries like Democratic Republic of Congo, Russia, Australia, and Canada.

Additional Information

• Ferro Alloys - Nickel
• Nickel is considered a ferroalloy metal due to its use in producing stainless steel and other alloys.
• It is highly valued for its corrosion resistance and ability to withstand high temperatures.
• Nickel is mined in countries such as Indonesia, Philippines, Russia, and Canada.
• Nickel alloys are used in industries like aviation, aerospace, electronics, and construction.
• Precious metal - Silver
• Silver is a precious metal known for its high value, rarity, and extensive use in jewelry, coins, and industrial applications.
• It is highly conductive and is widely used in electronics and solar panels.
• Major producers of silver include countries such as Mexico, Peru, China, and Australia.
• Non-metallic mineral - Diamond
• Diamond is a non-metallic mineral and the hardest known natural material.
• It is used extensively in jewelry and industrial cutting tools.
• Diamonds are formed deep within the Earth's mantle under high pressure and temperature.
• Countries like Russia, Botswana, Canada, and Australia are major producers of diamonds.

The Correct answer is Afghanistan.

Key Points

• The Rabatak inscription is a significant historical record related to the reign of the Kushan emperor Kanishka the Great.
• It was discovered in the Rabatak area of present-day Afghanistan.
• This inscription provides crucial evidence for understanding the chronology and rule of Kanishka, particularly his efforts in governance and religious patronage.
• It is written in the Bactrian language, using the Greek script, which was common in the region during the Kushan period.
• The Rabatak inscription mentions Kanishka's genealogy, his empire's vast territories, and his support for Buddhism.
• It also highlights the transition of official records from Greek to Bactrian, signifying cultural and administrative changes under the Kushan rule.
• The inscription is considered one of the most important sources for reconstructing the history of the Kushan Empire.
• Afghanistan was a major center of the Kushan Empire, which played a crucial role in the spread of Buddhism to Central and East Asia.

Additional Information

• Nepal
• Nepal, a Himalayan country, has been historically significant in the spread of Buddhism, as it is the birthplace of Lord Buddha (Lumbini).
• However, the Rabatak inscription is not related to Nepal but to the Kushan Empire, which ruled significant parts of Central and South Asia.
• Pakistan
• Pakistan was also part of the Kushan Empire during Kanishka's reign, with important centers like Taxila playing a prominent role in trade and education.
• While Kushan inscriptions and artifacts have been found in Pakistan, the Rabatak inscription specifically pertains to Afghanistan.
• India
• India was another significant region of the Kushan Empire, especially North India, where Kanishka's rule was influential.
• The Kushans contributed to the flourishing of Buddhism in India, including constructing the famous Kanishka Stupa near Peshawar (in present-day Pakistan).
• While the Rabatak inscription mentions India as part of the empire, its discovery site is in Afghanistan, making it more relevant to that region.

Given:

Ratio of sides of triangle = 3 : 4 : 5

Perimeter = 36 cm

Formula used:

Sum of ratio parts × common factor = Perimeter

Area of right-angled triangle = (1 ÷ 2) × base × height

Calculations:

Sum of ratios = 3 + 4 + 5 = 12

⇒ Common factor = 36 ÷ 12 = 3

⇒ Sides are:

3 × 3 = 9 cm

4 × 3 = 12 cm

5 × 3 = 15 cm

Since 3 : 4 : 5 is a right-angled triangle

⇒ Base = 9 cm, Height = 12 cm

⇒ Area = (1 ÷ 2) × 9 × 12

⇒ Area = 54 cm²

∴ The area of the triangle is 54 cm².

The Correct answer is The Northern Atlantic sea route.

Key Points

• The Northern Atlantic sea route is the busiest sea route in the world.
• This route connects the major industrial and commercial hubs of North America and Europe.
• It is often referred to as the "Gateway of Europe and America" due to its strategic and economic significance.
• The route primarily facilitates the transportation of crude oil, machinery, automobiles, and consumer goods.
• Major ports along this route include New York, Rotterdam, Hamburg, and London.
• The Northern Atlantic sea route is a key driver of global trade, contributing significantly to the economies of participating regions.
• It benefits from having relatively calm waters and proximity to the world's largest economies, making it ideal for heavy trade traffic.

Additional Information

• The North Pacific sea route
• The North Pacific sea route connects Asia and North America, facilitating trade between countries such as China, Japan, South Korea, and the United States.
• This route is important for the transportation of raw materials like coal, petroleum, and natural gas, as well as manufactured goods.
• However, it is less busy than the Northern Atlantic route due to lower trade volumes and longer distances between key ports.
• The South Pacific sea route
• The South Pacific sea route connects regions such as Australia, New Zealand, and South America.
• It primarily handles the export of agricultural products, minerals, and raw materials from these regions.
• While significant, it does not match the trade intensity of the Northern Atlantic sea route.
• The Southern Atlantic sea route
• The Southern Atlantic sea route links South America and Africa, facilitating the exchange of goods such as coffee, sugar, and oil.
• Its importance lies in connecting emerging economies, but the trade volume is considerably lower than the Northern Atlantic route.

The correct answer is Largest National Park in India.

Key Points

• Jim Corbett National Park is located in the state of Uttarakhand, India, and is not the largest national park in India. The largest national park in India is the Hemis National Park, located in Ladakh.
• Jim Corbett National Park is renowned as the oldest national park in India, established in the year 1936 as Hailey National Park. It was renamed later in honor of the famous hunter and naturalist Jim Corbett.
• It is situated at the Himalayan foothills, offering a stunning landscape of hills, grasslands, rivers, and dense forests.
• The park is a significant habitat for the endangered Royal Bengal Tiger and is also one of the most popular tiger reserves in India under the Project Tiger, launched in 1973.
• It covers an area of 520.8 sq. km, which makes it smaller compared to other national parks like the Hemis National Park (4,400 sq. km).

Additional Information

• Oldest National Park in India
• Jim Corbett National Park holds the title of the oldest national park in India, established in 1936.
• It was initially named Hailey National Park to honor the then Governor of the United Provinces, Sir Malcolm Hailey.
• Located at the Himalayan foothills
• Jim Corbett National Park is situated in the Himalayan foothills in the districts of Nainital and Pauri Garhwal in Uttarakhand.
• Its location provides a diverse ecosystem with a variety of flora and fauna.
• Home for the endangered Royal Bengal Tiger
• The park is one of the most critical tiger habitats in India and is included in the Project Tiger initiative.
• The population of Royal Bengal Tigers in the park makes it a significant spot for wildlife enthusiasts and conservation efforts.

The Correct answer is (A) is true, but (R) is false.

Key Points

• In deep sea, water appears to be coloured blue due to the phenomenon of absorption and selective scattering of light.
• Water absorbs light of longer wavelengths like red, yellow, and green more strongly, leaving shorter wavelengths like blue to be scattered, which gives the water its blue colour.
• The blue colour is not due to scattering alone, but primarily due to the absorption of light.
• Scattering of light in deep sea is minimal because particles causing scattering are fewer at greater depths.
• Assertion (A) is correct as water indeed appears coloured, but Reason (R) is incorrect because scattering is not the main cause of this phenomenon.

Additional Information

• Scattering of Light
• Scattering occurs when light interacts with small particles or molecules, causing the light to be redirected in multiple directions.
• It is responsible for phenomena like the blue colour of the sky, but its effect is limited in deep water as fewer particles are present.
• Scattering is more prominent in shallow waters or near the surface due to the presence of suspended particles.
• Absorption of Light
• Absorption is the process where light energy is taken in by a medium, such as water.
• Water absorbs light of specific wavelengths, primarily red, orange, and green.
• The remaining blue light is transmitted and scattered, giving the water its blue appearance.

The correct answer is Anguttara Nikaya.

Key Points

• Anguttara Nikaya is one of the collections in the Buddhist scriptures known as the Sutta Pitaka, which is part of the Tipitaka.
• The Tipitaka is the primary canon of Theravada Buddhism, consisting of three "baskets" or collections: the Sutta Pitaka, the Vinaya Pitaka, and the Abhidhamma Pitaka.
• The Anguttara Nikaya is a compilation of discourses (suttas) attributed to the Buddha and is organized numerically for ease of reference.
• The text describes significant geographical, political, and cultural aspects of ancient India, including the names of the 16 Mahajanapadas (great kingdoms).
• The 16 Mahajanapadas were major political entities in ancient India during the time of the Buddha, and they played a crucial role in shaping the socio-political and economic conditions of the region.
• The Anguttara Nikaya helps scholars understand the historical context of the Buddha's teachings and the political landscape during his lifetime.

Additional Information

• Buddhacharita
• Buddhacharita is an epic poem written by Ashvaghosha, a Buddhist monk and philosopher.
• The text is a biography of the Buddha, detailing his life from birth, enlightenment, and teachings to his passing away.
• Buddhacharita is considered one of the earliest and most comprehensive works on the life of Buddha.
• Lalitavistara
• Lalitavistara is a sacred Buddhist text that recounts the life story of the Buddha, focusing mainly on his early life and the events leading to his enlightenment.
• The text is associated with the Mahayana tradition of Buddhism and highlights the spiritual journey of Siddhartha Gautama.
• It is considered an important narrative for understanding the life and teachings of the Buddha.
• Sutta Nipata
• The Sutta Nipata is part of the Sutta Pitaka and contains a collection of early Buddhist discourses.
• It includes teachings that are poetic and philosophical in nature, addressing ethical and spiritual issues.
• The Sutta Nipata is especially revered for its simplicity and directness in explaining the Buddha's teachings.

Calculation

Given sound attenuation = 20 dB.

The relation between sound level and intensity is

L = 10 log₁₀(I / I₀)

Substituting the given value,

20 = 10 log₁₀(I / I₀)

⇒ log₁₀(I / I₀) = 2

⇒ I / I₀ = 10⁻² = 1 / 100

This shows that the sound intensity reduces to one-hundredth of its original value.

Therefore, the intensity decreases by a factor of 100.

Calculation

Given the angle between the polaroid sheets is 30° and the incident light is unpolarized with intensity I₀.

After passing through the first polaroid, the intensity becomes

⇒ I₁ = I₀ / 2

According to Malus’ law, the intensity after the second polaroid is

I = I₁ cos²θ

For θ = 30°, cos 30° = √3 / 2

⇒ I = (I₀ / 2) × (3 / 4) = 3I₀ / 8

Thus,

⇒ I / I₀ = 3 / 8

Therefore, the correct answer is Option 3.

Explanation

The Celsius and Kelvin scales have identical interval sizes.

⇒ A change of 1°C corresponds to a change of 1 K.

The relation between the two scales is

T_K = T_C + 273.15

When considering temperature change, the constant offset cancels out,

⇒ ΔT_K = ΔT_C

Therefore, an increase of 15°C results in an equal increase of 15 K.

This confirms that temperature differences are numerically the same on both scales.

Calculation

Given mass of each bullet m = 0.05 kg,

speed v = 1000 m/s,

number of bullets n = 20, and time t = 4 s.

Total momentum imparted is

⇒ Δp = n × m × v = 20 × 0.05 × 1000 = 1000 kg·m/s

The average force exerted is obtained from

⇒ F_avg = Δp / t

⇒ F_avg = 1000 / 4 = 250 N

Thus, the average force exerted by the hero on the gun is 250 N.

Therefore, the correct answer is Option 1.

Calculation

Two convex lenses of the same material are separated by distance d.

For zero chromatic aberration, the condition is

⇒ d = (f₁ + f₂) / 2

For minimum spherical aberration, the condition is

⇒ d = f₁ − f₂

Equating both expressions,

⇒ (f₁ + f₂) / 2 = f₁ − f₂

⇒ f₁ + f₂ = 2f₁ − 2f₂

⇒ f₁ = 3f₂

Hence,

⇒ f₁ / f₂ = 3

Therefore, the correct answer is Option 4.

Calculation

Given proper mean lifetime τ₀ = 2.4 × 10⁻⁸ s and velocity v = 0.8c.

According to time dilation, the apparent mean lifetime is

⇒ τ = τ₀ / √(1 − v²/c²)

Substituting the values,

⇒ √(1 − 0.8²) = √(1 − 0.64) = √0.36 = 0.6

⇒ τ = (2.4 × 10⁻⁸) / 0.6 = 4.0 × 10⁻⁸ s

Thus, the apparent mean lifetime of the π⁺ mesons is 4.0 × 10⁻⁸ s.

Therefore, the correct answer is Option 2.

Calculation

Given initial velocity u = 80 m/s, tower height h = 400 m, and g = 10 m/s².

At maximum height, v = 0,

⇒ 0 = 80 − 10t₁ ⇒ t₁ = 8 s

Height gained above the tower is

⇒ H = ut₁ − (1/2)gt₁² = 80×8 − 5×64 = 320 m

Total height from ground = 400 + 320 = 720 m.

For downward motion,

⇒ 720 = (1/2)gt₂² ⇒ t₂ = 12 s

Total time taken,

⇒ T = t₁ + t₂ = 20 s

Therefore, the correct answer is Option 4.

Calculation

Let two masses M₁ and M₂ be separated by distance d.

The gravitational field becomes zero at a point where the fields due to both masses are equal in magnitude.

Let this point be at distance r from M₁.

⇒ G M₁ / r² = G M₂ / (d − r)²

Canceling G and taking square root,

⇒ √M₁ / r = √M₂ / (d − r)

Rearranging,

⇒ r = d √M₁ / (√M₁ + √M₂)

Thus, the point of zero gravitational intensity lies at this distance from M₁.

Therefore, the correct answer is Option 1.

Explanation

A handshake involves direct physical contact between the hands of two individuals.

The force responsible for contact interactions arises due to repulsion and attraction between electrons and atoms in the outer shells.

These interactions are governed by electromagnetic forces, which act between charged particles.

Weak and strong nuclear forces operate only at subatomic scales, while gravitational force is negligibly small at the human scale.

⇒ The force responsible for a handshake is electromagnetic in nature.

Therefore, the correct answer is Option 2.

Explanation

A heat sink is attached to a transistor to improve heat dissipation.

During operation, transistors generate heat due to power loss across junctions.

If heat is not removed efficiently, the temperature may rise beyond safe limits, affecting performance and reliability.

⇒ The role of a heat sink is to maintain the operating temperature within permissible range.

Hence, it prevents excessive temperature rise in the transistor.

Therefore, the correct answer is Option 4.

Explanation

The efficiency of a Carnot engine operating between temperatures T₁ (source) and T₂ (sink) is

⇒ η = 1 − (T₂ / T₁)

Since temperatures are measured on the Kelvin scale, T₂ is always greater than zero and T₁ > T₂.

⇒ The ratio T₂ / T₁ is always less than 1, so η is always less than 1.

The assertion is true.

The reason is also true, but it does not fully explain the assertion, which follows from the second law of thermodynamics.

Calculation

For a freely falling body starting from rest, the distance covered in the n^th second is:

S_n = u + (1/2) g (2n − 1)

Here, u = 0.

For n = 1:

⇒ S₁ = (1/2) g

For n = 2:

⇒ S₂ = (1/2) g · 3 = (3/2) g

For n = 3:

⇒ S₃ = (1/2) g · 5 = (5/2) g

Ratio of distances:

⇒ S₁ : S₂ : S₃ = (1/2)g : (3/2)g : (5/2)g

⇒ 1 : 3 : 5

Therefore, the correct answer is Option 2.

Calculation

Given wavelength λ = 2.0 cm and slit width a = 5.0 cm.

For single-slit diffraction, the first minima occur at:

sinθ = λ / a

⇒ sinθ = 2.0 / 5.0 = 0.4

⇒ θ = sin⁻¹(0.4) ≈ 23.6°

The angular width of the central maximum extends between the first minima on both sides.

⇒ Total angular width = 2θ

⇒ θ_total = 2 × 23.6° = 47.2°

Therefore, the correct answer is Option 3.

Calculation

Given radius of the solid sphere R = 5 cm.

Moment of inertia of a solid sphere about its diameter is:

I = (2/5) MR²

Radius of gyration K is defined by:

I = MK²

⇒ K = √(I / M)

Substituting I:

⇒ K = √[(2/5) R²]

⇒ K = R √(2/5)

Putting R = 5 cm:

⇒ K = 5 √(2/5) = √10 cm

Therefore, the correct answer is Option 3.

Calculation

The given values represent molar specific heat capacities at room temperature.

Carbon has a very low molar specific heat.

⇒ B – i (6.1 J mol⁻¹ K⁻¹)

Lead has the highest molar specific heat among the given metals.

⇒ C – ii (26.5 J mol⁻¹ K⁻¹)

Silver has molar specific heat close to 25.5.

⇒ D – iii (25.5 J mol⁻¹ K⁻¹)

Aluminium has molar specific heat around 24.4.

⇒ A – iv (24.4 J mol⁻¹ K⁻¹)

Thus, the correct matching is A–iv, B–i, C–ii, D–iii.

Calculation

Given number of protons per second = 1.1 × 10¹⁸ and number of electrons per second = 3.1 × 10¹⁸.

Charge of a proton or electron, e = 1.6 × 10⁻¹⁹ C.

Current due to protons:

⇒ I_p = (1.1 × 10¹⁸) × (1.6 × 10⁻¹⁹) = 0.176 A

Current due to electrons:

⇒ I_e = (3.1 × 10¹⁸) × (1.6 × 10⁻¹⁹) = 0.496 A

Net current in the tube:

⇒ I = I_e − I_p = 0.496 − 0.176 = 0.320 A

Therefore, the correct answer is Option 1.

Calculation

The position vector is given by

⇒ R = xî + yĵ + zk̂, with magnitude R = √(x² + y² + z²)

Using vector identities:

 grad(1/R) = −R / R³, which is non-zero except at R = 0

⇒ div R = ∂x/∂x + ∂y/∂y + ∂z/∂z = 3

⇒ curl R = 0, since components are linear in x, y, z

Thus, grad(1/R) ≠ 0 in general.

The statement grad(1/R) = 0 is incorrect.

Therefore, the correct answer is Option 3.

Calculation

The dimensional formulae of the given physical quantities are identified as follows.

Energy is work done, having dimensions

⇒ [Energy] = ML²T⁻²

Force is mass × acceleration, so

⇒ [Force] = MLT⁻²

Power is energy per unit time, hence

⇒ [Power] = ML²T⁻³

Pressure is force per unit area, giving

⇒ [Pressure] = ML⁻¹T⁻²

Thus, the correct matching is:

⇒ A–iii, B–iv, C–i, D–ii

Therefore, the correct answer is Option 3.

Calculation

Given velocity v = c/3 and stationary time t = 1 hour = 3600 s.

Time dilation relation is

⇒ t′ = t √(1 − v²/c²)

Substituting v = c/3,

⇒ t′ = 3600 √(1 − 1/9) = 3600 √(8/9)

⇒ t′ ≈ 3394.1 s

The time difference is

⇒ Δt = t − t′ = 3600 − 3396.6 ≈ 205.8 s

⇒ Δt ≈ 205.8 / 60 ≈ 3.43 min

Thus, the moving clock runs slow by about 3.43 minutes.

Therefore, the correct answer is Option 1.

Calculation

Given speed at lowest point v = 3 m/s, length L = 0.5 m, and g = 10 m/s².

By conservation of mechanical energy,

⇒ (1/2)mv² = mgh + (1/2)mv₁²

Here, h = L(1 − cosθ). For θ = 60°, cos60° = 0.5.

⇒ (1/2)v² = gL(1 − 0.5) + (1/2)v₁²

⇒ v₁² = v² − 2gL(1 − 0.5)

⇒ v₁² = 9 − 2×10×0.5×0.5 = 4.0

⇒ v₁ ≈ √4 ≈ 2.0 m/s

Therefore, the correct answer is Option 2.

Explanation

In β⁻-decay, a neutron inside the nucleus transforms into a proton.

This process is accompanied by the emission of an electron.

To conserve energy, momentum, and lepton number, another neutral particle is also emitted.

⇒ This particle is an anti-neutrino.

Thus, along with the electron, an anti-neutrino is released during β⁻-decay.

Therefore, the correct answer is Option 3.

Calculation

The Boolean expressions are simplified using De Morgan’s laws.

AND gate output is A·B, which can be written as

⇒ A·B = (A + B)

OR gate output is A + B, which is

⇒ A + B = (A · B)

NAND gate output is

⇒ (A · B)

NOR gate output is

⇒ (A + B) = A · B

Thus, the correct matching is:

⇒ A–iv, B–iii, C–ii, D–i

Calculation

Given potential at P, V_P = 10 V and at Q, V_Q = −4 V.

Number of electrons n = 100 and charge of one electron e = 1.6 × 10⁻¹⁹ C.

Potential difference is

⇒ ΔV = V_Q − V_P = −4 − 10 = −14 V

Total charge moved is

⇒ q = n × e = 100 × 1.6 × 10⁻¹⁹ = 1.6 × 10⁻¹⁷ C

Work done is

⇒ W = qΔV = (1.6 × 10⁻¹⁷) × (−14) = −2.24 × 10⁻¹⁶ J

The work done is - 2.24 × 10⁻¹⁶ J.

Explanation

The retina is the innermost light-sensitive layer of the human eye.

It contains specialized neural cells such as rods and cones.

These cells detect light and convert it into electrical signals.

⇒ The signals are then transmitted to the brain through the optic nerve.

The cornea, iris, and lens are different parts of the eye and do not form the retina.

Therefore, the retina consists of sensitive neural cells.

Hence, the correct answer is Option 3.

Explanation

Elasticity refers to the ability of a material to regain its original shape after the deforming force is removed.

In physics, elasticity is measured by the modulus of elasticity.

Steel has a much higher modulus of elasticity than rubber.

⇒ This means steel requires a much larger force to produce the same deformation.

Although rubber stretches more, it has a lower elastic modulus.

Hence, steel is considered far more elastic than rubber.

Therefore, the correct answer is Option 1.

Explanation

The given beam is circularly polarized.

When circularly polarized light passes normally through a quarter-wave plate, a phase difference of λ/4 (π/2) between orthogonal components is removed.

⇒ The light emerging from the quarter-wave plate becomes plane polarized.

When this plane-polarized light is analyzed using a rotating Nicol prism, the intensity varies from maximum to zero.

⇒ Complete extinction confirms linear polarization after the quarter-wave plate.

This behavior is possible only if the incident light was circularly polarized.

Therefore, the given beam of light is circularly polarized.

Explanation

Degrees of freedom represent the independent ways in which a molecule can store energy.

Monoatomic gas molecules possess only translational motion along three mutually perpendicular directions.

⇒ Hence, they have exactly three degrees of freedom.

Diatomic gases such as O₂, H₂, and N₂ also exhibit rotational (and sometimes vibrational) degrees of freedom.

Helium (He) is a monoatomic gas.

⇒ It has only translational degrees of freedom.

Therefore, the correct answer is Option 4.

Explanation

When a source emitting a line spectrum is placed in a magnetic field, the applied field interacts with atomic magnetic moments.

This interaction causes a single spectral line to split.

⇒ In a sufficiently strong magnetic field, the line splits into three distinct components.

This characteristic three-line splitting corresponds to the normal Zeeman effect.

Hence, the observed phenomenon is the normal Zeeman effect.

Therefore, the correct answer is Option 1.

Calculation

A particle of mass m moves with uniform speed v in a circular path of radius r.

When it goes from one point to the diametrically opposite point, the direction of velocity reverses.

⇒ Initial momentum = mv, final momentum = −mv

The change in momentum is

⇒ Δp = |−mv − mv| = 2mv

The speed remains constant throughout the motion.

⇒ Kinetic energy, which depends only on speed, does not change.

Thus, momentum changes by 2mv while kinetic energy remains constant.

Therefore, the correct answer is Option 3.

Calculation

Two waves are given as:

⇒ y₁ = 10 sin(100πt)

⇒ y₂ = 10 sin(108πt)

The angular frequency ω is related to frequency f by:

⇒ ω = 2πf

For the first wave:

⇒ 100π = 2πf₁ ⇒ f₁ = 50 Hz

For the second wave:

⇒ 108π = 2πf₂ ⇒ f₂ = 54 Hz

The number of beats per second (beat frequency) is:

⇒ |f₂ − f₁| = |54 − 50| = 4 Hz

Thus, the number of beats produced per second is 4.

Therefore, the correct answer is Option 4.

Calculation

According to the Stefan–Boltzmann law, the radiant energy emitted per unit surface area of a black body per unit time is directly proportional to the fourth power of its absolute temperature:

⇒ E = σT⁴

Here:

⇒ E represents energy radiated per unit area per unit time

⇒ σ is Stefan’s constant

⇒ T is absolute temperature

The dimensional formula of energy per unit time (power) is:

⇒ [Power] = ML²T⁻³

Since E is energy radiated per unit area per unit time:

⇒ [E] = (ML²T⁻³) / L² = MT⁻³

The dimensional formula of temperature is:

⇒ [T] = K

From the Stefan–Boltzmann law:

⇒ σ = E / T⁴

Substituting dimensional formulas:

⇒ [σ] = [MT⁻³] / [K⁴]

⇒ [σ] = MT⁻³K⁻⁴

Thus, the dimensional formula of Stefan’s constant is:

[MT⁻³K⁻⁴]

Therefore, the correct answer is Option 1.

Calculation

The question asks for the unit that is used to measure very short lengths.

Interpretation of the given options:

⇒ Parsec is used to measure extremely large interstellar distances.

⇒ Astronomical unit is used to measure distances within the solar system.

⇒ Light year represents the distance travelled by light in one year and is also a large astronomical unit.

⇒ Fermi (10⁻¹⁵ m) is used to measure nuclear dimensions and subatomic-scale lengths.

Since nuclear and subatomic distances are extremely small, Fermi is the appropriate unit for short lengths.

Therefore, the correct answer is Option 2.

Calculation

Three identical bodies of mass M and radius R are considered about the YY′ axis.

Moment of inertia about the central diameter:

I₁ = 1/2 MR²

The other two bodies rotate about a tangent axis.

Using the parallel axis theorem:

I₂ = I₃ = 1/2 MR² + MR² ⇒ 3/2 MR²

Total moment of inertia about YY′:

I_YY′ = I₁ + I₂ + I₃

⇒ I_YY′ = 1/2 MR² + 3/2 MR² + 3/2 MR²

⇒ I_YY′ = 7/2 MR²

Calculation

Given a forward-biased diode carrying forward current I.

Dynamic resistance is defined as:

R_d = dV / dI

For a diode in forward bias, dynamic resistance varies inversely with current.

⇒ R_d ∝ 1 / I

⇒ Increase in forward current causes a decrease in dynamic resistance.

This relation explains the conducting behavior of a diode under forward bias.

Therefore, the correct answer is Option 1.

Explanation

Assertion (A) states that internal energy (U) is a state function.

A state function depends only on the initial and final states of a system.

⇒ Internal energy is independent of the path followed.

Reason (R) states that internal energy depends on the path.

This contradicts the definition of a state function.

⇒ Reason (R) is incorrect.

Thus, Assertion (A) is true, but Reason (R) is false.

Therefore, the correct answer is Option 1.

Calculation

Electrical force per unit area is given by:

F / A = 1/2 ε₀E²

Using E = σ / ε₀ :

⇒ F / A = 1/2 ε₀(σ / ε₀)² = σ² / (2ε₀)

Projected area of the surface:

A = πR²

Net electrical force:

⇒ F = (σ² / 2ε₀) · (πR²)

In equilibrium, this equals the applied force.

⇒ F = πσ²R² / (2ε₀) ⇒ F ∝ σ²R² / ε₀

Calculation

Thermodynamic processes are matched using their defining properties.

Isothermal expansion occurs at constant temperature.

⇒ For an ideal gas, internal energy remains constant.

⇒ A – iv

Isobaric expansion occurs at constant pressure.

⇒ Temperature rises during expansion, so internal energy increases.

⇒ B – iii

Adiabatic expansion involves no heat exchange.

⇒ Work is done at the expense of internal energy.

⇒ C – ii

Isochoric process occurs at constant volume.

⇒ No work is done.

⇒ D – i

Thus, the correct match is A–iv, B–iii, C–ii, D–i.

Explanation

Lenz’s law describes the direction of induced current in electromagnetic induction.

It states that the induced current always opposes the change in magnetic flux producing it.

⇒ This opposition prevents spontaneous generation of energy.

According to the law of conservation of energy, energy can neither be created nor destroyed, only transformed.

If the induced current aided the change in flux, it would lead to continuous energy gain.

⇒ Such a situation violates energy conservation.

Thus, Lenz’s law is a direct consequence of the conservation of energy.

Therefore, the correct answer is Option 4.

Calculation

Given vector field A = grad ϕ.

From vector calculus, the curl of a gradient field is always zero.

⇒ curl(A) = curl(grad ϕ)

⇒ curl(A) = 0

A vector field with zero curl is described as irrotational.

This property holds irrespective of the form of the scalar function ϕ.

Therefore, the correct answer is Option 3.

Calculation

Given pressure P and energy density E for a monoatomic ideal gas.

Energy density equals internal energy per unit volume.

For a monoatomic gas:

E = (3/2) nRT

Pressure of an ideal gas is:

P = nRT

Dividing the two relations:

⇒ P / E = (nRT) / [(3/2) nRT]

⇒ P / E = 2 / 3

⇒ P = (2/3) E

This shows pressure is two-thirds of the energy density.

Therefore, the correct answer is Option 4.

Calculation

The Joule–Thomson coefficient μ is defined as the change in temperature with pressure at constant enthalpy.

μ = (∂T / ∂P)_H

For an ideal gas, intermolecular forces are absent.

⇒ Enthalpy depends only on temperature.

⇒ During throttling, temperature remains unchanged.

Hence, the Joule–Thomson coefficient for an ideal gas is:

⇒ μ = 0

This indicates no cooling or heating on expansion at constant enthalpy.

Therefore, the correct answer is Option 4.

Calculation

Assertion (A) states that an ammeter is always connected in series in a circuit.

This is correct because current must pass through the ammeter for measurement.

Reason (R) states that an ammeter has very low resistance.

Low resistance ensures negligible potential drop and prevents change in circuit current.

⇒ This property justifies series connection of the ammeter.

Thus, both Assertion (A) and Reason (R) are true.

⇒ Reason (R) correctly explains Assertion (A).

Therefore, the correct answer is Option 4.

Calculation

Given the depression at the free end of a cantilever of length l is δ.

For a cantilever beam, depression at a distance x from the fixed end varies as:

δ_x = δ · (x / l)²(3-2x/l)

At x = l / 4:

⇒ δ_x = δ · (1 / 4)²(3-1/2)

⇒ δ_x = δ 0.15625 ≈ 0.15 δ

This gives the depression at one-fourth the length from the fixed end.

Therefore, the correct answer is Option 1.

Explanation:

Assertion (A) states that the temperature coefficient of resistance for metals is positive.

This is correct because resistance of metals increases with rise in temperature.

Reason (R) states that the temperature coefficient of resistance for insulators is also positive.

Insulators generally show a decrease in resistance with increase in temperature.

⇒ Their temperature coefficient of resistance is negative.

Thus, Assertion (A) is true, but Reason (R) is false.

Therefore, the correct answer is Option 2.

Calculation

Let the wave function of the particle be ψ.

In quantum mechanics, the energy operator is:

Ĥ = iħ (∂ / ∂t)

The expectation value of energy is defined as:

⟨E⟩ = ∫ ψ* [ iħ (∂ψ / ∂t) ] dV

Here, ψ* represents the complex conjugate of the wave function.

This integral gives the average value of energy associated with the state ψ.

Therefore, the correct answer is Option 2.

Calculation

Given emf E = 10 V, internal resistance r = 3 Ω, and current I = 0.5 A.

Total resistance in the circuit equals external resistance plus internal resistance.

Using Ohm’s law:

E = I (R + r)

⇒ R = (E / I) − r

⇒ R = (10 / 0.5) − 3

⇒ R = 20 − 3

⇒ R = 17 Ω

The resistance of the external resistor is 17 Ω.

Therefore, the correct answer is Option 3.

Calculation

Given a liquid drop of radius R and surface tension T is broken into n identical drops.

Initial surface area of the large drop:

A₁ = 4πR²

From volume conservation:

⇒ R³ = n r³ ⇒ r = R · n^−1/3

Total surface area of n small drops:

A₂ = n · 4πr² = 4πR² n^2/3

Increase in surface area:

ΔA = 4πR²(n^2/3 − 1)

Work done = increase in surface energy:

⇒ W = T · ΔA = 4πR²T (n^2/3 − 1)

Therefore, the correct answer is Option 1.

Calculation

Unpolarised light of intensity I₀ is incident on two polarisers inclined at 30°.

After the first polariser:

⇒ I₁ = I₀ / 2

Using Malus’ law for the second polariser:

⇒ I₂ = (I₀ / 2) · cos²30°

Since cos30° = √3 / 2:

⇒ cos²30° = 3 / 4

⇒ I₂ = (I₀ / 2) · (3 / 4) = 3I₀ / 8

Percentage transmitted:

⇒ (3 / 8) × 100 = 37.5%

Therefore, the correct answer is Option 4.

Calculation

Given binary number = 1101.

Using positional weights of binary digits:

⇒ (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰)

⇒ 8 + 4 + 0 + 1

⇒ 13

The decimal equivalent of the binary number 1101 is 13.

Therefore, the correct answer is Option 1.

Calculation

The Clausius–Clapeyron equation relates pressure and temperature during a phase change.

It connects latent heat L, absolute temperature T, and the change in specific volumes of the two phases.

The standard form of the equation is:

⇒ dP / dT = L / [ T (V₂ − V₁) ]

Here, L is the latent heat of transition, T is the absolute temperature, and V₂ and V₁ are the specific volumes of the two phases.

This relation is derived from thermodynamic equilibrium conditions during phase transition.

Therefore, the correct answer is Option 3.

Explanation:

Each option is examined using definitions of speed and velocity.

Option 1 is incorrect because average speed can be zero only if total distance is zero, which requires speed to be zero throughout.

Option 2 is incorrect since average speed depends on total distance, whereas average velocity depends on displacement.

Option 3 is incorrect because if speed is always zero, the particle does not move, so average speed is also zero.

Option 4 states that speed is the magnitude of velocity.

⇒ By definition, speed equals the magnitude of velocity.

Therefore, the correct answer is Option 4.

Calculation

The sodium D-line arises due to electronic transitions between the 3p and 3s energy levels.

⇒ Hence, transition 3p → 3s is correct.

Sodium D-lines belong to the principal series.

⇒ This statement is correct.

The allowed selection rules are:

⇒ ΔL = ±1 and ΔJ = 0, ±1

This condition is satisfied for sodium D-line transitions.

Spin–orbit interaction causes splitting of the 3p level into two states.

⇒ The 3s level does not split.

Thus, the statement claiming that both 3p and 3s split is incorrect.

Therefore, the correct answer is Option 4.

Explanation:

A Zener diode is designed to operate in the reverse breakdown region.

⇒ In this region, it maintains a nearly constant voltage across its terminals despite variations in current.

This property makes the Zener diode suitable for stabilizing voltage in electronic circuits.

⇒ It is not primarily used as a current source, rectifier, or amplifier.

Therefore, the correct answer is Option 2: Voltage regulator.

Explanation:

In a stationary sound wave, pressure variations arise due to the interference of sound waves.

⇒ Nodes are points where the displacement amplitude is minimum.

⇒ Antinodes are points where the displacement amplitude is maximum.

Pressure variation is directly related to the amplitude of oscillation.

⇒ At nodes, pressure variation is minimum.

⇒ At antinodes, pressure variation is maximum.

Therefore, the correct answer is Option 2.

Calculation

Assertion (A): In Simple Harmonic Motion (SHM), the motion is to and fro and periodic.

⇒ This statement is true by definition of SHM, where the particle oscillates about a mean position with a fixed time period.

Reason (R): The velocity of a particle in SHM is given by $v = ω√(a² − x²)$.

⇒ This expression correctly represents the instantaneous velocity of a particle in SHM.

⇒ However, this velocity equation does not explain why the motion is to and fro and periodic; that behavior arises from the restoring force being proportional to displacement.

Conclusion:

⇒ Assertion (A) is true.

⇒ Reason (R) is true.

⇒ Reason (R) is not the correct explanation of Assertion (A).

Therefore, the correct answer is Option 1.

Calculation

Assertion (A): When two vibrating tuning forks of frequencies 256 Hz and 512 Hz are held near each other, beats cannot be heard.

⇒ Beat formation requires the frequencies of the two sources to be nearly equal.

⇒ Here, the frequency difference is 512 − 256 = 256 Hz, which is very large.

⇒ Hence, beats are not produced, so Assertion (A) is true.

Reason (R): The principle of superposition is valid if the frequencies of oscillations are nearly equal.

⇒ This statement is correct and explains a general condition for beat formation.

⇒ However, it does not directly explain why beats are absent in this specific case of widely differing frequencies.

Conclusion:

⇒ Assertion (A) is true.

⇒ Reason (R) is true.

⇒ Reason (R) is not the correct explanation of Assertion (A).

Therefore, the correct answer is Option 2.

Calculation

Given:

b = distance of the point of observation from the wavefront

λ = wavelength of light

⇒ In Fresnel diffraction, the area of a Fresnel zone depends on the distance from the wavefront and the wavelength.

⇒ Area of a Fresnel zone = 2πbλ

⇒ Substituting the given parameters, the area is directly expressed as 2πbλ.

Therefore, the correct answer is Option 1.

Calculation

Given:

Charge of one electron, e = 1.6 × 10⁻¹⁹ C

Number of electrons per second, n = 10⁹ s⁻¹

Total charge required, Q = 1 C

⇒ Charge transferred per second = n × e = 10⁹ × 1.6 × 10⁻¹⁹ = 1.6 × 10⁻¹⁰ C

⇒ Time required, t = Q / (n × e) = 1 / (1.6 × 10⁻¹⁰) = 6.25 × 10⁹ s

⇒ 1 year = 3.1536 × 10⁷ s

⇒ t ≈ 6.25 × 10⁹ / 3.1536 × 10⁷ ≈ 198 years

Therefore, the correct answer is Option 4.

CONCEPT:

Hoffmann Bromamide Reaction

• The Hoffmann Bromamide reaction is a chemical reaction in which an amide (aliphatic, aromatic, or heterocyclic) reacts with an alkaline hypohalite (e.g., sodium hydroxide solution with bromine or chlorine) to produce a primary amine.
• This reaction involves the conversion of an amide to a primary amine, with the loss of one carbon atom from the original amide group.
• The reaction occurs via a mechanism that includes the formation of an isocyanate intermediate, followed by hydrolysis to yield the primary amine.

EXPLANATION:

• In the given reaction:

Amide (Aromatic/Aliphatic/Heterocyclic) + Alkaline hypohalite (NaOH solution + Br₂/Cl₂) → Primary amine + Others

• 
• This is a characteristic reaction of the Hoffmann Bromamide reaction.
• The reaction mechanism involves the following steps:
• Amide reacts with bromine/chlorine in the presence of sodium hydroxide to form an N-bromoamide intermediate.
• The N-bromoamide undergoes rearrangement to form an isocyanate intermediate.
• The isocyanate is hydrolyzed in the aqueous solution to yield a primary amine and carbon dioxide as by-products..

Therefore, the correct answer is Hoffmann Bromamide Reaction.

CONCEPT:

Curie (Ci) and Decay Rate

• Radioactive decay refers to the process by which unstable atomic nuclei lose energy by emitting radiation.
• The Curie (Ci) is a unit of radioactivity that represents the number of decays per second.
• 1 Curie (Ci) corresponds to 3.7 × 10¹⁰ disintegrations per second.
• This unit is named after Marie Curie, who was a pioneer in the field of radioactivity.
• The Becquerel (Bq) is another unit used to measure radioactivity, but it is much smaller than the Curie. 1 Bq = 1 disintegration per second.

EXPLANATION:

• The question states that the decay rate is 3.7 × 10¹⁰ disintegrations per second.
• From the concept above, this matches the definition of 1 Curie (Ci).

Additional Information

• 1 mol (Mole): Represents the amount of substance containing Avogadro's number of entities (atoms, molecules, etc.).
• 1 rad (Radian): A unit of angle measurement, unrelated to radioactivity.
• 1 Bq (Becquerel): Represents only 1 disintegration per second, much smaller than 3.7 × 10¹⁰.
• Therefore, the correct answer is 1 Ci (Curie).

Thus, the amount of a radioactive substance with a decay rate of 3.7 × 10¹⁰ disintegrations per second is called 1 Ci (Curie).

CONCEPT:

Isotopic Effect on Vibrational Frequency (IR Spectroscopy)

• The stretching frequency of a bond in IR spectroscopy depends on the force constant and the reduced mass of the bonded atoms.
• The vibrational frequency is given by the relation:

ν̄ = (1 / 2πc) √(k / μ)

• For isotopic substitution, the force constant (k) remains almost the same, but the reduced mass (μ) changes.
• Frequency is inversely proportional to the square root of the reduced mass:

ν̄ ∝ 1 / √μ

EXPLANATION:

• For an alkane, the C–H stretching frequency is given as 2900 cm^-1.
• When hydrogen (H) is replaced by deuterium (D), the mass increases approximately two times.
• Therefore, the stretching frequency decreases according to:

ν_C–D = ν_C–H / √2

• Substituting the value:
• ν_C–D = 2900 / √2
• ν_C–D ≈ 2050 cm^-1
• The nearest value among the given options is 2250 cm^-1.

Therefore, the correct answer is 2250 cm^-1.

CONCEPT:

Energy of Electron in Hydrogen Atom (Bohr’s Model)

• According to Bohr’s model, the energy of an electron in the n^th orbit of a hydrogen atom is given by:

E_n = E₁ / n²

• Where,
• E₁ = energy of the first orbit
• n = principal quantum number
• The negative sign indicates that the electron is in a bound state.

EXPLANATION:

Given:

• Energy of first orbit, E₁ = −2.17 × 10⁻¹⁸ J/atom
• For 5^th orbit, n = 5

Using the formula:

E₅ = E₁ / 5²

E₅ = (−2.17 × 10⁻¹⁸) / 25

E₅ = −0.0868 × 10⁻¹⁸ J

E₅ = −8.68 × 10⁻²⁰ J/atom

So, the correct answer is −8.68 × 10⁻²⁰ J/atom

CONCEPT:

Bond Angle in Hydrides

• The bond angle in hydrides (AH₃) depends on the electronegativity of the central atom (A) and the lone pair-bond pair repulsion.
• As the size of the central atom increases down the group in the periodic table, the bond angle decreases due to reduced lone pair-bond pair repulsion.
• The trend in bond angles for NH₃, PH₃, AsH₃, and SbH₃ can be explained as follows:
• NH₃ has the smallest central atom (Nitrogen), so it has the largest bond angle.
• PH₃, AsH₃, and SbH₃ have progressively larger central atoms, leading to smaller bond angles.

EXPLANATION:

• 

• 
• Correct matching based on bond angles:
• A (NH₃) - iii (107.8°)
• B (PH₃) - iv (93.3°)
• C (AsH₃) - i (91.8°)
• D (SbH₃) - ii (91.3°)

Correct Answer: 1) A-iii, B-iv, C-i, D-ii

CONCEPT:

Shifts in Absorption Spectroscopy

• Absorption spectroscopy involves the measurement of light absorbed by a substance as a function of wavelength.
• Various shifts in absorption bands are observed in spectroscopy due to changes in molecular structure or environment. These include:
• Red Shift: Shift of absorption to longer wavelengths (lower energy).
• Blue Shift: Shift of absorption to shorter wavelengths (higher energy).
• Hyperchromic Shift: Increase in molar absorptivity (intensity of absorption).
• Hypsochromic Shift: Shift of absorption to shorter wavelengths (higher energy).
• Hypochromic Shift: Decrease in molar absorptivity (intensity of absorption).

EXPLANATION:

• Option A (Red shift - Shift of absorption to longer wavelength): This is correct. A red shift corresponds to a shift of absorption to longer wavelengths.
• Option B (Hyperchromic shift - Increase in molar absorptivity): This is correct. A hyperchromic shift refers to an increase in the intensity of absorption.
• Option C (Blue shift - Decrease in absorption intensity): This is incorrect. A blue shift refers to a shift of absorption to shorter wavelengths (not a decrease in intensity).
• **Option D (**Hypsochromic shift means shift to shorter wavelength, not decrease in molar absorptivity.

So, Option C is not correctly matched.

Therefore, the correct answer is Option 3 (C).

CONCEPT:

Unpaired Electrons in Coordination Complexes

• The number of unpaired electrons in a coordination complex depends on:
• The oxidation state of the central metal atom/ion.
• The geometry of the complex (tetrahedral, octahedral, etc.).
• The nature of the ligands (strong field or weak field ligands, as per crystal field theory).
• In tetrahedral geometry, the crystal field splitting energy (Δ_t) is smaller compared to octahedral geometry (Δ_o).
• Because of the smaller splitting energy in tetrahedral geometry, electrons tend to occupy higher energy orbitals rather than pairing up in lower energy orbitals.

EXPLANATION:

![Solved] Hybridisation of [NiCl4]2- is ...](https://cdn.testbook.com/images/production/quesImages/qImage695d48e7ac6db816acbc90ef.png)

• In the given complex [NiCl₄]^2-:
• Nickel (Ni) is in the +2 oxidation state, so its electronic configuration is 3d⁸.
• Chloride (Cl^-) is a weak field ligand, so it does not cause strong pairing of electrons.
• The tetrahedral geometry of the complex leads to a small crystal field splitting energy (Δ_t), so the electrons will remain unpaired.
• For a 3d⁸ configuration in tetrahedral geometry:
• The two lower energy orbitals (e set) will be occupied by four electrons.
• The three higher energy orbitals (t₂ set) will be occupied by the remaining four electrons, with two unpaired electrons.

Therefore, the number of unpaired electrons in [NiCl₄]^2- is 2.

CONCEPT:

Nuclear Fusion

• Nuclear fusion is a nuclear reaction in which two or more light nuclei combine to form a heavier nucleus.
• Fusion reactions release a very large amount of energy due to:
• Mass defect
• Conversion of mass into energy (E = mc²)
• Fusion reactions generally occur at:
• Very high temperature
• Very high pressure
• The Sun and stars produce energy by nuclear fusion.

EXPLANATION:

• ¹²C + ¹H → ¹³N
• Involves proton capture, not typical fusion of two light nuclei.
• ¹⁴N + ¹n → ¹²C + …
• Neutron-induced reaction, not fusion.
• ²H + ³H → ⁴He + energy
• Two light nuclei (deuterium and tritium) combine.
• A heavier nucleus (helium) is formed.
• This is a classic example of nuclear fusion.
• ²³⁵U + ¹n → ¹⁴¹Ba + ⁹²Kr + neutrons
• Heavy nucleus splits into lighter nuclei.
• This is nuclear fission, not fusion.

Therefore, the correct answer is ²H + ³H → ⁴He (nuclear fusion).

CONCEPT:

First Law of Thermodynamics

• The First Law of Thermodynamics represents the law of conservation of energy.
• According to the chemistry sign convention:

ΔE = q + w

• ΔE = Change in internal energy of the system
• q = Heat absorbed by the system
• w = Work done on the system
• In an adiabatic process, no heat is exchanged between the system and surroundings.
• Therefore, for an adiabatic process:

q = 0

EXPLANATION:

• Using the First Law of Thermodynamics:

ΔE = q + w

• For an adiabatic process:

q = 0

• Substituting q = 0 in the equation:

ΔE = 0 + w

• Hence: ΔE = w

Therefore, for an adiabatic process, the change in internal energy is equal to the work done on the system.

CONCEPT:

Hydrolysis of Esters in Acidic Medium

CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH

• The reaction given is the hydrolysis of an ester in the presence of an acid (H⁺):
• Rate of reaction depends primarily on the concentration of the ester.
• Since water is present in large excess, its concentration remains effectively constant during the reaction.
• Hence, the reaction behaves as a pseudo first-order reaction instead of a second-order reaction.

EXPLANATION:

Rate = k' [ester], where k' = k [H₂O]

• The actual rate law is:
  

Rate = k [ester][H₂O]

• Because [H₂O] >> [ester], its concentration can be considered constant:
• Thus, the reaction appears to follow first-order kinetics with respect to the ester.

Therefore, the correct answer is Option (3): Pseudo first-order reaction.

CONCEPT:

Oxidation of Glucose with Br₂/H₂O

• Glucose is a monosaccharide with an aldehyde functional group (-CHO) at one end of the molecule.
• When glucose is oxidized with bromine water (Br₂/H₂O), the aldehyde group (-CHO) is selectively oxidized to a carboxylic acid (-COOH).
• This reaction converts glucose into gluconic acid.
• The bromine water acts as a mild oxidizing agent, reacting specifically with the aldehyde group without affecting other groups like the alcohol groups present in glucose.

EXPLANATION:

• In the given reaction:

Glucose + Br₂/H₂O → Gluconic acid + HBr

• 
• Here:
• The aldehyde group (-CHO) of glucose is oxidized to a carboxylic acid group (-COOH).
• Gluconic acid is formed as the product.
• The other options are incorrect because:
• Levulinic acid is not formed in this reaction.
• Glucaric acid is formed when glucose is oxidized more strongly, not with Br₂/H₂O.
• Sorbitol is formed by the reduction of glucose, not oxidation.

Therefore, the correct answer is Gluconic acid.

CONCEPT:

Match List I with List II

• Acetic acid, Sodium phenate, Methyl cyanide, and Toluene react differently depending on the reaction mechanism applied.
• Each reaction has a specific reagent or mechanism associated with it, as follows:
• Acetic acid (A): Undergoes HVZ reaction (Hell-Volhard-Zelinsky reaction), which involves halogenation at the alpha position of a carboxylic acid.
• ​

• Sodium phenate (B): Participates in Kolbe’s reaction to yield salicylic acid derivatives.
• 
• Methyl cyanide (C): Converts into aldehydes using the Stephen reaction.
• 
• Toluene (D): Undergoes the Friedel-Crafts reaction to produce alkylated or acylated products.
• 

EXPLANATION:

• A. Acetic acid: Matches with iii. HVZ reaction.
• B. Sodium phenate: Matches with iv. Kolbe's reaction.
• C. Methyl cyanide: Matches with i. Stephen reaction.
• D. Toluene: Matches with ii. Friedel-Crafts reaction.

Therefore, the correct option is: 3) A-iii, B-iv, C-i, D-ii.

CONCEPT:

Spectral Series of Hydrogen and Related Regions

• The hydrogen atom emits light of specific wavelengths, which are categorized into spectral series. Each series corresponds to electronic transitions to or from a particular energy level.
• The major spectral series and their regions in the electromagnetic spectrum are as follows:
• Lyman series: Transitions to n=1. Lies in the ultraviolet (UV) region.
• Balmer series: Transitions to n=2. Lies in the visible region.
• Paschen series: Transitions to n=3. Lies in the infrared region.
• Brackett series: Transitions to n=4. Lies in the infrared region.
• Pfund series: Transitions to n=5. Lies in the infrared region.

EXPLANATION:

• In the given question, the spectral series and their corresponding regions are matched. We need to identify which one is incorrect.
• Options:
• a. Paschen – Infrared: Correct. The Paschen series lies in the infrared region.
• b. Brackett – Infrared: Correct. The Brackett series lies in the infrared region.
• c. Lyman – Microwave: Incorrect. The Lyman series lies in the ultraviolet (UV) region, not in the microwave region.
• d. Balmer – Visible: Correct. The Balmer series lies in the visible region.

Thus, the incorrect matching is c. Lyman – Microwave.