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The Correct answer is act as a concave lens.

Key Points

• The power of a lens indicates its ability to converge or diverge light rays. It is measured in diopters (D).
• The combined power of two lenses is given by the algebraic sum of their individual powers: P = P₁ + P₂.
• For the given lenses, the powers are +2.0 D and -2.5 D. Adding these powers: P = +2.0 - 2.5 = -0.5 D.
• A lens with a negative power acts as a concave lens, which diverges light rays.
• Concave lenses are used for applications such as correcting nearsightedness (myopia) or as part of optical instruments to spread out light rays.
• Thus, the combination of the lenses results in a concave lens due to its negative power.

 Additional Information

• act as a convex lens
• A lens with a positive power acts as a convex lens, which converges light rays.
• Convex lenses are used for applications such as correcting farsightedness (hyperopia) or as magnifying glasses.
• In this case, the combined power is negative (-0.5 D), so the combination cannot act as a convex lens.
• act as a simple mirror
• Mirrors reflect light, whereas lenses refract light by bending it. Mirrors do not have powers measured in diopters.
• This option is irrelevant in the context of lens power and combination.
• not form any image
• All lenses, whether convex or concave, form images by refracting light. The nature of the image depends on the type of lens and the position of the object.
• Even a concave lens forms virtual and upright images, so this option is incorrect.

The Correct answer is The momentum remains conserved, but not the kinetic energy.

Key Points

• In an inelastic collision, the total momentum of the system remains conserved due to the principle of conservation of momentum.
• The system’s kinetic energy, however, is not conserved in an inelastic collision.
• During the collision, a part of the kinetic energy is converted into other forms of energy such as heat, sound, or deformation energy.
• An inelastic collision often results in the two colliding objects sticking together or deforming permanently.
• Momentum conservation is applicable as long as there are no external forces acting on the system.
• Examples of inelastic collisions include a car crash, clay sticking together upon impact, or a ball of putty hitting the ground.
• The mathematical representation for momentum conservation in an inelastic collision is: m₁v₁ + m₂v₂ = (m₁ + m₂)v, where m₁ and m₂ are the masses, and v₁ and v₂ are the velocities before the collision.
• Although total energy (including all forms) is conserved in any collision, kinetic energy alone is not conserved in inelastic collisions.

 Additional Information

• The kinetic energy remains conserved, but not the momentum.
• This option is incorrect because in any type of collision (elastic or inelastic), the momentum is always conserved.
• Kinetic energy conservation is characteristic of elastic collisions, not inelastic ones.
• Both the kinetic energy and the momentum remain conserved.
• This statement applies only to elastic collisions.
• In an elastic collision, the objects bounce off without any loss of kinetic energy.
• Neither the kinetic energy nor the momentum remains conserved.
• This option is incorrect because the principle of conservation of momentum holds true for all types of collisions, whether elastic or inelastic.
• Momentum conservation is fundamental and does not depend on the type of collision.

The correct answer is 4500 m.

Key Points

• The train starts from rest, implying the initial velocity (u) is 0 km/h.
• The final velocity (v) is given as 108 km/h, which is converted to meters per second as 108 × (1000/3600) = 30 m/s.
• The time taken to attain this speed is 5 minutes, which is equal to 300 seconds.
• Using the formula for distance under uniform acceleration: s = ut + (1/2)at², where a is acceleration.
• Acceleration (a) can be calculated using a = (v - u) / t = (30 - 0) / 300 = 0.1 m/s².
• Substituting the values into the formula: s = 0 × 300 + (1/2) × 0.1 × (300)² = 4500 m.

Additional Information

• Uniform acceleration: It refers to constant acceleration, meaning the rate of change of velocity remains the same over time.
• Conversion of units: When solving physics problems, converting units like km/h to m/s is essential for consistency. The conversion factor is 1000/3600.
• Equations of motion: These equations (e.g., s = ut + (1/2)at²) are used to calculate distance, velocity, and acceleration in uniformly accelerated motion.
• SI units: In physics, calculations are performed using SI units (meters, seconds, kilograms) for universal standardization.
• Real-life applications: Understanding motion under uniform acceleration is important in areas such as transportation, engineering, and space exploration.

The correct answer is A real and inverted image would be formed at the focal point.

Key Points

• A concave mirror is a type of spherical mirror where the reflecting surface is curved inward, resembling the interior of a sphere.
• When an object is placed at infinity, the rays of light coming from the object are parallel to the principal axis of the mirror.
• These parallel rays converge at the focal point after reflecting off the concave mirror.
• The image formed is real, meaning it can be projected onto a screen, and it is inverted because of the nature of the reflection in concave mirrors.
• The position of the image is exactly at the focus (focal point) of the mirror, which is located between the center of curvature and the vertex of the mirror.
• This property of concave mirrors is widely used in applications such as telescopes, shaving mirrors, and headlights of vehicles.
• Real and inverted images are a hallmark of concave mirrors when the object is at infinity.

 Additional Information

• A virtual and inverted image would be formed at the focal point
• A virtual image is formed when rays of light appear to meet at a point, but in the case of a concave mirror, an image at the focal point is always real and inverted when the object is at infinity.
• This statement is incorrect as concave mirrors do not form virtual images at the focal point for objects at infinity.
• A real and erect image would be formed at infinity
• Real images formed by concave mirrors are always inverted, not erect, unless the object is between the pole and the focus.
• This statement is incorrect as the image of an object at infinity is formed at the focal point, not at infinity.
• A virtual and erect image would be formed at the focal point
• Virtual and erect images are formed only when the object is placed between the pole and the focus of the concave mirror.
• For an object at infinity, the image formed is real, inverted, and at the focal point, making this statement incorrect.

The Correct answer is carbon dioxide.

Key Points

• Carbon dioxide (CO₂) is the primary cause of ocean acidification, which is the ongoing decrease in the pH levels of the Earth's oceans.
• This process occurs when atmospheric CO₂ dissolves in seawater, forming carbonic acid (H₂CO₃).
• Carbonic acid dissociates into hydrogen ions (H⁺) and bicarbonate ions (HCO₃^-), leading to an increase in the ocean’s acidity.
• Since the onset of the Industrial Revolution, the combustion of fossil fuels, deforestation, and other human activities have significantly increased CO₂ concentrations in the atmosphere.
• Approximately 30-40% of the carbon dioxide released by human activities gets absorbed by the world's oceans.
• Ocean acidification can have detrimental effects on marine ecosystems, particularly for organisms like coral reefs, shellfish, and plankton that rely on calcium carbonate to build their shells and skeletons.
• As ocean pH decreases, the availability of carbonate ions decreases, making it harder for these organisms to survive and reproduce.

 Additional Information

• Carbon monoxide
• Carbon monoxide (CO) is a toxic gas that forms due to the incomplete combustion of fossil fuels.
• It does not contribute to ocean acidification but is a significant air pollutant that can affect human health by interfering with the body's ability to carry oxygen.
• Hydrogen sulfide
• Hydrogen sulfide (H₂S) is a colorless gas with a characteristic rotten egg smell, often found in volcanic gases, hot springs, and decaying organic matter.
• It does not play a role in ocean acidification but can contribute to the natural sulfur cycle in the environment.
• Chlorofluorocarbon
• Chlorofluorocarbons (CFCs) are synthetic compounds primarily used as refrigerants and propellants.
• They are responsible for the depletion of the ozone layer in the Earth's stratosphere but do not directly contribute to ocean acidification.
• Efforts like the Montreal Protocol (1987) have been implemented to phase out the use of CFCs globally.

The Correct answer is 1 and 2 only.

Key Points

• The Ordinance-making power of the Governor is derived from Article 213 of the Constitution of India.
• The Governor can promulgate ordinances only when the state legislature is not in session.
• The power is not a discretionary power. The Governor has to act on the advice of the Council of Ministers headed by the Chief Minister. Hence, statement 1 is incorrect.
• The Ordinance-making power of the Governor is restricted to subjects in the State List and the Concurrent List. It does not extend to all three lists (Union, State, and Concurrent). Therefore, statement 2 is incorrect.
• When the Governor promulgates an ordinance on a matter in the Concurrent List, it may require the President's assent if it is repugnant to a Union law. In such cases, the ordinance can prevail only if it has been enacted in accordance with the President’s instructions. Hence, statement 3 is correct.
• Thus, the correct answer is that statements 1 and 2 are not correct.

 Additional Information

• Article 213 of the Constitution
• It empowers the Governor to promulgate ordinances when the state legislature is not in session.
• However, the Governor cannot issue an ordinance without the aid and advice of the Council of Ministers.
• It is a temporary measure with the same force as a law passed by the legislature.
• State and Concurrent Lists
• The State List contains subjects on which only the state legislature has exclusive powers to legislate.
• The Concurrent List contains subjects where both the Union and State legislatures can make laws.
• The Governor’s power to issue ordinances is confined to these two lists.
• Repugnancy with Union Law
• If an ordinance conflicts with a Union law on a matter in the Concurrent List, the Union law generally prevails.
• However, if the ordinance has been made following the President's instructions, it will prevail over the Union law.

The correct answer is 1 and 3.

Key Points

• A curative petition can only be entertained by the Supreme Court of India, not by the High Courts.
• It is a legal remedy provided by the Supreme Court under its extraordinary powers to rectify any gross miscarriage of justice in its final judgments or orders.
• The petitioner must certify the curative petition with a Senior Advocate's approval, confirming that substantial grounds exist for reconsideration.
• Curative petitions are filed under the guidelines set by the Supreme Court in the landmark case of Rupa Ashok Hurra v. Ashok Hurra (2002).
• Curative petitions are rare and are entertained only after review petitions are dismissed, ensuring the finality of Supreme Court judgments is not undermined.

Additional Information

• Curative Petition: It is the final legal remedy available in the Indian judicial system to prevent any potential injustice caused by the Supreme Court's decision.
• Rupa Ashok Hurra Case (2002): This landmark case laid down the guidelines for filing curative petitions, ensuring they are used sparingly in exceptional cases.
• Certification by a Senior Advocate: The certification ensures that curative petitions are not misused and are filed only on legitimate grounds of injustice.
• Review Petition vs. Curative Petition: A review petition is filed to request the court to reconsider its judgment, while a curative petition is filed after the review petition is dismissed.
• Finality of Judgments: The purpose of curative petitions is to uphold justice without compromising the finality of Supreme Court judgments, which is vital for judicial integrity.

The correct answer is 'Both 1 and 2'

Key Points

• Statement 1:
• The Department of Economic Affairs (DEA) is indeed a nodal agency of the Government of India responsible for formulating and monitoring the country's economic policies and programs.
• These policies address both domestic and international aspects of economic management, including monetary policy, financial markets, and public finance.
• DEA plays a crucial role in managing India's macroeconomic framework, ensuring fiscal stability, and coordinating with other economic institutions globally.
• It provides strategic direction to economic reforms and policy interventions that aim to promote growth, stability, and development.
• Statement 2:
• The DEA is primarily responsible for preparing and presenting the Union Budget, which includes both the General Budget and the Railway Budget (merged with the General Budget since 2017).
• The department also formulates budgets for Union Territories without legislatures and for States under the President's Rule.
• This role is critical as the Union Budget outlines the government's expenditure and revenue estimates, impacting every sector of the economy.
• DEA coordinates with various ministries and departments to ensure alignment with fiscal policy and economic priorities.

Additional Information

• Incorrect Options:
• Option 1 (1 only): This option is incorrect because both statements 1 and 2 are correct, not just statement 1. While statement 1 accurately describes the DEA's role as a nodal agency, it does not encompass its responsibility for budget preparation, which is covered in statement 2.
• Option 2 (2 only): This option is also incorrect because it only acknowledges the DEA's responsibility for budget preparation while ignoring its broader role in economic policymaking and monitoring, as described in statement 1.
• Option 4 (Neither 1 nor 2): This option is entirely incorrect as both statements are factually accurate and describe the DEA's functions comprehensively.
• Functions of the Department of Economic Affairs:
• Formulation of macroeconomic policies including fiscal policy, public finance, and monetary policy.
• Management of government debt and external economic relations.
• Coordination with international financial institutions such as the IMF, World Bank, and ADB.
• Regulation of financial markets, including capital markets, money markets, and insurance.
• Preparation of the Union Budget and monitoring its implementation.
• Union Budget:
• The Union Budget is a comprehensive financial statement covering government revenue and expenditure for a fiscal year.
• It includes policies and allocations across sectors like health, education, defense, and infrastructure.
• The preparation of the budget is a collaborative effort involving the DEA and other ministries, ensuring alignment with economic priorities.

Important Points

• The Department of Economic Affairs is one of the five departments under the Ministry of Finance, alongside Revenue, Expenditure, Financial Services, and Investment & Public Asset Management.
• DEA also plays a critical role in policy formulation for capital markets and foreign direct investment (FDI).
• Its work is pivotal in ensuring fiscal discipline and achieving the government's economic objectives.
• The Union Budget serves as a key instrument for implementing economic policies and achieving developmental goals.

The correct answer is Both 1 and 2.

Key Points

• The District Planning Committee (DPC) is mandated under Article 243ZD of the Indian Constitution to consolidate and prepare development plans for the district.
• In the case of the DPC, at least 4/5 of the members are elected by the elected members of the district-level Panchayat and Municipalities in the district from among themselves, in proportion to the ratio of urban to rural population in the district.
• The Metropolitan Planning Committee (MPC) is mandated under Article 243ZE to prepare a draft development plan for the metropolitan area.
• For the MPC, at least 2/3^rd of the members are elected by the elected members of the Municipalities and the Chairpersons of the Panchayats in the metropolitan area, proportionate to the population ratio of urban and rural areas.
• Both committees aim to ensure integrated planning and balanced development for the respective areas by including representation from urban and rural governing bodies.

Additional Information

• District Planning Committee (DPC):
• Constitutional provision under Article 243ZD.
• Focuses on integrating the plans of Panchayats and Municipalities within the district.
• The State Legislature determines the composition and functioning of the committee.
• Metropolitan Planning Committee (MPC):
• Constitutional provision under Article 243ZE.
• Applicable for metropolitan areas with a population of over 10 lakh.
• Ensures representation proportional to urban and rural populations.
• Urban vs. Rural Representation: Both committees emphasize proportional representation based on population to balance development needs.
• Significance: These committees promote decentralized planning and ensure accountability by involving elected representatives.
• Implementation: State governments are responsible for creating rules and guidelines for the functioning of DPCs and MPCs in line with constitutional provisions.

The correct answer is 1, 2, 3, and 4.

Key Points

• Biotechnology Industry Research Assistance Council (BIRAC) was established by the Department of Biotechnology (DBT) under the Ministry of Science and Technology.
• BIRAC aims to foster innovations and entrepreneurship in the biotechnology sector.
• The council is focused on promoting affordable innovations in key social sectors such as healthcare, agriculture, and industrial biotechnology.
• It plays a critical role in empowering startups and small and medium enterprises (SMEs) by providing funding, mentorship, and incubation support.
• BIRAC encourages young investigators and promotes entrepreneurial and managerial development in SMEs within the biotechnology domain.

Additional Information

• Biotechnology: It involves using biological processes, organisms, or systems to develop products or technologies aimed at improving human life and the environment.
• Affordable Innovations: Innovations that are cost-effective and accessible to a larger population, especially in critical areas like healthcare and agriculture.
• Startup Ecosystem: A network of organizations, resources, and individuals that support new business ventures, particularly in sectors like biotechnology.
• Department of Biotechnology (DBT): A government department under the Ministry of Science and Technology responsible for promoting and regulating biotechnology-related activities in India.
• Incubation Support: Assistance provided to startups and SMEs in terms of workspace, mentorship, funding, and other resources to help them grow and succeed.