VIT University Vellore Entrance Exam Set

The question probes the understanding of the foundational principles of sustainable development, a core tenet in many of VIT University Vellore’s engineering and management programs. Sustainable development, as defined by the Brundtland Commission, is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. This inherently involves balancing economic growth, social equity, and environmental protection. Option (a) directly addresses this tripartite balance, recognizing that true sustainability requires integrated solutions across these dimensions. Option (b) is incorrect because focusing solely on economic growth, while important, neglects the crucial social and environmental pillars. Option (c) is also incorrect as environmental protection without considering economic viability or social justice can lead to impractical or inequitable outcomes. Option (d) is flawed because while technological innovation is a vital tool, it is not the sole determinant of sustainability; ethical considerations, policy frameworks, and societal participation are equally critical. Therefore, the most comprehensive and accurate understanding of sustainable development, as it would be approached in advanced studies at VIT University Vellore, emphasizes the interconnectedness and interdependence of economic, social, and environmental factors.

The question probes the understanding of the fundamental principles governing the operation of a basic transistor circuit, specifically focusing on the concept of biasing. In a common-emitter NPN transistor configuration, for the transistor to operate in the active region, the base-emitter junction must be forward-biased, and the collector-base junction must be reverse-biased. Forward biasing the base-emitter junction typically requires a voltage drop of approximately \(0.7V\) for silicon transistors. This forward bias allows a small base current (\(I_B\)) to control a larger collector current (\(I_C\)). The collector current is related to the base current by the current gain factor, beta (\(\beta\)), where \(I_C = \beta I_B\). For active region operation, the collector-emitter voltage (\(V_{CE}\)) must be sufficiently positive to ensure the collector-base junction remains reverse-biased. If \(V_{CE}\) is too low, the transistor can enter saturation, where the collector current is no longer controlled by the base current but is limited by the external circuitry. The question asks about the condition that *guarantees* active region operation. This implies ensuring both junction biasing conditions are met. A forward-biased base-emitter junction is essential for current amplification. A sufficiently positive \(V_{CE}\) is crucial to prevent saturation. Therefore, the condition that ensures the transistor is in the active region is when the base-emitter junction is forward-biased and the collector-emitter voltage is positive enough to maintain reverse bias across the collector-base junction. This translates to the base voltage being higher than the emitter voltage by at least the turn-on voltage (e.g., \(0.7V\)) and the collector voltage being significantly higher than the emitter voltage.

The question probes the understanding of the fundamental principles of academic integrity and research ethics, particularly as they apply to the rigorous academic environment at VIT University Vellore. The scenario describes a student, Anya, who has diligently conducted her research for a project in the School of Computer Science and Engineering. She has synthesized information from various sources, including published papers and online repositories, to develop a novel algorithm. The core ethical dilemma arises from her use of a pre-existing, but not widely published, code snippet from a former VIT student’s personal project repository. This snippet, while not directly copied verbatim, forms the foundational logic for a key component of Anya’s algorithm. The explanation of the correct answer hinges on the definition and implications of plagiarism in an academic context. Plagiarism is not limited to direct word-for-word copying; it also encompasses the appropriation of ideas, methodologies, or significant portions of code without proper attribution. Even if the source is not formally published, intellectual property still exists. The former student’s repository, while personal, represents their intellectual contribution. Failing to acknowledge this contribution, even if the code was modified or integrated, constitutes a breach of academic integrity. This is especially critical in a university like VIT, which emphasizes originality, ethical research practices, and the responsible use of intellectual property. The act of using the snippet without explicit permission or citation undermines the principles of scholarly work and fair attribution, which are cornerstones of academic research and development. The explanation would detail that proper academic practice would involve reaching out to the original author for permission and, at the very least, citing the source in her project documentation and code comments, even if it was a personal repository. This upholds the values of transparency and respect for intellectual contributions that VIT University Vellore actively promotes.

The question probes the understanding of the fundamental principles of sustainable development and its application within the context of a leading technological institution like VIT University Vellore. Sustainable development, as defined by the Brundtland Commission, is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. This encompasses three interconnected pillars: economic viability, social equity, and environmental protection. For VIT University Vellore, a premier institution fostering innovation and research, integrating these principles is crucial for its long-term vision and societal impact. Option A, focusing on a holistic approach that balances technological advancement with ecological preservation and social responsibility, directly aligns with the core tenets of sustainable development. This approach recognizes that progress in engineering and science must be tempered by an awareness of its broader consequences. It implies that VIT University Vellore’s curriculum, research initiatives, and campus operations should actively consider their environmental footprint and contribute positively to societal well-being. This includes promoting resource efficiency, developing green technologies, fostering inclusive learning environments, and engaging with local communities. Such an approach is not merely about compliance but about proactive integration, ensuring that the university’s growth and influence are ethically sound and environmentally conscious, preparing graduates who are not only technically proficient but also responsible global citizens. Option B, while mentioning environmental consciousness, is too narrow as it omits the crucial social equity and economic viability aspects of sustainability. Option C, focusing solely on economic growth and technological innovation, neglects the environmental and social dimensions, which are integral to sustainable development. Option D, emphasizing community engagement without explicitly linking it to environmental and economic considerations, presents an incomplete picture of sustainability. Therefore, the most comprehensive and accurate representation of sustainable development in the context of VIT University Vellore’s mission is the holistic approach described in Option A.

The question probes the understanding of the fundamental principles of sustainable development and its application in a technological context, particularly relevant to the interdisciplinary approach fostered at VIT University Vellore. Sustainable development, as defined by the Brundtland Commission, is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. This encompasses three interconnected pillars: economic viability, social equity, and environmental protection. In the context of technological innovation, particularly in fields like artificial intelligence and advanced manufacturing, which are areas of significant focus at VIT University Vellore, the ethical and long-term implications are paramount. The development of AI algorithms, for instance, must consider potential biases that could perpetuate social inequities, the energy consumption of large-scale data centers that impacts environmental sustainability, and the economic displacement of human labor. Similarly, advanced manufacturing techniques, while increasing efficiency, must be evaluated for their resource depletion, waste generation, and impact on local communities. Therefore, a holistic approach that integrates these three pillars is crucial. Option A, focusing on the synergistic integration of ecological preservation, equitable resource distribution, and long-term economic prosperity, directly addresses this multifaceted nature of sustainability. Option B, while acknowledging environmental concerns, overlooks the equally critical social and economic dimensions. Option C prioritizes economic growth above all else, which is antithetical to the core principles of sustainability. Option D focuses on short-term technological advancement without considering its broader societal and environmental consequences. The emphasis on “synergistic integration” and the explicit mention of the three core pillars (ecological, equitable, economic) make Option A the most comprehensive and accurate representation of sustainable development principles as applied to technological progress within an academic institution like VIT University Vellore.

The question probes the understanding of fundamental principles in digital logic design, specifically related to combinational circuits and their implementation using logic gates. The scenario describes a system that requires a specific output based on three binary inputs (A, B, C). The truth table provided maps these inputs to the desired output (Y). To determine the minimal Sum of Products (SOP) expression, one would typically use Karnaugh maps (K-maps) or the Quine-McCluskey algorithm. Let’s construct the truth table from the given information: | A | B | C | Y | |—|—|—|—| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | The minterms for which Y=1 are: 001, 011, 101, 111. In standard notation, these are m1, m3, m5, and m7. The SOP expression is therefore: \(Y = A’B’C + A’BC + AB’C + ABC\) Now, we simplify this expression using Boolean algebra or a K-map. Using a K-map for three variables: “` BC 00 01 11 10 A 0 | 0 1 1 0 | 1 | 0 1 1 0 | “` Grouping the adjacent 1s: 1. Group of four 1s: The 1s in cells 001, 011, 101, 111 can be grouped. This group covers the minterms where C is 1, and A and B can be anything. Thus, this group simplifies to C. 2. Group of two 1s: There are no other valid groups of two or four that are not already covered by the group of four. Therefore, the minimal SOP expression is \(Y = C\). This simplification demonstrates that the output Y is solely dependent on the input C. This is a fundamental concept in digital logic design, emphasizing the importance of simplification to achieve efficient circuit implementations, a core skill for students at VIT University Vellore. Understanding such simplifications is crucial for designing complex integrated circuits and systems, aligning with VIT’s focus on cutting-edge technology and research. The ability to derive and simplify Boolean expressions is a foundational skill for various engineering disciplines offered at VIT, including Computer Science, Electronics and Communication Engineering, and Electrical Engineering, where efficient hardware design is paramount.

The question probes the understanding of the fundamental principles of sustainable development and its application in the context of technological advancement, a core area of focus at VIT University Vellore. The calculation here is conceptual, not numerical. We are evaluating the alignment of a proposed technological initiative with the three pillars of sustainability: economic viability, social equity, and environmental protection. Let’s analyze the scenario: A new solar energy project is proposed for a rural community. 1. **Economic Viability:** The project aims to reduce electricity costs for the community and create local jobs during installation and maintenance. This aligns with economic sustainability. 2. **Social Equity:** The project intends to provide reliable and affordable electricity to households previously underserved, improving quality of life and access to education and healthcare. This addresses social equity. 3. **Environmental Protection:** Solar energy is a renewable resource that significantly reduces greenhouse gas emissions compared to fossil fuels, thereby protecting the environment. Therefore, a project that demonstrably integrates and balances these three aspects is considered the most aligned with sustainable development principles as taught and researched at VIT University Vellore, which emphasizes responsible innovation. The other options represent partial or incomplete approaches to sustainability. For instance, focusing solely on economic benefits without considering environmental impact or social equity would be a flawed approach. Similarly, prioritizing environmental protection without ensuring economic feasibility or social acceptance would hinder long-term success. The question requires an understanding that true sustainability is a holistic concept, requiring the synergistic integration of all three pillars.

The question revolves around understanding the fundamental principles of sustainable development and its application within the context of technological innovation, a core focus at VIT University Vellore. The scenario describes a hypothetical project aiming to improve agricultural yield in a resource-scarce region. To assess the sustainability of this project, one must consider its impact across environmental, social, and economic dimensions. Environmental sustainability would involve evaluating the project’s resource consumption (water, energy, land), waste generation, and potential for pollution or biodiversity loss. Social sustainability would examine its impact on local communities, including employment, equitable distribution of benefits, and cultural preservation. Economic sustainability would assess its long-term financial viability, cost-effectiveness, and contribution to local economic growth without creating undue debt or dependency. The correct answer, “Prioritizing a closed-loop system for water and nutrient recycling, coupled with community-led training on organic farming practices and a transparent revenue-sharing model,” encapsulates all three pillars of sustainability. A closed-loop system minimizes water and nutrient waste, directly addressing environmental concerns. Community-led training empowers local farmers, fostering social equity and knowledge transfer. A transparent revenue-sharing model ensures economic benefits are distributed fairly, promoting long-term social and economic stability. The other options, while potentially beneficial, are less comprehensive in their sustainability approach. Focusing solely on advanced irrigation technology (option b) might address water scarcity but neglects social and broader economic impacts. Introducing genetically modified crops (option c) could boost yield but raises concerns about biodiversity, farmer dependency, and potential environmental risks if not managed sustainably. Relying entirely on external funding (option d) creates economic dependency and is not a sustainable long-term solution, as it lacks local ownership and economic self-sufficiency. Therefore, the integrated approach is the most robust for achieving true sustainability.

The scenario describes a student at VIT University Vellore, named Anya, who is working on a project involving the development of a novel bio-sensor for early disease detection. The core challenge lies in selecting an appropriate material that exhibits high sensitivity, specificity, and stability under physiological conditions, while also being cost-effective for potential widespread application. Anya is considering various nanomaterials. Graphene oxide (GO) is known for its excellent electrical conductivity and large surface area, making it suitable for signal transduction. However, GO can exhibit aggregation in aqueous solutions, potentially affecting sensor performance and reproducibility. Quantum dots (QDs) offer tunable optical properties and high photoluminescence quantum yield, useful for optical detection methods, but their synthesis can be complex and involve toxic heavy metals, raising environmental and safety concerns for a university project aiming for sustainable innovation. Metal-organic frameworks (MOFs) provide highly porous structures with tunable pore sizes and surface chemistries, offering excellent selectivity for specific analytes. However, their stability in biological fluids can be a limiting factor, and their conductivity might not be as high as graphene-based materials. Silicon nanowires (SiNWs) are biocompatible and possess excellent electrical properties, making them ideal for label-free electrochemical detection. Their surface can be functionalized to enhance specificity. Considering the need for a balance between sensitivity, specificity, stability, cost-effectiveness, and the university’s emphasis on sustainable and impactful research, SiNWs, when appropriately functionalized, present the most robust and versatile option for Anya’s bio-sensor project. Their inherent biocompatibility and electrical properties align well with the requirements for sensitive and specific detection in biological environments, and advancements in their synthesis and functionalization are actively pursued within research institutions like VIT University Vellore, aligning with the institution’s focus on cutting-edge materials science and biomedical engineering.

The question probes the understanding of the fundamental principles of sustainable development and its application within the context of technological innovation, a core area of focus at VIT University Vellore. The scenario describes a hypothetical project aiming to improve rural connectivity using drone technology. The key is to identify the aspect that most directly aligns with the triple bottom line of sustainability: environmental, social, and economic viability. Option (a) focuses on ensuring the drone technology is energy-efficient and minimizes its carbon footprint. This directly addresses the environmental pillar of sustainability by reducing negative ecological impact. Furthermore, it considers the long-term economic feasibility by lowering operational costs associated with energy consumption. The social aspect is implicitly addressed by providing improved connectivity, which can lead to better access to education, healthcare, and economic opportunities for rural communities, thereby enhancing social well-being. Option (b) suggests prioritizing the lowest initial cost for drone acquisition. While economic viability is a component of sustainability, focusing solely on the initial purchase price overlooks long-term operational costs, maintenance, and the environmental impact of manufacturing and disposal, making it a less comprehensive sustainable approach. Option (c) emphasizes rapid deployment and widespread adoption, even if it means compromising on the durability and repairability of the drones. This prioritizes immediate social impact but potentially sacrifices long-term economic sustainability (due to frequent replacements) and environmental responsibility (due to increased waste). Option (d) highlights the development of proprietary software for drone control, aiming for market exclusivity. While this addresses economic potential through intellectual property, it doesn’t inherently guarantee environmental or social benefits, and could even create barriers to access if not managed carefully, thus not fully embodying the holistic nature of sustainability. Therefore, the most aligned approach with the core tenets of sustainable development, as would be valued in an institution like VIT University Vellore, is the one that integrates environmental responsibility with long-term economic and social benefits.

The question probes the understanding of the fundamental principles of sustainable development and its application in the context of technological advancement, a core area of focus at VIT University Vellore. The scenario involves a hypothetical research project at VIT aimed at developing an eco-friendly energy source. The core concept being tested is the integration of environmental, social, and economic considerations, often referred to as the “triple bottom line.” The calculation is conceptual, not numerical. We are evaluating which of the given approaches best embodies the principles of sustainable development as understood in advanced academic discourse. Approach 1 (Focus solely on energy output efficiency): This prioritizes the economic aspect (energy generation) but neglects environmental impact and social equity. It’s a narrow, potentially unsustainable view. Approach 2 (Focus on minimizing initial capital cost): This prioritizes immediate economic feasibility but might lead to higher long-term environmental or social costs (e.g., reliance on non-renewable materials, poor labor practices). Approach 3 (Holistic integration of environmental, social, and economic factors): This approach directly aligns with the widely accepted definition of sustainable development. It considers the long-term viability of the project by balancing resource conservation, community well-being, and economic prosperity. This is crucial for research endeavors at institutions like VIT, which emphasize responsible innovation. Approach 4 (Prioritizing rapid market adoption regardless of long-term consequences): This is purely market-driven and can lead to unsustainable practices, ignoring the core tenets of sustainability. Therefore, the approach that demonstrates the most profound understanding of sustainable development, as expected in advanced studies at VIT University Vellore, is the one that integrates all three pillars.

The scenario describes a student at VIT University Vellore Entrance Exam University who is developing a novel algorithm for optimizing energy consumption in smart grids. The core challenge is to ensure the algorithm remains robust and efficient even when faced with unpredictable fluctuations in renewable energy sources (like solar and wind) and varying demand patterns. This requires a deep understanding of adaptive control systems and predictive modeling. The student is considering different approaches to handle these uncertainties. Option 1 (Correct): Implementing a multi-agent reinforcement learning (MARL) framework where each smart device (e.g., a smart thermostat, an EV charging station) acts as an independent agent learning to optimize its energy usage based on local conditions and global grid signals. This approach allows for decentralized decision-making and adaptation to dynamic environments, which is crucial for smart grids. The agents learn through trial and error, adjusting their strategies to maximize rewards (e.g., cost savings, grid stability) and minimize penalties (e.g., blackouts, high energy prices). This aligns with VIT’s focus on cutting-edge research in AI and its applications. Option 2 (Incorrect): Utilizing a purely deterministic, rule-based system. While simple, such systems struggle to adapt to the inherent stochasticity of renewable energy generation and demand. They would likely lead to suboptimal performance or instability when faced with unforeseen events. Option 3 (Incorrect): Employing a static, pre-programmed optimization model. This would fail to account for the real-time, dynamic nature of smart grids, rendering it ineffective in handling the continuous variability of energy sources and consumption. Option 4 (Incorrect): Relying solely on historical data analysis without incorporating real-time feedback loops. While historical data is valuable for initial training, it cannot capture the instantaneous changes and emergent behaviors characteristic of a smart grid environment. The MARL approach offers the most sophisticated and adaptive solution, directly addressing the need for real-time responsiveness and learning in a complex, uncertain system, reflecting the advanced research capabilities fostered at VIT University Vellore Entrance Exam University.

The question probes the understanding of the fundamental principles of sustainable development and its application within the context of technological innovation, a core area of focus at VIT University Vellore. Specifically, it examines how the integration of circular economy models can address the environmental and resource challenges inherent in rapid technological advancement. The correct answer emphasizes the holistic approach required, encompassing not just technological solutions but also policy frameworks and societal engagement. Circular economy principles aim to decouple economic growth from resource consumption by designing out waste and pollution, keeping products and materials in use, and regenerating natural systems. When applied to the electronics sector, for instance, this involves designing for durability, repairability, and recyclability, thereby reducing the reliance on virgin materials and minimizing electronic waste. This aligns with VIT University Vellore’s commitment to fostering innovation that is both technologically advanced and environmentally responsible. The explanation of the correct option highlights the interconnectedness of technological design, material sourcing, product lifecycle management, and end-of-life strategies. It underscores that a truly sustainable approach requires a systemic shift, moving beyond linear “take-make-dispose” models. This involves creating closed-loop systems where materials are continuously cycled, minimizing environmental impact and maximizing resource efficiency. Such a perspective is crucial for students aspiring to contribute to fields like advanced manufacturing, sustainable engineering, and green technology, all of which are integral to VIT University Vellore’s academic offerings. The other options, while touching upon aspects of sustainability, fail to capture this comprehensive, systemic integration of circular economy principles with technological progress, making them less accurate in addressing the core of the question.

The question probes the understanding of the fundamental principles of sustainable development and its application in a technologically driven educational institution like VIT University Vellore. Sustainable development, as defined by the Brundtland Commission, is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. This encompasses environmental, social, and economic dimensions. For an institution like VIT University Vellore, which aims to foster innovation and technological advancement, integrating sustainability is crucial. This involves not just reducing its environmental footprint through energy efficiency and waste management, but also ensuring social equity in its operations and educational programs, and fostering economic viability in its long-term planning. The concept of “circular economy” is a key strategy for achieving environmental sustainability by minimizing waste and maximizing resource utilization through reuse, repair, refurbishment, and recycling. Applying this to a university setting means designing systems and processes that keep resources in use for as long as possible, extracting maximum value from them whilst in use, and then recovering and regenerating products and materials at the end of each service life. This aligns with VIT University Vellore’s commitment to responsible innovation and preparing students for a future where resource scarcity and environmental challenges are paramount. Therefore, the most effective approach to enhance sustainability at VIT University Vellore, considering its academic and research focus, would be to embed circular economy principles into its campus operations and curriculum, fostering a culture of resourcefulness and long-term thinking.

The question assesses understanding of the foundational principles of sustainable development and its application in a university setting, specifically relating to VIT University Vellore’s commitment to environmental stewardship and innovation. The core concept is the integration of economic viability, social equity, and environmental protection. Option A correctly identifies the synergistic approach required, where technological innovation, community engagement, and resource efficiency are interwoven. This aligns with VIT University’s emphasis on research-driven solutions and its role as a catalyst for societal progress. Option B is incorrect because focusing solely on technological advancement without considering social equity or resource constraints leads to unsustainable outcomes. Option C is flawed as prioritizing short-term economic gains over long-term environmental and social well-being contradicts the essence of sustainability. Option D is also incorrect because while regulatory compliance is important, it represents a minimum standard rather than a proactive strategy for achieving holistic sustainability, which involves innovation and broader stakeholder involvement. The explanation of the correct answer emphasizes the interconnectedness of these elements, crucial for any institution aiming for genuine sustainable practices, mirroring VIT University’s broader mission.

The question assesses understanding of the fundamental principles of sustainable development and its application in technological innovation, a core focus at VIT University Vellore. The scenario describes a hypothetical project aiming to improve rural sanitation. The key is to identify which proposed solution best embodies the triple bottom line of sustainability: environmental protection, social equity, and economic viability. Option A, the bio-digester system, directly addresses waste management by converting organic waste into biogas and fertilizer. This has clear environmental benefits (reduced pollution, renewable energy) and economic potential (energy generation, fertilizer sales). Socially, it can improve sanitation and health outcomes in rural communities. This holistic approach aligns with the integrated nature of sustainable development. Option B, while addressing a social need, focuses primarily on infrastructure without a strong emphasis on environmental or economic sustainability. The reliance on imported materials and potential for increased water consumption might create long-term environmental and economic challenges. Option C, the solar-powered water purification unit, is environmentally sound and addresses a critical need. However, its economic viability might be limited by the initial cost of solar panels and maintenance, and its direct impact on sanitation waste management is less pronounced than the bio-digester. Option D, the community education program, is crucial for social impact but lacks a direct technological or infrastructural component that addresses the core sanitation challenge in a sustainable, self-sufficient manner. While important, it’s a supporting element rather than a primary solution for the described problem. Therefore, the bio-digester system represents the most comprehensive and integrated sustainable solution for the given scenario, aligning with VIT University Vellore’s commitment to innovation for societal good.

The question probes the understanding of fundamental principles of digital signal processing, specifically concerning the Nyquist-Shannon sampling theorem and its implications for aliasing. The scenario describes a continuous-time signal \(x(t) = \cos(200\pi t) + \sin(500\pi t)\). The highest frequency component in this signal is determined by the arguments of the cosine and sine functions. For \(\cos(200\pi t)\), the angular frequency is \(\omega_1 = 200\pi\) radians/second. The corresponding frequency in Hertz is \(f_1 = \frac{\omega_1}{2\pi} = \frac{200\pi}{2\pi} = 100\) Hz. For \(\sin(500\pi t)\), the angular frequency is \(\omega_2 = 500\pi\) radians/second. The corresponding frequency in Hertz is \(f_2 = \frac{\omega_2}{2\pi} = \frac{500\pi}{2\pi} = 250\) Hz. Therefore, the maximum frequency component, \(f_{max}\), present in the signal \(x(t)\) is 250 Hz. According to the Nyquist-Shannon sampling theorem, to perfectly reconstruct a continuous-time signal from its samples, the sampling frequency, \(f_s\), must be at least twice the maximum frequency component present in the signal. This minimum sampling frequency is known as the Nyquist rate, which is \(2f_{max}\). In this case, the Nyquist rate is \(2 \times 250 \text{ Hz} = 500\) Hz. If the signal is sampled at a frequency lower than the Nyquist rate, aliasing will occur, where higher frequencies masquerade as lower frequencies. The question states that the signal is sampled at \(f_s = 400\) Hz. Since \(400 \text{ Hz} < 500 \text{ Hz}\), aliasing will occur. The aliased frequency, \(f_{alias}\), of a frequency \(f\) sampled below the Nyquist rate can be found using the formula \(f_{alias} = |f – k \cdot f_s|\), where \(k\) is an integer chosen such that \(0 \le f_{alias} < \frac{f_s}{2}\). For the 100 Hz component, since \(100 \text{ Hz} < \frac{400 \text{ Hz}}{2} = 200 \text{ Hz}\), it will not be aliased and will appear at 100 Hz. For the 250 Hz component, since \(250 \text{ Hz} > 200 \text{ Hz}\), it will be aliased. We need to find an integer \(k\) such that \(0 \le |250 – k \cdot 400| < 200\). If \(k=1\), \(|250 – 1 \cdot 400| = |-150| = 150\) Hz. Since \(0 \le 150 < 200\), the 250 Hz component will be aliased to 150 Hz. Therefore, the sampled signal will contain components at 100 Hz and 150 Hz. The question asks for the highest frequency present in the sampled signal. Comparing the frequencies 100 Hz and 150 Hz, the highest frequency is 150 Hz. This understanding is crucial in digital signal processing courses at VIT University Vellore, where students learn to analyze and process signals, ensuring accurate representation and avoiding distortion. The ability to identify and mitigate aliasing is fundamental for applications in telecommunications, audio processing, and medical imaging, all areas of active research and study at VIT.

The question probes the understanding of the ethical considerations in scientific research, specifically focusing on the principle of informed consent and its application in a hypothetical scenario involving vulnerable populations. The scenario describes a research project at VIT University Vellore Entrance Exam University aiming to understand the impact of a new educational intervention on primary school students. The core ethical dilemma arises from the potential for coercion or undue influence when obtaining consent from parents or guardians, especially if the intervention is presented as highly beneficial or if there are perceived incentives. Informed consent requires that participants (or their legal guardians) voluntarily agree to participate after being fully informed about the research’s purpose, procedures, potential risks, and benefits. For vulnerable populations, such as children, additional safeguards are necessary. These safeguards aim to protect their rights and welfare, recognizing their limited capacity to consent independently. This often involves obtaining assent from the child (if age-appropriate) in addition to consent from the parent or guardian. Furthermore, researchers must ensure that the consent process is free from coercion or undue influence. Coercion involves overt threats of harm or negative consequences for non-participation, while undue influence involves offering excessive or inappropriate rewards that could compromise a person’s judgment. In the given scenario, the research team is developing a new pedagogical approach. While the intention is to improve learning outcomes, the way the intervention is presented to parents could inadvertently create pressure. If the intervention is framed as a guaranteed pathway to academic excellence, or if there are tangible benefits offered to participating families that are disproportionate to the research activity itself, it could be considered undue influence. This is particularly relevant in an academic setting like VIT University Vellore Entrance Exam University, where the pursuit of knowledge and innovation must be balanced with rigorous ethical standards. Therefore, the most critical ethical consideration is ensuring that the consent obtained from parents is truly voluntary and not swayed by an exaggerated portrayal of benefits or implicit pressure to participate, thereby respecting the autonomy of the families involved.

The question probes the understanding of the fundamental principles of sustainable development, a core tenet in many of VIT University Vellore’s engineering and management programs. Sustainable development, as defined by the Brundtland Commission, is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. This involves balancing economic growth, social equity, and environmental protection. Option A, “Integrating ecological restoration with economic incentives for local communities,” directly addresses this balance. Ecological restoration aims to repair damaged ecosystems, ensuring long-term environmental health. Economic incentives for local communities foster social equity and provide a tangible benefit for engaging in sustainable practices, thereby aligning economic growth with environmental stewardship. This approach recognizes that environmental protection is not solely a regulatory burden but can be a source of livelihood and community well-being, a perspective vital for students at VIT University Vellore who are often encouraged to innovate for societal benefit. Option B, “Prioritizing rapid industrialization to boost national GDP, deferring environmental concerns,” fundamentally contradicts sustainable development by advocating for short-term economic gains at the expense of long-term environmental viability and intergenerational equity. Option C, “Implementing strict, top-down environmental regulations without community involvement,” while aiming for environmental protection, neglects the social equity pillar and often faces resistance, hindering effective and lasting implementation. Sustainable development requires a participatory approach. Option D, “Focusing solely on technological advancements for pollution control, ignoring resource depletion,” addresses only one aspect of environmental protection and overlooks the critical issue of resource management and the broader socio-economic implications, which are integral to a holistic sustainable development strategy taught at VIT University Vellore.

The question probes the understanding of the ethical considerations in Artificial Intelligence development, specifically within the context of a leading technological institution like VIT University Vellore. The core issue revolves around the potential for bias in AI algorithms, which can lead to discriminatory outcomes. When developing AI systems, particularly those intended for broad societal application, it is paramount to proactively identify and mitigate biases that may be inherent in the training data or the algorithmic design itself. This requires a multi-faceted approach that includes diverse data sourcing, rigorous testing for fairness across different demographic groups, and transparent documentation of the AI’s limitations and potential biases. A crucial aspect of responsible AI development, emphasized in academic and research settings like VIT University Vellore, is the principle of “fairness by design.” This means embedding ethical considerations and bias mitigation strategies from the very inception of a project, rather than attempting to patch them later. For instance, if an AI system is being trained to assist in university admissions, as might be relevant to VIT University Vellore’s own processes, it must be ensured that the data used does not disproportionately favor or disadvantage applicants based on their background, gender, or socioeconomic status. This involves careful data preprocessing, employing fairness metrics during model evaluation, and potentially using techniques like adversarial debiasing or re-weighting data points. Furthermore, ongoing monitoring and auditing of deployed AI systems are essential to detect and correct emergent biases. The commitment to ethical AI development at VIT University Vellore necessitates a proactive stance on identifying and rectifying potential discriminatory impacts, ensuring that technological advancements serve all members of society equitably.

The question probes the understanding of the foundational principles of sustainable development, a key area of focus in many engineering and science programs at VIT University Vellore. The calculation, while not numerical, involves weighing different aspects of development against the core tenets of sustainability. Sustainable development aims to meet the needs of the present without compromising the ability of future generations to meet their own needs. This involves balancing economic growth, social equity, and environmental protection. * **Economic Growth:** This refers to increasing the production of goods and services, leading to higher incomes and improved living standards. However, unchecked economic growth can lead to resource depletion and pollution. * **Social Equity:** This encompasses fairness and justice in the distribution of resources and opportunities, ensuring that all members of society benefit from development and that no one is left behind. This includes access to education, healthcare, and basic necessities. * **Environmental Protection:** This involves conserving natural resources, reducing pollution, and protecting biodiversity to ensure the long-term health of the planet. This is crucial for the well-being of both current and future generations. The scenario presented highlights a common dilemma in development projects: the potential conflict between immediate economic gains and long-term environmental and social well-being. Consider a hypothetical large-scale infrastructure project proposed near a vital wetland ecosystem, which is crucial for local biodiversity and provides natural flood control. The project promises significant job creation and economic stimulus for the region. However, environmental impact assessments indicate potential for habitat destruction, water contamination, and disruption of natural water cycles. To align with the principles of sustainable development as taught at VIT University Vellore, the project must integrate all three pillars. Simply maximizing economic output without considering environmental degradation or social disparities would be unsustainable. Similarly, prioritizing environmental preservation to the absolute exclusion of economic and social needs might not be feasible or equitable. The most sustainable approach involves finding a synergistic balance. This means implementing stringent environmental mitigation measures, investing in community development and fair labor practices, and exploring innovative technologies that minimize ecological footprint while maximizing long-term economic viability and social benefit. The core idea is to achieve progress that is ecologically sound, socially just, and economically viable for the long haul. Therefore, the approach that best embodies sustainable development, and is thus the correct answer, is one that actively seeks to integrate and harmonize economic progress with robust environmental stewardship and equitable social outcomes, ensuring that the project contributes positively to the region’s future without mortgaging its environmental or social capital.

The question probes the understanding of the ethical considerations in scientific research, specifically focusing on the principle of informed consent and its application in a hypothetical scenario involving a novel diagnostic tool developed at VIT University Vellore. The core of the ethical dilemma lies in balancing the potential benefits of rapid deployment of a new technology with the imperative to fully inform participants about its experimental nature and potential risks. Informed consent is a cornerstone of ethical research, requiring that participants voluntarily agree to participate after being fully apprised of the study’s purpose, procedures, potential risks, benefits, and their right to withdraw at any time without penalty. The scenario describes a situation where a new diagnostic tool, while promising, is still undergoing validation. The researchers are aware of potential, albeit unquantified, risks associated with its use. Option A correctly identifies that the researchers have a primary ethical obligation to ensure participants are fully informed about the experimental nature of the diagnostic tool, including any known or potential risks, before they agree to its use. This aligns with the fundamental principles of autonomy and non-maleficence in research ethics, which are deeply ingrained in the academic and research ethos of institutions like VIT University Vellore. Option B is incorrect because while seeking regulatory approval is important, it does not supersede the direct ethical obligation to obtain informed consent from individual participants. Regulatory approval addresses broader safety and efficacy standards, but informed consent is about individual autonomy and understanding. Option C is incorrect because the potential for widespread public health benefit, while a noble goal, cannot justify circumventing the informed consent process. Ethical research prioritizes individual rights and well-being even when pursuing societal good. Option D is incorrect because while documenting the process is necessary, the primary ethical imperative is the *quality* and *completeness* of the information provided to the participant, not merely the existence of documentation. The focus must be on genuine understanding and voluntary agreement. Therefore, prioritizing full disclosure of the tool’s experimental status and potential risks is the most ethically sound approach.

The question probes the understanding of the fundamental principles of sustainable development and its application within an academic institution like VIT University Vellore. Sustainable development, as defined by the Brundtland Commission, is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. This concept encompasses three interconnected pillars: environmental protection, economic viability, and social equity. At VIT University Vellore, integrating sustainability involves a multi-faceted approach. Environmental protection would manifest through initiatives like waste reduction and recycling programs, energy efficiency measures in buildings, water conservation efforts, and promoting green transportation. Economic viability relates to ensuring that the university’s operations are financially sound while also considering long-term resource management and potentially exploring green revenue streams or cost savings through sustainable practices. Social equity pertains to fostering an inclusive campus environment, ensuring fair labor practices, promoting community engagement, and providing access to education and resources for all students, regardless of their background. Considering these pillars, the most effective approach for VIT University Vellore to embed sustainability would be through a comprehensive strategy that addresses all three dimensions. This would involve developing clear policies, setting measurable goals, engaging the entire university community (students, faculty, staff, and administration) in sustainability initiatives, and fostering a culture of environmental responsibility and social consciousness. This holistic approach ensures that sustainability is not merely an add-on but an integral part of the university’s mission and operations, aligning with its commitment to responsible education and societal contribution.

The core concept tested here is the understanding of the scientific method and experimental design, particularly the distinction between independent, dependent, and control variables. In the given scenario, the researcher is investigating the impact of varying nutrient concentrations on plant growth. The independent variable is the factor that the researcher intentionally manipulates or changes to observe its effect. In this case, it is the **concentration of nitrogen in the fertilizer solution**. The researcher is systematically altering this to see how it influences plant development. The dependent variable is the factor that is measured or observed to see if it is affected by the change in the independent variable. Here, it is the **average height of the tomato plants**. This is the outcome the researcher is interested in quantifying. Control variables are all other factors that could potentially influence the dependent variable and must be kept constant across all experimental groups to ensure that only the independent variable is responsible for any observed changes. Examples include the amount of sunlight, the type of soil, the watering schedule, the ambient temperature, and the initial size of the seedlings. Therefore, the factor that the researcher is directly altering to observe its impact on plant growth is the nitrogen concentration.

The question probes the understanding of the fundamental principles of sustainable development and its integration into technological innovation, a core tenet at VIT University Vellore. The scenario describes a hypothetical project aiming to improve agricultural yield in a water-scarce region. To determine the most appropriate approach, we must evaluate each option against the principles of sustainability, which encompass environmental, social, and economic viability. Option 1: Focusing solely on increasing crop yield through intensive irrigation and synthetic fertilizers. This approach prioritizes immediate economic gain but neglects long-term environmental consequences (water depletion, soil degradation) and social equity (potential for increased costs for small farmers). This is not aligned with VIT’s emphasis on responsible innovation. Option 2: Implementing advanced genetically modified crops resistant to drought and pests, coupled with a strict top-down distribution system for seeds and resources. While drought resistance is beneficial, a purely top-down approach can disregard local knowledge, social structures, and economic accessibility for all farmers, potentially creating dependency and inequity. This overlooks the social pillar of sustainability. Option 3: Developing and deploying a system that combines drought-resistant, locally adapted crop varieties with precision irrigation techniques powered by renewable energy, alongside farmer training programs on water conservation and organic soil management. This approach addresses environmental concerns by conserving water and improving soil health, economic viability through efficient resource use and potentially reduced input costs, and social equity through knowledge sharing and empowerment of local communities. This holistic strategy aligns perfectly with the integrated approach to sustainability championed by VIT University Vellore’s research and educational programs. Option 4: Introducing a large-scale, centralized desalination plant to provide ample water for conventional high-yield farming, with the assumption that technological advancement will automatically solve all associated environmental and social issues. This is a technologically driven solution but fails to consider the significant energy demands of desalination, potential environmental impacts of brine disposal, and the economic feasibility for widespread adoption by all farmers. It also doesn’t address soil health or local adaptation. Therefore, the approach that best embodies the principles of sustainable development and responsible technological application, as expected in the context of VIT University Vellore’s academic environment, is the one that integrates ecological, economic, and social considerations.

The question probes the understanding of the ethical considerations in AI development, specifically concerning bias mitigation in machine learning models. A core principle in responsible AI, as emphasized in the academic discourse at institutions like VIT University Vellore, is the proactive identification and correction of biases that can lead to unfair or discriminatory outcomes. When developing an AI system for, say, a university admissions process, a critical step is to audit the training data for demographic imbalances or historical biases that might disadvantage certain groups. For instance, if past admissions data disproportionately favored applicants from specific socioeconomic backgrounds due to systemic inequalities, an AI trained on this data might perpetuate or even amplify these biases. To address this, a multi-faceted approach is necessary. This involves not just technical solutions like re-sampling or re-weighting data, but also a deeper understanding of the societal context and the potential impact of the AI. Techniques such as adversarial debiasing, where a secondary model tries to predict the sensitive attribute from the primary model’s output, can help identify and reduce bias. Fairness metrics, such as demographic parity, equalized odds, or predictive parity, provide quantitative measures to evaluate the fairness of the model across different groups. The choice of metric depends on the specific definition of fairness being adopted, which itself is a subject of ongoing research and ethical debate. Furthermore, transparency in the model’s decision-making process, often achieved through explainable AI (XAI) techniques, is crucial for building trust and accountability. This allows for the identification of specific features or data points that contribute to biased outcomes. Continuous monitoring and re-evaluation of the model’s performance in real-world deployment are also essential, as societal dynamics and data distributions can change over time. Therefore, a comprehensive strategy for bias mitigation in AI development at VIT University Vellore would integrate data preprocessing, algorithmic fairness techniques, rigorous evaluation using appropriate metrics, and ongoing monitoring, all underpinned by a strong ethical framework that prioritizes equity and social justice.

The question probes the understanding of fundamental principles in digital logic design, specifically concerning the minimization of Boolean expressions and the implications of using different logic gates. The scenario describes a situation where a designer is tasked with implementing a specific logic function using only NAND gates, a common constraint in digital circuit design due to the universal nature of NAND gates. The function to be implemented is \(F(A, B, C) = \sum m(1, 3, 6, 7)\), which represents the minterms where the output is true. First, we can represent this function using a Karnaugh map (K-map) or by directly manipulating the sum-of-products (SOP) form. The minterms are 1 (\(A’B’C\)), 3 (\(A’BC\)), 6 (\(AB’C\)), and 7 (\(ABC\)). The SOP form is \(F(A, B, C) = A’B’C + A’BC + AB’C + ABC\). We can simplify this expression using Boolean algebra: \(F = A’B’C + A’BC + AB’C + ABC\) \(F = A’C(B’ + B) + AC(B’ + B)\) (Factoring out common terms) \(F = A’C(1) + AC(1)\) (Since \(B’ + B = 1\)) \(F = A’C + AC\) \(F = C(A’ + A)\) (Factoring out C) \(F = C(1)\) (Since \(A’ + A = 1\)) \(F = C\) So, the simplified function is \(F(A, B, C) = C\). Now, we need to implement this function \(F = C\) using only NAND gates. A single input \(C\) directly connected to the output of a NAND gate with its inputs tied together effectively acts as a buffer for the input signal, but the output of a NAND gate with identical inputs is the inverse of the input. That is, \(C \text{ NAND } C = (C \cdot C)’ = C’\). To obtain the original signal \(C\), we need to invert the output of the first NAND gate. Inverting a signal requires another NAND gate. We can achieve this by connecting the output of the first NAND gate (which is \(C’\)) to the input of a second NAND gate, with both inputs of the second NAND gate tied together. This second NAND gate will perform \((C’) \text{ NAND } (C’) = ((C’) \cdot (C’))’ = (C’)’ = C\). Therefore, to implement the function \(F = C\) using only NAND gates, we require two NAND gates. The first NAND gate takes the input \(C\) (with both inputs tied together) to produce \(C’\), and the second NAND gate takes \(C’\) (with both inputs tied together) to produce \(C\). This configuration is equivalent to a NOT gate implemented with a NAND gate, applied twice. The question asks about the minimum number of NAND gates required. The simplified function is \(F=C\). To implement a direct connection (buffer) or simply pass the signal \(C\) through a logic gate structure that uses only NAND gates, we need to consider how to achieve this. A single NAND gate with its inputs tied together performs inversion: \(C \text{ NAND } C = C’\). To get \(C\) back, we need to invert \(C’\). This requires another NAND gate: \(C’ \text{ NAND } C’ = (C’)’ = C\). Thus, two NAND gates are necessary and sufficient. The other options represent different numbers of gates or incorrect implementations. For instance, one NAND gate alone cannot produce \(C\) from \(C\) directly; it would produce \(C’\). Three or four NAND gates might be used in more complex implementations or if the initial simplification was not performed, but for the simplified function \(F=C\), two are minimal. The concept of universal gates is central here, as NAND gates can construct any other logic gate, including NOT gates. The efficiency of implementation, measured by the number of gates, is a key consideration in digital design, aligning with the practical aspects taught at institutions like VIT University Vellore. Understanding Boolean algebra and K-maps for simplification is crucial for minimizing gate count, which impacts cost, power consumption, and speed of the resulting circuit.

The question probes the understanding of the fundamental principles of sustainable development and its application within the context of a leading technological institution like VIT University Vellore. Sustainable development, as defined by the Brundtland Commission, is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. This involves balancing economic growth, social equity, and environmental protection. For VIT University Vellore, a premier institution focused on innovation and research, integrating these principles is crucial for its long-term vision and societal impact. Considering the options: Option a) focuses on resource efficiency and waste reduction, which are core tenets of environmental sustainability. Implementing advanced recycling programs, optimizing energy consumption through smart technologies, and promoting water conservation directly contribute to minimizing the university’s ecological footprint. This aligns with the “environmental protection” pillar of sustainable development. Furthermore, such initiatives often lead to cost savings (economic growth) and can foster a culture of responsibility among students and staff (social equity). Option b) emphasizes solely on technological advancement without explicit consideration for environmental or social impact. While technology is a driver of progress, its unbridled pursuit without a sustainability lens can lead to unintended consequences, such as increased e-waste or energy demands. This option neglects the holistic nature of sustainable development. Option c) prioritizes economic growth through increased student enrollment and revenue generation. While financial viability is important for any institution, focusing solely on economic metrics without addressing the environmental and social implications of expansion would be a deviation from sustainable development principles. Rapid growth without adequate infrastructure or resource management can strain the environment and potentially impact the quality of education and student life. Option d) centers on social equity and community engagement, which are vital components of sustainable development. However, it omits the critical aspect of environmental stewardship and resource management, which are equally important for long-term viability. A balanced approach is necessary. Therefore, the most comprehensive and aligned approach for VIT University Vellore to embody sustainable development principles is through a multifaceted strategy that integrates resource efficiency, waste minimization, and the adoption of eco-friendly technologies, as represented by option a. This approach not only addresses environmental concerns but also contributes to economic prudence and social well-being, reflecting the interconnectedness of the three pillars of sustainability.

The question revolves around the fundamental principles of sustainable development and its application in an academic institution like VIT University Vellore. Sustainable development, as defined by the Brundtland Commission, is development that meets the needs of the present without compromising the ability of future generations to meet their own needs. This encompasses three interconnected pillars: environmental protection, economic viability, and social equity. In the context of VIT University Vellore, implementing sustainable practices requires a holistic approach that integrates these pillars into its operations, curriculum, and research. Environmental protection would involve initiatives like energy efficiency, waste reduction and recycling, water conservation, and promoting green spaces. Economic viability would mean ensuring that these initiatives are cost-effective in the long run, perhaps through energy savings or by fostering innovation in green technologies. Social equity would entail ensuring that the benefits of these practices are shared by all members of the university community, including students, faculty, staff, and the surrounding local population, and that no group is disproportionately burdened. Considering the options: Option A (Integrating sustainability into curriculum and research, promoting resource efficiency, and fostering community engagement) directly addresses all three pillars of sustainable development and aligns with the comprehensive approach expected of a leading educational institution. It covers the educational aspect (curriculum and research), operational aspect (resource efficiency), and societal aspect (community engagement). Option B (Focusing solely on reducing carbon emissions through technological upgrades) addresses only the environmental pillar and is too narrow. While important, it neglects the economic and social dimensions. Option C (Prioritizing economic growth through increased student enrollment without considering environmental impact) directly contradicts the core principle of sustainable development by potentially compromising future generations’ ability to meet their needs. Option D (Emphasizing social welfare programs for students while ignoring operational resource management) addresses only the social pillar and overlooks the crucial environmental and economic aspects necessary for long-term sustainability. Therefore, the most comprehensive and effective approach for VIT University Vellore to embody sustainable development principles is to integrate them across its academic, operational, and community outreach efforts.

The question probes the understanding of the fundamental principles of sustainable development and its application in the context of technological advancement, a core area of focus at VIT University Vellore. The concept of “leapfrogging” refers to the ability of developing economies or regions to bypass older technologies and adopt newer, more efficient ones directly. This is particularly relevant to sustainable development as it allows for the adoption of cleaner, more resource-efficient technologies from the outset, avoiding the environmental burdens associated with legacy systems. For instance, a nation might skip the widespread adoption of fossil-fuel-dependent transportation infrastructure and directly invest in electric vehicle networks and renewable energy sources for power generation. This approach aligns with the triple bottom line of sustainability (economic, social, and environmental), as it can lead to economic growth through innovation, improved social well-being through cleaner air and better infrastructure, and significant environmental benefits by reducing greenhouse gas emissions and resource depletion. The other options, while related to development, do not encapsulate the specific strategic advantage of adopting advanced, sustainable technologies without the intermediate stages, which is the essence of leapfrogging in a sustainability context.