National Institute of Technology NITK Surathkal Entrance Exam Set

The question probes the understanding of how a specific material property, the coefficient of thermal expansion, influences the structural integrity of a bridge under varying ambient temperatures, a concept central to civil engineering and materials science, both prominent disciplines at NITK Surathkal. The scenario describes a steel bridge experiencing a temperature increase from \(10^\circ C\) to \(40^\circ C\). Steel has a coefficient of thermal expansion, denoted by \(\alpha\), approximately \(12 \times 10^{-6} \, ^\circ C^{-1}\). The change in temperature, \(\Delta T\), is \(40^\circ C – 10^\circ C = 30^\circ C\). The resulting strain due to thermal expansion is given by \(\epsilon = \alpha \Delta T\). Therefore, \(\epsilon = (12 \times 10^{-6} \, ^\circ C^{-1}) \times (30^\circ C) = 360 \times 10^{-6}\). This strain, if unaccommodated, would induce significant stress. However, bridges are designed with expansion joints to allow for this expansion. The question asks about the *primary* consequence of this temperature change on the bridge’s *structural behavior* in the absence of expansion joints. Without expansion joints, the material would resist the natural tendency to expand, leading to compressive stress. The magnitude of this stress is related to the material’s Young’s modulus (\(E\)) and the induced strain: \(\sigma = E \epsilon\). For steel, \(E \approx 200 \, GPa\). Thus, the induced stress would be approximately \(\sigma = (200 \times 10^9 \, Pa) \times (360 \times 10^{-6}) = 72 \times 10^6 \, Pa = 72 \, MPa\). This compressive stress, while significant, is well within the yield strength of structural steel. However, the question asks about the *behavior* and the *most direct physical manifestation* of this unaccommodated expansion. The unhindered expansion would cause an increase in length. The increase in length, \(\Delta L\), is given by \(\Delta L = \alpha L \Delta T\), where \(L\) is the original length of the bridge. While the stress is a consequence of resisting this expansion, the fundamental physical change is the tendency to elongate. The question is designed to test the understanding of the direct physical effect of thermal expansion on a structure before considering stress-induced effects or mitigation measures. The most direct and observable physical change in the bridge’s dimensions due to the temperature increase, if it were free to expand, would be an increase in its length. The options provided test the understanding of the primary effect versus secondary effects or misinterpretations of the physical process. The development of internal compressive stress is a consequence of the material’s resistance to this expansion, not the expansion itself. A reduction in the bridge’s load-bearing capacity is a potential downstream effect but not the immediate physical behavior. A change in the bridge’s natural frequency is a dynamic property influenced by stiffness and mass, which can be indirectly affected by stress, but the primary thermal effect is dimensional change. Therefore, the most accurate description of the bridge’s behavior due to the temperature increase, in the absence of expansion joints, is an increase in its overall length.

The question probes the understanding of the fundamental principles governing the operation of a synchronous generator, specifically focusing on the relationship between excitation current, terminal voltage, and power factor under varying load conditions. In a synchronous generator, the terminal voltage is influenced by the internal generated voltage (which is directly proportional to the excitation current) and the synchronous reactance drop. As the load increases, the armature reaction also plays a role, effectively weakening the magnetic field. When a synchronous generator operates at unity power factor, the armature reaction is neither strongly magnetizing nor demagnetizing, and the terminal voltage is primarily determined by the internal generated voltage and the synchronous reactance drop. As the load is reduced while maintaining the same excitation, the synchronous reactance drop decreases, leading to a higher terminal voltage. Conversely, if the excitation is reduced to maintain a constant terminal voltage under a lighter load, the internal generated voltage will be lower. The scenario describes a synchronous generator operating at a leading power factor and then transitioning to a lagging power factor while maintaining the same terminal voltage and output power. To maintain the same terminal voltage at a leading power factor, the excitation current is typically higher than at unity power factor because the demagnetizing effect of the armature reaction at leading power factors is compensated by increased excitation. When the power factor shifts to lagging, the armature reaction becomes more demagnetizing. To maintain the same terminal voltage, the internal generated voltage must increase to overcome the increased synchronous reactance drop and the stronger demagnetizing effect. This increase in internal generated voltage necessitates a higher excitation current. Since the output power is kept constant, and power is given by \(P = \sqrt{3} V_t I_a \cos \phi\), where \(V_t\) is terminal voltage and \(\cos \phi\) is power factor, a change in power factor while keeping \(P\) and \(V_t\) constant implies a change in armature current \(I_a\). Specifically, for a lagging power factor, the armature current will be higher than for a leading power factor at the same output power and terminal voltage. This increased armature current, combined with the demagnetizing effect of armature reaction at lagging power factor, requires a greater excitation current to maintain the terminal voltage. Therefore, the excitation current must increase.

The question probes the understanding of the fundamental principles of sustainable engineering design, a core tenet emphasized in various programs at National Institute of Technology NITK Surathkal. The scenario involves a coastal community in Karnataka facing increased erosion and saltwater intrusion due to climate change. The goal is to identify the most appropriate engineering intervention that aligns with NITK’s commitment to environmentally responsible and community-centric solutions. The core concept here is the integration of ecological principles with engineering practices. Option (a) proposes a multi-pronged approach: constructing a permeable seawall that allows for natural sediment transport and tidal exchange, coupled with the restoration of mangrove forests. Permeable structures are designed to dissipate wave energy more gradually than solid barriers, reducing scour and allowing for the passage of marine life and sediment. Mangrove restoration is a well-established nature-based solution that stabilizes shorelines, filters water, and provides habitat. This approach directly addresses both the physical erosion and the ecological degradation, reflecting a holistic, systems-thinking perspective often fostered at NITK. Option (b) suggests a solid concrete barrier. While it might offer immediate protection, it often exacerbates erosion downdrift and creates a hard boundary that disrupts natural coastal processes and marine ecosystems, a less sustainable and integrated approach. Option (c) focuses solely on artificial dune construction without addressing the underlying causes of increased erosion or the saltwater intrusion issue, making it a partial and potentially less effective solution. Option (d) proposes a drainage system, which is relevant for managing freshwater runoff but does not directly tackle the primary coastal erosion and saltwater intrusion problems caused by sea-level rise and increased wave action, thus missing the core challenges presented. Therefore, the integrated approach of permeable seawalls and mangrove restoration is the most comprehensive and sustainable engineering solution, aligning with the advanced, interdisciplinary problem-solving expected at National Institute of Technology NITK Surathkal.

The question probes the understanding of the fundamental principles of digital signal processing, specifically concerning the aliasing phenomenon and its mitigation through sampling. The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a signal from its samples, the sampling frequency (\(f_s\)) must be at least twice the highest frequency component (\(f_{max}\)) present in the signal. This minimum sampling frequency is known as the Nyquist rate, \(f_{Nyquist} = 2f_{max}\). In this scenario, the analog signal contains frequency components up to \(15 \text{ kHz}\). Therefore, \(f_{max} = 15 \text{ kHz}\). To avoid aliasing, the sampling frequency must satisfy \(f_s \ge 2 \times 15 \text{ kHz}\), which means \(f_s \ge 30 \text{ kHz}\). The question asks for the *minimum* sampling frequency required to prevent aliasing. Based on the Nyquist-Shannon theorem, this minimum is exactly twice the maximum frequency. Thus, the minimum sampling frequency is \(2 \times 15 \text{ kHz} = 30 \text{ kHz}\). Understanding this concept is crucial for students at National Institute of Technology NITK Surathkal, particularly in programs like Electrical, Electronics, and Computer Engineering, where signal processing is a core discipline. Proper sampling ensures that digital representations of analog signals accurately capture the original information, preventing distortion and loss of data. Incorrect sampling can lead to aliasing, where higher frequencies masquerade as lower frequencies, rendering the reconstructed signal unusable. This fundamental principle underpins many digital technologies, from audio and video processing to telecommunications and medical imaging, all areas of active research and development at NITK.

The question probes the understanding of the fundamental principles governing the operation of a resonant RLC circuit, specifically focusing on the quality factor (\(Q\)) and its relationship with bandwidth (\(BW\)) and the impedance at resonance. For a series RLC circuit, the resonant frequency (\(\omega_0\)) is given by \(\omega_0 = \frac{1}{\sqrt{LC}}\). The impedance at resonance is purely resistive and equal to \(R\). The quality factor for a series RLC circuit is defined as \(Q = \frac{\omega_0 L}{R} = \frac{1}{\omega_0 CR}\). The bandwidth (\(BW\)) of a resonant circuit is the range of frequencies over which the power delivered is at least half the power delivered at resonance. For a series RLC circuit, the bandwidth is given by \(BW = \frac{R}{L}\) in rad/s or \(BW = \frac{R}{2\pi L}\) in Hz. The relationship between \(Q\), \(\omega_0\), and \(BW\) is \(Q = \frac{\omega_0}{BW}\). This means that a higher quality factor corresponds to a narrower bandwidth for a given resonant frequency. In this scenario, we are given a series RLC circuit with \(R = 100 \Omega\), \(L = 20 \, \text{mH}\), and \(C = 0.5 \, \mu\text{F}\). First, calculate the resonant frequency: \(\omega_0 = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{(20 \times 10^{-3} \, \text{H})(0.5 \times 10^{-6} \, \text{F})}} = \frac{1}{\sqrt{10 \times 10^{-9} \, \text{s}^2}} = \frac{1}{10^{-4} \, \text{s}} = 10^4 \, \text{rad/s}\) Next, calculate the quality factor: \(Q = \frac{\omega_0 L}{R} = \frac{(10^4 \, \text{rad/s})(20 \times 10^{-3} \, \text{H})}{100 \, \Omega} = \frac{200}{100} = 2\) Now, calculate the bandwidth in rad/s: \(BW = \frac{R}{L} = \frac{100 \, \Omega}{20 \times 10^{-3} \, \text{H}} = \frac{100}{0.02} \, \text{rad/s} = 5000 \, \text{rad/s}\) Alternatively, using the relationship \(Q = \frac{\omega_0}{BW}\): \(BW = \frac{\omega_0}{Q} = \frac{10^4 \, \text{rad/s}}{2} = 5000 \, \text{rad/s}\) The question asks about the implications of increasing the resistance while keeping inductance and capacitance constant. If \(R\) increases, the quality factor \(Q = \frac{\omega_0 L}{R}\) will decrease. Simultaneously, the bandwidth \(BW = \frac{R}{L}\) will increase. A decrease in \(Q\) signifies a less selective circuit, meaning it will respond to a wider range of frequencies around the resonant frequency. This broader response is directly indicated by an increased bandwidth. Therefore, increasing resistance in a series RLC circuit leads to a lower quality factor and a wider bandwidth, making the circuit less selective. This concept is crucial in understanding filter design and signal processing applications, areas of significant research and academic focus at National Institute of Technology NITK Surathkal. The ability to tune the selectivity of circuits by adjusting resistive components is a fundamental skill for engineers graduating from National Institute of Technology NITK Surathkal, particularly in fields like Electronics and Communication Engineering.

The question probes the understanding of the fundamental principles of digital signal processing, specifically concerning the aliasing phenomenon and its mitigation through sampling. The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a signal from its samples, the sampling frequency (\(f_s\)) must be at least twice the highest frequency component (\(f_{max}\)) present in the signal, i.e., \(f_s \ge 2f_{max}\). This minimum sampling frequency is known as the Nyquist rate. In the given scenario, the analog signal contains frequency components up to 15 kHz. Therefore, \(f_{max} = 15 \text{ kHz}\). To avoid aliasing, the sampling frequency must satisfy \(f_s \ge 2 \times 15 \text{ kHz}\), which means \(f_s \ge 30 \text{ kHz}\). The question asks for the *minimum* sampling frequency required to avoid aliasing. This directly corresponds to the Nyquist rate. Thus, the minimum sampling frequency is 30 kHz. Understanding this concept is crucial for students at NITK Surathkal, particularly in programs like Electrical, Electronics, and Computer Engineering, where signal processing is a core discipline. Proper sampling ensures that information is not lost during the analog-to-digital conversion process, which is fundamental for any digital system that interacts with the real world, from communication systems to control systems and medical imaging. Failure to adhere to the Nyquist criterion leads to aliasing, where higher frequencies masquerade as lower frequencies, corrupting the signal and rendering subsequent processing inaccurate. This question tests a foundational concept that underpins many advanced topics in digital signal processing and communications.

The question probes the understanding of the fundamental principles of digital signal processing, specifically focusing on the Nyquist-Shannon sampling theorem and its implications in the context of analog-to-digital conversion, a core concept in many engineering disciplines at National Institute of Technology NITK Surathkal. The Nyquist-Shannon sampling theorem states that to perfectly reconstruct an analog signal from its samples, the sampling frequency (\(f_s\)) must be at least twice the highest frequency component (\(f_{max}\)) present in the signal. This minimum sampling rate is known as the Nyquist rate, \(f_{Nyquist} = 2f_{max}\). In this scenario, the analog signal has a maximum frequency component of \(15 \text{ kHz}\). Therefore, according to the Nyquist-Shannon sampling theorem, the minimum sampling frequency required to avoid aliasing and ensure perfect reconstruction is \(2 \times 15 \text{ kHz} = 30 \text{ kHz}\). The question asks for the *minimum* sampling rate. The options provided are: a) \(30 \text{ kHz}\) b) \(15 \text{ kHz}\) c) \(45 \text{ kHz}\) d) \(7.5 \text{ kHz}\) Option a) \(30 \text{ kHz}\) directly satisfies the Nyquist criterion. Option b) \(15 \text{ kHz}\) is less than the Nyquist rate and would lead to aliasing, making reconstruction impossible. Option c) \(45 \text{ kHz}\) is greater than the Nyquist rate. While it would also allow for reconstruction, it is not the *minimum* required rate. Option d) \(7.5 \text{ kHz}\) is significantly lower than the Nyquist rate and would result in severe aliasing. Therefore, the correct answer, representing the minimum sampling frequency, is \(30 \text{ kHz}\). This concept is crucial for students at National Institute of Technology NITK Surathkal, particularly in fields like Electronics and Communication Engineering, Computer Science, and Instrumentation Engineering, where understanding signal processing is fundamental for designing and analyzing systems involving data acquisition and digital communication. The ability to apply the Nyquist theorem correctly ensures the integrity of sampled data and the fidelity of reconstructed signals, directly impacting the performance of various technological applications.

The question probes the understanding of the fundamental principles governing the operation of a synchronous generator, specifically focusing on the relationship between excitation current, terminal voltage, and power factor under varying load conditions. For a synchronous generator operating at a constant terminal voltage and frequency, the relationship between the excitation current (\(I_f\)) and the power factor is not linear and is influenced by the machine’s internal characteristics, particularly its synchronous reactance (\(X_s\)) and armature resistance (\(R_a\)). Consider the phasor diagram of a synchronous generator. The terminal voltage (\(V_t\)) is the reference. The back EMF (\(E_f\)) is given by \(E_f = V_t + I_a(R_a + jX_s)\), where \(I_a\) is the armature current. The magnitude of \(E_f\) is directly proportional to the field excitation current (\(I_f\)). When the generator is operating at unity power factor (lagging or leading), the armature current \(I_a\) is in phase or 180 degrees out of phase with \(V_t\). As the load is increased at unity power factor, \(I_a\) increases, and to maintain constant \(V_t\), \(E_f\) must also increase, thus requiring an increase in \(I_f\). Now consider operation at a lagging power factor. The armature current \(I_a\) lags \(V_t\). The term \(I_a(R_a + jX_s)\) will have a larger component in phase with \(V_t\) (due to \(I_a R_a\)) and a component that leads \(V_t\) (due to \(jI_a X_s\)). To maintain the same \(V_t\) with the same \(I_a\) magnitude as at unity power factor, \(E_f\) must be larger. This implies a higher excitation current (\(I_f\)) is needed for lagging power factor operation compared to unity power factor operation for the same armature current. Conversely, at a leading power factor, the armature current \(I_a\) leads \(V_t\). The term \(jI_a X_s\) will now have a component that lags \(V_t\). This means that to maintain the same \(V_t\) with the same \(I_a\) magnitude, a smaller \(E_f\) is required compared to unity power factor operation. Consequently, the excitation current (\(I_f\)) needed for leading power factor operation is lower than that for unity power factor operation. Therefore, to maintain a constant terminal voltage and deliver a constant amount of real power (which implies a constant armature current magnitude if the power factor is also constant), the excitation current must be adjusted. Specifically, as the power factor shifts from leading to lagging, the required excitation current increases to compensate for the voltage drop across the synchronous reactance and armature resistance. The question asks about the scenario where the generator is delivering a constant real power output and the power factor is changing from leading to lagging. This means the armature current magnitude is constant (since real power \(P = V_t I_a \cos \phi\), and \(V_t\) and \(P\) are constant, \(I_a \cos \phi\) is constant. If \(\cos \phi\) decreases (moves towards lagging), \(I_a\) must increase to maintain the product. However, the question implies a scenario where the *load* is adjusted such that the power factor changes, and we are observing the excitation needed to maintain constant voltage. A more precise interpretation is that the generator is supplying a constant real power, and the load’s power factor is varied. If the load’s power factor changes from leading to lagging, the armature current magnitude \(I_a\) will increase to maintain constant real power \(P\). As \(I_a\) increases and the power factor becomes more lagging, the required excitation voltage \(E_f\) to maintain constant terminal voltage \(V_t\) will increase. This increase in \(E_f\) necessitates an increase in the field excitation current \(I_f\). Thus, as the power factor shifts from leading to lagging while supplying constant real power, the excitation current must increase. The correct answer is that the excitation current must increase.

The question probes the understanding of the fundamental principles governing the operation of a synchronous generator, specifically focusing on the relationship between excitation current, terminal voltage, and power factor under varying load conditions. For a synchronous generator operating at a constant prime mover input and neglecting saturation, the relationship between the field excitation current (\(I_f\)) and the terminal voltage (\(V_t\)) is not linear. As the load increases (power factor lagging), the armature reaction weakens the main field, requiring an increase in excitation to maintain terminal voltage. Conversely, as the load decreases or becomes leading, the armature reaction strengthens the main field, allowing for a reduction in excitation. The provided scenario describes a generator initially operating at a specific power factor and terminal voltage. When the load is increased while maintaining the same power output, and the power factor shifts to a more lagging condition, the generator’s internal characteristics necessitate an adjustment in excitation. To maintain the terminal voltage at the same level despite the increased lagging reactive power demand (which causes a greater voltage drop due to armature resistance and synchronous reactance, and a more pronounced demagnetizing effect from armature reaction), the excitation current must be increased. This increased excitation compensates for the additional voltage drop and the demagnetizing influence of the increased lagging reactive current, thereby stabilizing the terminal voltage. The question implicitly asks for the condition that would require the *most* increase in excitation to maintain a constant terminal voltage. This occurs when the generator is supplying the maximum possible lagging reactive power, as this scenario presents the most significant demagnetizing effect from armature reaction and the largest voltage drop due to the internal impedance. Therefore, operating at a unity power factor and then shifting to a highly lagging power factor, while keeping the real power output constant, would demand the greatest increase in excitation to counteract the increased voltage drop and armature reaction.

The question probes the understanding of the fundamental principles governing the operation of a synchronous generator connected to an infinite bus, specifically focusing on the impact of excitation current on its power factor and reactive power output. When a synchronous generator is connected to an infinite bus, its terminal voltage is dictated by the infinite bus. The real power output is primarily determined by the mechanical input power (minus losses) and the angle between the rotor and the synchronously rotating magnetic field of the infinite bus. The reactive power output, however, is directly influenced by the generator’s excitation current. Increasing the excitation current (over-excitation) leads to a higher internal generated voltage (\(E_f\)) relative to the terminal voltage (\(V_t\)). This difference in voltage, along with the synchronous reactance (\(X_s\)), dictates the reactive power flow. A higher \(E_f\) causes a leading power factor and results in the generator supplying reactive power to the system. Conversely, decreasing the excitation current (under-excitation) results in a lagging power factor and the generator absorbing reactive power. The question asks about the effect of increasing excitation current on a synchronous generator connected to an infinite bus. As excitation increases, \(E_f\) increases. The reactive power output (\(Q\)) can be approximated by \(Q \approx \frac{E_f V_t}{X_s} \cos(\delta) – \frac{V_t^2}{X_s}\), where \(\delta\) is the power angle. A more direct relationship for reactive power delivered to the bus is \(Q = V_t (I_a \sin(\phi))\), where \(I_a\) is the armature current and \(\phi\) is the power factor angle. When \(E_f\) increases, the armature current \(I_a\) will adjust such that the generator delivers more reactive power. This means the power factor angle \(\phi\) becomes more leading (closer to zero or even negative if \(E_f\) is sufficiently high). Therefore, increasing excitation current leads to a leading power factor and an increase in reactive power supplied by the generator. The correct answer is that the generator will supply more reactive power and operate at a leading power factor.

The scenario describes a project at National Institute of Technology NITK Surathkal Entrance Exam University focused on sustainable urban development, specifically addressing water scarcity in a coastal region. The core challenge is to integrate advanced water management techniques with community engagement and policy considerations. The question asks to identify the most critical factor for the project’s long-term success, considering the multidisciplinary nature of the problem and the university’s emphasis on practical, impactful research. The project involves hydrological modeling (requiring understanding of water cycles, rainfall patterns, and groundwater dynamics), material science for desalination technologies, civil engineering for infrastructure, environmental science for ecological impact assessment, and social sciences for community adoption and policy formulation. Given the complexity and the need for sustained impact beyond initial implementation, the most crucial element is not just the technical feasibility of the chosen water purification method, nor the initial funding, nor even the academic rigor of the research itself. While all are important, the long-term viability hinges on the seamless integration of the technological solution with the socio-economic and political landscape of the region. This means ensuring that the community not only accepts but actively participates in the management of the water system, and that supportive policies are in place to sustain it. Therefore, the effective integration of technological solutions with robust community participation and supportive policy frameworks represents the most critical determinant of enduring success for such an initiative at National Institute of Technology NITK Surathkal Entrance Exam University.

The scenario describes a research project at National Institute of Technology NITK Surathkal Entrance Exam University focused on optimizing the structural integrity of a novel composite material for aerospace applications. The core problem is to determine the most effective method for assessing the material’s fatigue life under cyclic loading, a critical parameter for safety and performance in aircraft. The project team is considering three primary approaches: a) Accelerated fatigue testing with rigorous statistical analysis of failure modes, b) Finite Element Analysis (FEA) simulations calibrated with limited experimental data, c) Non-destructive testing (NDT) techniques like ultrasonic C-scanning to detect internal defects, and d) Microstructural analysis using electron microscopy to understand crack initiation mechanisms. For advanced engineering students at NITK Surathkal, understanding the trade-offs between these methods is crucial. Accelerated fatigue testing, while providing direct experimental data, can be time-consuming and expensive, and may not perfectly replicate real-world service conditions. FEA offers predictive capabilities but its accuracy is heavily dependent on the quality of input data and material models, which are often complex for new composites. NDT is excellent for identifying existing flaws but doesn’t directly measure fatigue life. Microstructural analysis provides fundamental insights into failure mechanisms but is not a direct measure of overall component fatigue performance. The question asks for the *most* effective approach for assessing fatigue life in this context. Given the need for reliable performance data for aerospace, a method that directly measures the material’s response to cyclic stress and provides statistically significant results is paramount. Accelerated fatigue testing, when conducted with appropriate protocols and analysis, directly addresses the fatigue life assessment. While other methods are valuable for understanding material behavior or detecting defects, they are often supplementary to direct fatigue testing for determining the operational lifespan of a component under cyclic stress. Therefore, accelerated fatigue testing with rigorous statistical analysis of failure modes is the most direct and comprehensive method for assessing fatigue life in this scenario, aligning with the rigorous research standards expected at NITK Surathkal.

The question probes the understanding of fundamental principles of sustainable urban planning and resource management, particularly relevant to the National Institute of Technology NITK Surathkal’s focus on engineering and environmental solutions. The scenario involves a hypothetical city grappling with increased population density and its impact on water resources and waste management. The core concept being tested is the integration of circular economy principles into urban infrastructure. To arrive at the correct answer, one must analyze the proposed solutions in the context of minimizing resource depletion and waste generation. * **Option A (Integrated Water Cycle Management and Bioremediation for Waste):** This option directly addresses both water scarcity and waste management through a holistic approach. Integrated Water Cycle Management (IWCM) emphasizes reusing treated wastewater, rainwater harvesting, and efficient distribution, thus reducing reliance on fresh sources. Bioremediation for waste converts organic waste into valuable resources like biogas and compost, closing the loop in material flow. This aligns with circular economy principles by treating waste as a resource and minimizing the need for virgin materials and landfill. This approach is highly sustainable and directly tackles the interconnected challenges presented. * **Option B (Increased Desalination Capacity and Advanced Incineration):** While desalination addresses water scarcity, it is energy-intensive and can have environmental impacts (brine disposal). Advanced incineration can reduce waste volume and potentially recover energy, but it doesn’t fully embrace the “reduce, reuse, recycle” hierarchy and can still produce emissions and ash requiring disposal. This is less aligned with a circular economy than Option A. * **Option C (Expansion of Conventional Water Treatment Plants and Landfill Expansion):** This represents a linear, end-of-pipe approach. Conventional treatment plants primarily focus on treating wastewater to a discharge standard, not necessarily for reuse. Landfill expansion is the antithesis of circular economy principles, as it sequesters resources and creates long-term environmental liabilities. This is the least sustainable option. * **Option D (Strict Water Rationing and Centralized Composting Facilities):** Strict water rationing is a temporary measure and doesn’t address the root cause of water scarcity or promote efficient use. Centralized composting is a step towards resource recovery but might not be as comprehensive as bioremediation, which can handle a broader range of organic waste and produce more diverse outputs. It also doesn’t fully integrate water management. Therefore, the most comprehensive and sustainable solution, embodying circular economy principles for both water and waste, is the integration of advanced water cycle management and bioremediation for waste.

The question probes the understanding of the fundamental principles of digital signal processing, specifically concerning the Nyquist-Shannon sampling theorem and its implications in the context of signal reconstruction. The theorem states that to perfectly reconstruct a continuous-time signal from its samples, the sampling frequency (\(f_s\)) must be at least twice the highest frequency component (\(f_{max}\)) present in the signal. This minimum sampling frequency is known as the Nyquist rate, \(f_{Nyquist} = 2f_{max}\). In this scenario, the analog signal has a maximum frequency component of 15 kHz. Therefore, according to the Nyquist-Shannon sampling theorem, the minimum sampling frequency required for perfect reconstruction is \(2 \times 15 \text{ kHz} = 30 \text{ kHz}\). The question asks about the consequence of sampling at a frequency *below* this minimum requirement. When a signal is sampled below its Nyquist rate, a phenomenon called aliasing occurs. Aliasing causes higher frequency components in the original analog signal to be misrepresented as lower frequencies in the sampled digital signal. This distortion is irreversible; once aliasing has occurred, the original high-frequency information cannot be recovered from the sampled data, even with ideal reconstruction filters. The sampled signal will contain spectral replicas of the original signal that overlap, leading to a corrupted representation. Therefore, sampling below the Nyquist rate will result in the loss of high-frequency information and the introduction of spurious lower-frequency components that were not present in the original signal. This directly impacts the fidelity of the reconstructed analog signal, making it an inaccurate representation of the original.

The question probes the understanding of the foundational principles of material science and engineering, specifically concerning the relationship between microstructure and macroscopic properties, a core area of study at NITK Surathkal. The scenario describes a novel alloy developed by researchers at NITK for high-performance aerospace applications. The key to answering lies in recognizing that while enhanced tensile strength and reduced density are desirable, the method of achieving these through controlled grain refinement and interstitial atom manipulation directly impacts the alloy’s ductility and fracture toughness. Specifically, a finer grain structure generally increases strength but can sometimes decrease ductility if not properly balanced. The introduction of interstitial atoms, while potentially strengthening, can also lead to embrittlement if their concentration or distribution is not optimized. Therefore, the most critical factor for the successful implementation of this alloy, beyond the initial improvements, is the *predictability and control of its behavior under extreme mechanical stress and varying environmental conditions*. This encompasses understanding how the refined microstructure and interstitial atom distribution influence fatigue life, creep resistance, and susceptibility to stress corrosion cracking. Without this deep understanding, the alloy’s performance in critical aerospace applications would remain uncertain, despite the initial positive results. The other options, while related to material characterization, do not capture the overarching concern for reliable performance in demanding operational environments, which is paramount for aerospace materials. For instance, while precise elemental composition is important, it’s the *consequences* of that composition on the microstructure and subsequent properties that truly matter for application. Similarly, the initial tensile strength and density improvements are the *starting point*, not the ultimate measure of success. The cost-effectiveness of the synthesis process is a secondary consideration to performance and reliability in such a critical field.

The question probes the understanding of the fundamental principles of sustainable urban development, a core area of study within engineering and environmental science programs at National Institute of Technology NITK Surathkal. The scenario involves a hypothetical city, “NITC-Nagar,” aiming to integrate renewable energy and efficient resource management. The core concept tested is the interconnectedness of urban planning, environmental impact, and socio-economic viability. To arrive at the correct answer, one must analyze the potential outcomes of each proposed strategy. * **Strategy 1: Extensive reliance on a single, large-scale solar farm.** While solar energy is renewable, a single large-scale farm presents vulnerabilities to weather disruptions, land use conflicts, and potential grid instability if not managed with advanced storage and distribution systems. It might not be the most resilient or integrated approach for a diverse urban environment. * **Strategy 2: Mandating electric vehicle adoption without upgrading charging infrastructure.** This would lead to significant strain on the existing power grid, potential energy shortages during peak hours, and user dissatisfaction due to inadequate charging facilities, undermining the sustainability goal. * **Strategy 3: Implementing a comprehensive waste-to-energy program coupled with decentralized renewable energy microgrids and smart water management.** This strategy addresses multiple facets of urban sustainability. Waste-to-energy reduces landfill burden and generates power. Decentralized microgrids enhance energy resilience and can integrate various renewable sources (solar, wind, etc.) at a local level. Smart water management conserves a critical resource and reduces energy consumption for water treatment and distribution. This holistic approach fosters a more robust and sustainable urban ecosystem, aligning with the interdisciplinary focus at National Institute of Technology NITK Surathkal. * **Strategy 4: Prioritizing high-density construction in all new developments.** While density can reduce sprawl, without concurrent investments in green spaces, public transportation, and efficient resource systems, it can exacerbate issues like heat island effects, pollution, and strain on infrastructure, potentially hindering overall sustainability. Therefore, the most effective and integrated approach for achieving long-term urban sustainability, as envisioned in advanced engineering and urban planning curricula at National Institute of Technology NITK Surathkal, is the combination of waste-to-energy, decentralized microgrids, and smart water management.

The question probes the understanding of the fundamental principles of sustainable development and its application in the context of a technological institution like National Institute of Technology NITK Surathkal. The core concept revolves around balancing economic growth, social equity, and environmental protection. Option A, focusing on integrating green technology adoption, resource efficiency, and community engagement into the institute’s operational framework, directly addresses these three pillars. Green technology adoption aligns with environmental protection and can drive economic efficiency. Resource efficiency minimizes waste and conserves natural capital, crucial for long-term sustainability. Community engagement ensures social equity by involving stakeholders and addressing local needs, fostering a sense of shared responsibility. This holistic approach is paramount for an institution aiming to be a leader in technological innovation while upholding ethical and societal responsibilities, as is the ethos at National Institute of Technology NITK Surathkal. Option B, while relevant to environmental aspects, overlooks the social equity and economic viability components of sustainability. Option C focuses primarily on economic growth without adequately addressing the environmental and social dimensions. Option D emphasizes research and development but might not directly translate into immediate operational sustainability across the entire institution. Therefore, the comprehensive integration of all three pillars, as presented in Option A, represents the most effective strategy for achieving sustainability at National Institute of Technology NITK Surathkal.

The question probes the understanding of fundamental principles in materials science and engineering, specifically focusing on the relationship between crystal structure, bonding, and macroscopic properties, a core area of study at NITK Surathkal, particularly within its Civil and Mechanical Engineering departments. The scenario describes a novel ceramic composite designed for high-temperature applications, implying a need to analyze its structural integrity and thermal behavior. The core concept tested is how the arrangement of atoms (crystal structure) and the nature of the forces holding them together (bonding) dictate a material’s response to stress and temperature. For a ceramic composite to exhibit superior high-temperature performance, it typically requires a combination of strong, directional covalent or ionic bonds to resist thermal degradation and a stable crystal lattice that minimizes defects and phase transformations. The presence of a reinforcing phase, often with a different crystal structure and bonding, aims to enhance mechanical properties like fracture toughness and creep resistance. Consider a hypothetical scenario where a research team at National Institute of Technology NITK Surathkal is developing a new ceramic composite for aerospace engine components. This composite consists of a matrix phase and a reinforcing phase. The matrix phase is a silicon carbide (SiC) variant with a cubic zincblende structure, known for its high hardness and thermal conductivity, but it can undergo phase transformations at extreme temperatures. The reinforcing phase is a novel boron nitride nanotube (BNNT) material, which possesses a hexagonal structure with strong covalent bonds, offering exceptional tensile strength and thermal stability. The research team observes that when the composite is subjected to thermal cycling between \(1200^\circ\text{C}\) and \(1500^\circ\text{C}\), the matrix phase exhibits micro-cracking, while the BNNTs remain largely intact. This differential behavior is attributed to the differing thermal expansion coefficients and the inherent stability of their respective crystal structures and bonding. The cubic SiC matrix, while strong, has a higher coefficient of thermal expansion compared to the hexagonal BNNTs. During heating, the SiC expands more than the BNNTs, inducing tensile stresses at the interface and within the matrix. Upon cooling, the SiC contracts more, leading to compressive stresses. Repeated cycling exacerbates these stresses, particularly tensile ones, leading to crack initiation and propagation in the SiC matrix. The strong, planar covalent bonding in the hexagonal BNNTs, coupled with their lower thermal expansion, allows them to withstand these thermal stresses without significant degradation. The interface between SiC and BNNT also plays a crucial role; a well-bonded interface can effectively transfer load and mitigate stress concentrations. However, if the interface is weak or prone to reaction at high temperatures, it can become a failure initiation site. The question asks to identify the most critical factor contributing to the observed micro-cracking in the matrix phase under thermal cycling. The correct answer is the inherent instability of the matrix’s crystal structure and bonding under repeated thermal stress, leading to differential expansion and contraction. This is a fundamental concept in materials science, emphasizing how atomic arrangement and interatomic forces dictate a material’s performance under varying conditions. The cubic zincblende structure of SiC, while robust, can be more susceptible to defect generation and phase changes under thermal cycling compared to the highly stable hexagonal structure of BNNTs. The differential thermal expansion is a direct consequence of these material properties.

The question probes the understanding of the fundamental principles of **digital signal processing (DSP)**, specifically concerning the **Nyquist-Shannon sampling theorem** and its implications in the context of signal reconstruction. The theorem states that to perfectly reconstruct a signal from its samples, the sampling frequency (\(f_s\)) must be at least twice the highest frequency component (\(f_{max}\)) present in the signal, i.e., \(f_s \ge 2f_{max}\). This minimum sampling rate is known as the Nyquist rate. In this scenario, a sensor at NITK Surathkal is designed to capture a physiological signal. The signal is known to contain frequencies up to \(150 \text{ Hz}\). To avoid aliasing, which is the distortion that occurs when a signal is sampled at a rate lower than its Nyquist rate, the sampling frequency must be greater than or equal to twice the maximum frequency. Therefore, the minimum required sampling frequency is \(2 \times 150 \text{ Hz} = 300 \text{ Hz}\). The question asks about the most appropriate sampling frequency for this sensor to ensure accurate data acquisition for subsequent analysis, which is a core concern in many engineering disciplines at NITK, including Electrical, Electronics, and Biomedical Engineering. Choosing a sampling frequency significantly below the Nyquist rate would lead to loss of information and distorted representations of the physiological data. Conversely, while a much higher sampling rate might capture the signal, it would also lead to increased data storage and processing overhead, which is often undesirable in practical applications. Therefore, a sampling frequency that is slightly above the theoretical minimum, providing a small margin of safety, is generally preferred. Among the given options, \(320 \text{ Hz}\) is the closest value above the Nyquist rate of \(300 \text{ Hz}\), making it the most suitable choice for accurate signal reconstruction without excessive data burden. This reflects the practical engineering consideration of balancing fidelity with resource efficiency, a key aspect of the curriculum at NITK.

The question probes the understanding of the fundamental principles of digital signal processing, specifically concerning the Nyquist-Shannon sampling theorem and its implications in the context of real-world signal acquisition at an institution like National Institute of Technology NITK Surathkal. The theorem states that to perfectly reconstruct a signal, the sampling frequency (\(f_s\)) must be at least twice the highest frequency component (\(f_{max}\)) present in the signal, i.e., \(f_s \ge 2f_{max}\). This minimum sampling rate is known as the Nyquist rate. In the given scenario, a sensor at National Institute of Technology NITK Surathkal is designed to capture variations in a physical phenomenon that exhibits a maximum frequency component of 15 kHz. To avoid aliasing, which is the distortion that occurs when a signal is sampled at a rate lower than its Nyquist rate, the sampling frequency must be strictly greater than twice this maximum frequency. Therefore, the minimum required sampling frequency is \(2 \times 15 \text{ kHz} = 30 \text{ kHz}\). Any sampling frequency below this value would result in the loss of information and the introduction of spurious frequencies, making accurate reconstruction impossible. The question tests the candidate’s ability to apply this core theorem to a practical engineering problem, emphasizing the importance of selecting appropriate sampling parameters for reliable data acquisition, a crucial aspect in research and development at National Institute of Technology NITK Surathkal. Understanding this concept is vital for students in fields like electronics, communication, and computer engineering, all of which are core disciplines at National Institute of Technology NITK Surathkal.

The question probes the understanding of the 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 \(x(t) = \cos(2\pi \cdot 500t) + \sin(2\pi \cdot 1200t)\) being sampled at a rate \(f_s = 1000\) Hz. According to the Nyquist-Shannon sampling theorem, for perfect reconstruction of a band-limited signal, the sampling frequency \(f_s\) must be at least twice the highest frequency component present in the signal. This minimum sampling frequency is known as the Nyquist rate, \(f_N = 2 \cdot f_{max}\). In the given signal \(x(t)\), the frequency components are \(f_1 = 500\) Hz and \(f_2 = 1200\) Hz. Therefore, the maximum frequency component is \(f_{max} = 1200\) Hz. The Nyquist rate for this signal is \(f_N = 2 \cdot 1200 \text{ Hz} = 2400\) Hz. The actual sampling frequency provided is \(f_s = 1000\) Hz. Since \(f_s < f_N\), aliasing will occur. Aliasing is the phenomenon where high-frequency components in the original signal are misrepresented as lower frequencies in the sampled signal. When a signal with frequency \(f\) is sampled at a rate \(f_s\), the sampled signal will contain frequencies \(f' = f \pmod{f_s}\) and \(f'' = |f – k \cdot f_s|\) for some integer \(k\), such that \(f'\) or \(f''\) falls within the range \([0, f_s/2]\). The folding frequency is \(f_s/2\). For the component \(f_1 = 500\) Hz: Since \(500 \text{ Hz} < f_s/2 = 1000/2 = 500\) Hz, this component would ideally be sampled without aliasing if it were the only component and the sampling was done at exactly the Nyquist rate. However, the theorem states \(f_s > 2f_{max}\) for unambiguous reconstruction. More precisely, for a frequency \(f\) to be unambiguously represented, it must satisfy \(|f| \le f_s/2\). Here, \(500 \text{ Hz} \le 500 \text{ Hz}\), so this component is at the boundary. For the component \(f_2 = 1200\) Hz: Since \(1200 \text{ Hz} > f_s/2 = 500\) Hz, this component will be aliased. The aliased frequency \(f’_2\) can be found by considering the closest multiple of \(f_s\) to \(f_2\). \(f’_2 = |f_2 – k \cdot f_s|\) where \(k\) is an integer such that \(f’_2 \le f_s/2\). Let’s try \(k=1\): \(f’_2 = |1200 \text{ Hz} – 1 \cdot 1000 \text{ Hz}| = |200 \text{ Hz}| = 200\) Hz. Since \(200 \text{ Hz} \le 500\) Hz, the 1200 Hz component will appear as 200 Hz in the sampled signal. The sampled signal will therefore contain a component at 500 Hz and a component at 200 Hz. The original signal had frequencies at 500 Hz and 1200 Hz. The 1200 Hz component has been aliased to 200 Hz. The 500 Hz component, being exactly at the Nyquist frequency (\(f_s/2\)), is also problematic for reconstruction and can lead to distortion or be indistinguishable from other aliased components if not handled carefully. However, the most direct and significant aliasing effect is the 1200 Hz component folding to 200 Hz. The question asks about the presence of frequencies in the sampled signal that are not in the original signal’s unique representation within the baseband. The 200 Hz component is a result of aliasing of the 1200 Hz component. The 500 Hz component is at the edge of the Nyquist zone. The presence of a 200 Hz component in the sampled signal, which was not directly present at that frequency in the original signal, is a clear manifestation of aliasing. The correct answer is the presence of a frequency component that is a result of aliasing. The 1200 Hz component aliases to 200 Hz. The 500 Hz component is at the Nyquist frequency, which is also problematic. The question asks what will be present in the sampled signal due to the sampling process. The 200 Hz component is a direct consequence of aliasing of the 1200 Hz component. Final Answer: The sampled signal will contain a component at 200 Hz, which is an aliased version of the original 1200 Hz component.

The question probes the understanding of the fundamental principles of digital signal processing, specifically concerning the Nyquist-Shannon sampling theorem and its practical implications in the context of audio signal acquisition at the National Institute of Technology NITK Surathkal. The theorem states that to perfectly reconstruct a signal, the sampling frequency must be at least twice the highest frequency component present in the signal. Let \(f_{max}\) be the maximum frequency component in the analog audio signal. According to the Nyquist-Shannon sampling theorem, the minimum sampling frequency \(f_s\) required for perfect reconstruction is \(f_s \ge 2 \cdot f_{max}\). The problem states that the analog audio signal has a maximum frequency component of 20 kHz. Therefore, to avoid aliasing and ensure faithful reconstruction, the sampling frequency must be at least: \(f_s \ge 2 \cdot 20 \text{ kHz}\) \(f_s \ge 40 \text{ kHz}\) The question asks for the minimum sampling frequency required. Thus, the minimum sampling frequency is 40 kHz. This concept is crucial for students at NITK Surathkal, particularly in programs like Electrical and Electronics Engineering or Computer Science, where digital signal processing is a core subject. Understanding sampling is fundamental to analog-to-digital conversion (ADC), which is the first step in processing any real-world signal digitally. Without adequate sampling, information is lost, leading to distortion and an inability to accurately represent the original signal. This has direct applications in audio engineering, telecommunications, medical imaging, and many other fields that NITK Surathkal actively engages with through its research and curriculum. The ability to determine appropriate sampling rates is a foundational skill for anyone working with digital representations of analog phenomena.

The question probes the understanding of the fundamental principles governing the operation of a basic semiconductor diode in a forward-biased configuration, specifically focusing on the voltage drop across it. In a forward-biased diode, the applied voltage overcomes the built-in potential barrier of the p-n junction. For silicon diodes, this barrier potential, often referred to as the turn-on voltage or threshold voltage, is approximately \(0.7\) volts. Once this threshold is reached, the diode begins to conduct current significantly. The voltage across the diode then remains relatively constant, close to this threshold voltage, even with further increases in the applied forward voltage, until breakdown occurs (which is not relevant in this forward-bias scenario). Therefore, if a silicon diode is forward-biased with an applied voltage of \(5\) volts, and the diode’s characteristics are such that it has a typical turn-on voltage, the voltage drop across the diode will be approximately \(0.7\) volts. The remaining \(5 – 0.7 = 4.3\) volts will be dropped across any series resistance in the circuit. The question asks for the voltage *across the diode* itself.

The question probes the understanding of the foundational principles of digital signal processing, specifically focusing on the concept of aliasing and its mitigation through anti-aliasing filters. The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a signal, the sampling frequency \(f_s\) must be at least twice the highest frequency component \(f_{max}\) present in the signal, i.e., \(f_s \ge 2f_{max}\). If this condition is not met, higher frequencies in the analog signal are misrepresented as lower frequencies in the sampled digital signal, a phenomenon known as aliasing. Consider an analog signal with a maximum frequency component of \(f_{max} = 15\) kHz. If this signal is sampled at a rate of \(f_s = 20\) kHz, the Nyquist frequency, which is \(f_s/2\), is \(20/2 = 10\) kHz. Since \(f_{max} > f_s/2\), aliasing will occur. Frequencies above \(f_s/2\) will fold back into the range \(0\) to \(f_s/2\). Specifically, a frequency \(f\) where \(f > f_s/2\) will appear as \(|f – k \cdot f_s|\) for some integer \(k\), such that the aliased frequency is within \(0\) to \(f_s/2\). For instance, a frequency of 15 kHz, when sampled at 20 kHz, will alias to \(|15 – 1 \cdot 20| = 5\) kHz. To prevent this, an anti-aliasing filter, which is a low-pass filter, is applied to the analog signal *before* sampling. This filter attenuates or removes frequencies above a certain cutoff frequency. For effective anti-aliasing, the cutoff frequency of the anti-aliasing filter must be set below the Nyquist frequency (\(f_s/2\)) and above the highest frequency of interest in the signal. In this scenario, the highest frequency of interest is 15 kHz, but to avoid aliasing with a 20 kHz sampling rate, the filter must ensure that no frequencies above 10 kHz are present in the signal before it is sampled. Therefore, the anti-aliasing filter should have a cutoff frequency that is less than or equal to the Nyquist frequency. The most appropriate cutoff frequency for the anti-aliasing filter to prevent aliasing of the 15 kHz component when sampling at 20 kHz is at or below 10 kHz.

The question probes the understanding of the fundamental principles governing the design and operation of a synchronous sequential circuit, specifically focusing on the critical race condition and its resolution. A race condition occurs in a synchronous sequential circuit when the output or state of the circuit depends on the order in which certain events occur, and this order is not guaranteed due to variations in propagation delays. In the context of flip-flops, particularly when multiple flip-flops share common input signals or are triggered by the same clock edge, a race condition can arise if the setup or hold time requirements of these flip-flops are violated. Consider a scenario with two D flip-flops, FF1 and FF2, clocked by the same clock signal. Let the input to FF1 be \(D_1\) and its output be \(Q_1\). Let the input to FF2 be \(D_2\) and its output be \(Q_2\). Suppose \(D_2\) is a function of \(Q_1\), for instance, \(D_2 = Q_1\). If the propagation delay from the clock edge to the output \(Q_1\) is significant, and this \(Q_1\) then immediately affects \(D_2\), which is then sampled by the *same* clock edge for FF2, a race condition can occur. If the delay through FF1 is such that \(Q_1\) changes after the clock edge has passed the setup time for FF2, then FF2 might capture the old value of \(Q_1\) instead of the new one, or it might capture an intermediate, unstable value, leading to unpredictable behavior. The most effective method to prevent such race conditions in synchronous sequential circuits, especially those involving feedback loops or complex interdependencies between flip-flops, is to ensure that all combinational logic feeding into flip-flop inputs is evaluated and settled *before* the clock edge arrives. This is achieved by carefully designing the combinational logic and ensuring that its maximum propagation delay is less than the clock period minus the setup time of the flip-flops. However, a more robust and common design practice, particularly for advanced circuits and to mitigate timing uncertainties, is the use of **state separation** or **level-sensitive latches with edge-triggered flip-flops**. A common technique involves using a master-slave configuration or, more generally, ensuring that the combinational logic is placed between two clock phases or between a latch and a flip-flop, effectively creating a one-clock-cycle delay for the feedback path. This ensures that the input to a flip-flop is stable and derived from the state of the previous clock cycle. Another critical aspect is the **clock skew**, which is the difference in arrival times of the clock signal at different flip-flops. While not directly a race condition within a single flip-flop’s operation, significant clock skew can exacerbate timing issues and contribute to the overall instability of the circuit, potentially leading to meta-stability or incorrect state transitions. Considering the options: 1. **Ensuring all combinational logic has a propagation delay less than the clock period minus the setup time:** This is a fundamental timing constraint but might not be sufficient for complex feedback paths or if propagation delays are highly variable. It’s a necessary condition but not always the most robust solution for preventing races in all scenarios. 2. **Introducing a delay element in the feedback path to ensure the input to the flip-flop is stable:** This is a valid technique. If \(D_2 = Q_1\), inserting a delay element (e.g., another flip-flop or a buffer with a known delay) in the path of \(Q_1\) before it reaches \(D_2\) would ensure that \(D_2\) is updated based on the state of \(Q_1\) from the *previous* clock cycle, thus preventing a race condition on the current clock edge. This is a form of state separation. 3. **Using asynchronous reset signals for all flip-flops:** Asynchronous reset ensures the circuit starts in a known state but does not prevent race conditions during normal operation. 4. **Increasing the clock frequency:** This would generally worsen race conditions by reducing the time available for logic to settle. The most effective and conceptually sound method to prevent a race condition in a synchronous sequential circuit, especially when feedback is involved, is to ensure that the inputs to the flip-flops are derived from the stable state of the previous clock cycle. This is precisely what introducing a delay element in the feedback path achieves, effectively decoupling the input sampling from the output transition of the same clock edge. This aligns with the principle of state separation and ensures that the combinational logic has sufficient time to settle. Calculation: No direct numerical calculation is required as the question is conceptual. The reasoning above leads to the identification of the most robust method for preventing race conditions. Final Answer is the option that describes introducing a delay element in the feedback path.

The scenario describes a signal with components up to 15 kHz being sampled at 20 kHz. The Nyquist-Shannon sampling theorem dictates that to avoid aliasing, the sampling frequency (\(f_s\)) must be at least twice the highest frequency component (\(f_{max}\)) in the signal, i.e., \(f_s \ge 2f_{max}\). In this case, the signal’s maximum frequency is 15 kHz. Therefore, the minimum sampling frequency required to avoid aliasing would be \(2 \times 15 \text{ kHz} = 30 \text{ kHz}\). Since the sampling frequency is only 20 kHz, which is less than 30 kHz, aliasing will occur. The Nyquist frequency, which is half the sampling frequency, is \(f_s/2 = 20 \text{ kHz}/2 = 10 \text{ kHz}\). Any frequency component in the original signal that is above the Nyquist frequency (10 kHz) will be aliased into the frequency range of \([0, 10 \text{ kHz}]\). For example, the 15 kHz component will alias to \(|15 \text{ kHz} – 1 \times 20 \text{ kHz}| = 5 \text{ kHz}\). Similarly, a frequency of 11 kHz would alias to \(|11 \text{ kHz} – 1 \times 20 \text{ kHz}| = 9 \text{ kHz}\). This means that the higher frequency components from the original signal will fold back and interfere with the lower frequency components, corrupting the sampled data. To prevent this, an anti-aliasing filter is used *before* the sampling process. This is a low-pass filter that attenuates or removes frequencies above the Nyquist frequency. In this specific case, to ensure that the sampled signal accurately represents the original signal’s content up to 10 kHz without distortion from higher frequencies, an anti-aliasing filter with a cutoff frequency at or below 10 kHz is essential. This filter would remove the 15 kHz component and any other components between 10 kHz and 15 kHz before they can cause aliasing. The National Institute of Technology NITK Surathkal, with its emphasis on rigorous engineering principles and practical applications, would expect students to understand that sampling a signal with components above the Nyquist frequency without prior filtering inevitably leads to aliasing, rendering the sampled data inaccurate for representing the intended signal band.

The question probes the understanding of the fundamental principles of digital signal processing, specifically concerning the Nyquist-Shannon sampling theorem and its implications in the context of a hypothetical advanced research project at National Institute of Technology NITK Surathkal. The scenario involves a researcher, Dr. Anya Sharma, working on a novel bio-signal acquisition system. The core concept being tested is the relationship between the highest frequency component of a signal and the minimum sampling rate required to perfectly reconstruct it. The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a continuous-time signal from its samples, the sampling frequency (\(f_s\)) must be greater than twice the highest frequency component (\(f_{max}\)) present in the signal. Mathematically, this is expressed as \(f_s > 2f_{max}\). In this scenario, the bio-signal is described as having its significant frequency components extending up to 15 kHz. Therefore, \(f_{max} = 15 \text{ kHz}\). According to the theorem, the minimum sampling frequency required for perfect reconstruction is \(f_{s,min} = 2 \times f_{max}\). Substituting the given value: \(f_{s,min} = 2 \times 15 \text{ kHz} = 30 \text{ kHz}\). However, the theorem specifies that the sampling frequency must be *greater than* twice the maximum frequency. This strict inequality (\(>\)) is crucial to avoid aliasing, which occurs when frequencies above half the sampling rate are incorrectly represented as lower frequencies. Therefore, any sampling rate strictly above 30 kHz would theoretically allow for perfect reconstruction. The question asks for the *minimum theoretical sampling rate* that guarantees perfect reconstruction without aliasing. This corresponds to the lower bound of the acceptable sampling frequencies, which is infinitesimally greater than \(2f_{max}\). In practical terms and for exam purposes, this is often represented as the threshold value itself, with the understanding that the actual sampling must be *just above* this. Thus, the minimum theoretical sampling rate is 30 kHz. The explanation should elaborate on the concept of aliasing, explaining how sampling below the Nyquist rate leads to distortion and the loss of information. It should also touch upon the practical considerations in signal processing, such as the need for anti-aliasing filters before sampling, which remove frequencies above the Nyquist limit to ensure the theorem’s conditions are met. The relevance to bio-signal processing at an institution like National Institute of Technology NITK Surathkal, known for its research in areas like biomedical engineering, would be highlighted, emphasizing the importance of accurate data acquisition for diagnostic and research purposes. The choice of a bio-signal with a relatively high frequency component (15 kHz) is designed to test a thorough understanding of the theorem’s application beyond typical audio frequencies.

The question assesses understanding of the principles of sustainable urban development and the role of technological innovation, specifically in the context of a premier engineering institution like National Institute of Technology NITK Surathkal. The scenario describes a city facing common urban challenges: resource depletion, waste management, and traffic congestion. The core task is to identify the most appropriate strategic approach for addressing these multifaceted issues, aligning with the ethos of an institution that emphasizes research-driven solutions and societal impact. The correct answer, “Implementing an integrated smart city framework leveraging IoT for resource optimization and citizen engagement,” directly addresses all the stated problems. IoT (Internet of Things) enables real-time data collection and analysis for efficient resource management (water, energy), intelligent traffic control, and improved waste collection. Citizen engagement platforms foster participation in sustainability initiatives. This approach is holistic and technologically advanced, reflecting the kind of forward-thinking solutions expected from National Institute of Technology NITK Surathkal graduates. The other options, while containing elements of good practice, are less comprehensive or less aligned with a cutting-edge, integrated approach. Focusing solely on public transportation upgrades, while important, doesn’t address resource depletion or waste management comprehensively. A purely regulatory approach might lack the technological dynamism and citizen buy-in needed for effective implementation. Similarly, prioritizing localized renewable energy generation, while beneficial, is a component of a larger smart city strategy rather than a complete solution to the interconnected urban challenges presented. The National Institute of Technology NITK Surathkal Entrance Exam seeks candidates who can synthesize diverse solutions into a coherent, impactful strategy.

The question probes the understanding of the fundamental principles of sustainable development and its application in the context of engineering projects, a core consideration at National Institute of Technology NITK Surathkal. The scenario describes a proposed infrastructure project near a coastal ecosystem, which is a common challenge faced by engineering disciplines at NITK, particularly those with strong ties to environmental engineering and civil engineering. The core of the problem lies in balancing economic growth with ecological preservation. The calculation to arrive at the correct answer involves a conceptual evaluation of the project’s impact across the three pillars of sustainability: economic, social, and environmental. 1. **Economic Viability:** The project aims for economic upliftment through job creation and improved connectivity. This is a positive economic indicator. 2. **Social Equity:** The project promises improved living standards and access to resources for local communities, addressing social aspects. 3. **Environmental Integrity:** The primary concern is the potential negative impact on the sensitive coastal ecosystem, including marine life and water quality. This is where the conflict arises. A truly sustainable approach, as emphasized in the curriculum at National Institute of Technology NITK Surathkal, requires a holistic assessment that prioritizes long-term ecological health alongside economic and social benefits. Therefore, a comprehensive Environmental Impact Assessment (EIA) that includes detailed studies on the coastal ecosystem’s resilience, potential mitigation strategies for pollution and habitat disruption, and the integration of eco-friendly construction techniques is paramount. This assessment must inform the decision-making process, ensuring that any development does not irrevocably damage the natural environment. The inclusion of community consultation and the development of robust monitoring mechanisms further strengthen the sustainability framework. The correct answer, therefore, is the option that most comprehensively addresses these multifaceted considerations, emphasizing proactive environmental stewardship and adaptive management. The calculation is conceptual: * Economic Benefit (Positive) + Social Benefit (Positive) – Environmental Risk (High Negative) = Net Impact (Potentially Negative if environmental risks are not mitigated). * Sustainable Solution requires: Maximizing Economic & Social Benefits + Minimizing Environmental Risks through rigorous assessment and mitigation. * The most sustainable option is the one that integrates these elements most effectively. Final Answer is the option that represents a comprehensive, proactive, and integrated approach to managing the environmental risks while pursuing economic and social goals, reflecting the ethos of responsible engineering education at National Institute of Technology NITK Surathkal.

The question probes the understanding of the fundamental principles of signal processing, specifically concerning the Nyquist-Shannon sampling theorem and its implications for aliasing. The scenario describes a continuous-time signal \(x(t)\) with a maximum frequency component of \(f_{max}\). The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a band-limited continuous-time signal from its discrete samples, the sampling frequency \(f_s\) must be strictly greater than twice the maximum frequency component of the signal, i.e., \(f_s > 2f_{max}\). This minimum sampling frequency, \(2f_{max}\), is known as the Nyquist rate. If the sampling frequency is less than the Nyquist rate (\(f_s < 2f_{max}\)), aliasing occurs. Aliasing is a phenomenon where higher frequencies in the original signal are misrepresented as lower frequencies in the sampled signal, leading to distortion and loss of information. In the given scenario, the signal \(x(t)\) has a maximum frequency of \(f_{max}\). To avoid aliasing, the sampling frequency \(f_s\) must satisfy \(f_s > 2f_{max}\). The question asks for the condition under which the sampled signal \(x[n] = x(nT)\) accurately represents the original continuous-time signal \(x(t)\), where \(T\) is the sampling period and \(f_s = 1/T\). Accurate representation implies no loss of information due to sampling, which means no aliasing. Therefore, the sampling frequency \(f_s\) must be greater than twice the maximum frequency of the signal, \(f_{max}\). This translates to \(1/T > 2f_{max}\), or \(T < 1/(2f_{max})\). The value \(2f_{max}\) is the Nyquist rate. The correct answer is that the sampling frequency must be greater than twice the maximum frequency component of the signal. This ensures that each frequency component in the original signal is sampled at a rate sufficient to distinguish it from other frequencies, thereby preventing the folding of higher frequencies into lower frequency bands. This principle is foundational in digital signal processing, crucial for applications ranging from audio and image processing to telecommunications and control systems, areas of significant research and academic focus at institutions like NITK Surathkal. Understanding this concept is vital for designing effective digital systems that accurately capture and process real-world analog information.