National Higher School of Technology Entrance Exam Set

The scenario describes a system where a feedback loop is introduced to stabilize an unstable equilibrium point of a dynamic system. The core concept being tested is the impact of negative feedback on system stability. An unstable equilibrium point is characterized by a tendency to diverge from that point when perturbed. Negative feedback, by definition, opposes changes. When applied to an unstable system, it introduces a corrective action proportional to the deviation from the desired state. This corrective action acts to counteract the divergence, effectively pulling the system back towards the equilibrium. For instance, if a system’s state variable \(x\) is increasing away from equilibrium \(x_0\), a negative feedback mechanism would generate a control signal that decreases \(x\). The strength of this feedback, often represented by a gain factor, determines how effectively the instability is suppressed. A sufficiently large negative feedback gain can transform an unstable equilibrium into a stable one, or at least significantly dampen oscillations and reduce the rate of divergence. The question probes the understanding of this fundamental control theory principle: negative feedback’s role in stabilizing inherently unstable dynamic behaviors, a crucial concept in many engineering disciplines taught at the National Higher School of Technology.

The question probes the understanding of the fundamental principles of data integrity and the role of hashing in ensuring it, particularly in the context of software development and system security, which are core to the National Higher School of Technology’s curriculum. The scenario describes a software development team at the National Higher School of Technology using a version control system. They are concerned about unauthorized modifications to critical code files. The core concept being tested is how to detect such modifications. Hashing algorithms, such as SHA-256, generate a unique fixed-size string (hash) for any given input data. If even a single bit of the input data changes, the resulting hash will be drastically different. This property makes hashing ideal for detecting data tampering. By generating a hash of a code file at a known good state and storing it securely, any subsequent change to the file can be detected by re-hashing the file and comparing the new hash to the stored one. If the hashes do not match, it indicates that the file has been altered. Option a) describes this process accurately. Storing cryptographic hashes of the original code files and comparing them against re-generated hashes of the current files is the standard and most effective method for detecting unauthorized modifications. Option b) is incorrect because while digital signatures use hashing, they also involve private/public key cryptography for authentication and non-repudiation, which is a more complex process than simply detecting modification. The primary goal here is detection, not necessarily proving authorship or origin. Option c) is incorrect because checksums, while related to data integrity, are often simpler algorithms (like CRC) that are more susceptible to deliberate manipulation or collision attacks compared to cryptographic hash functions. For critical code integrity, stronger cryptographic hashes are preferred. Option d) is incorrect because encryption protects the confidentiality of data, preventing unauthorized access to its content. It does not inherently detect modifications. An encrypted file could be altered, and the alteration might not be apparent until the file is decrypted and used, and even then, detecting the specific alteration might be difficult without additional mechanisms. Therefore, the most appropriate and direct method for detecting unauthorized modifications to code files in a version control system, aligning with the security and integrity principles emphasized at the National Higher School of Technology, is the use of cryptographic hashing.

The core principle tested here is the understanding of how a system’s overall behavior emerges from the interactions of its individual components, particularly in the context of complex systems often studied at institutions like the National Higher School of Technology. This concept is fundamental to fields such as artificial intelligence, robotics, and advanced materials science, all of which are integral to the National Higher School of Technology’s curriculum. The scenario describes a swarm of autonomous drones designed for environmental monitoring. Each drone possesses limited sensing capabilities and simple decision-making rules for navigation and data collection. The emergent behavior of the swarm, specifically its ability to collectively map a large area efficiently and adapt to unforeseen obstacles, arises not from a central command but from the decentralized, local interactions between individual drones. This is a classic example of emergent complexity, where the macro-level properties of the system (efficient mapping, adaptability) are not explicitly programmed into any single agent but arise from the aggregation of simple, local rules. The question probes the candidate’s ability to recognize this phenomenon and distinguish it from other system design paradigms.

The scenario describes a system where a feedback loop is used to stabilize a process. The core concept being tested is the understanding of control systems and the impact of feedback on system stability and response. In a closed-loop system, the controller compares the desired output (setpoint) with the actual output (measured variable) and generates a control signal to minimize the error. The question asks about the primary benefit of implementing a negative feedback mechanism in such a system, specifically in the context of achieving a stable and predictable output despite external disturbances. Negative feedback works by counteracting deviations from the setpoint. If the output increases beyond the desired level, the feedback signal will cause the controller to reduce its output, thereby bringing the system back towards the setpoint. Conversely, if the output drops below the setpoint, the feedback will prompt the controller to increase its output. This continuous adjustment process is what leads to enhanced stability and robustness against unpredictable variations or noise. Without negative feedback, the system would be considered “open-loop,” and any deviation would likely persist or even amplify, leading to instability. Therefore, the most significant advantage of negative feedback in this context is its ability to maintain the system’s output close to the desired value, effectively rejecting disturbances and ensuring consistent performance, which is a fundamental principle in many engineering disciplines taught at the National Higher School of Technology.

The scenario describes a system where a signal is processed through a series of filters. The first filter is a low-pass filter with a cutoff frequency of \(f_c = 10 \text{ kHz}\). The second filter is a band-pass filter with a lower cutoff frequency of \(f_{l} = 5 \text{ kHz}\) and an upper cutoff frequency of \(f_{h} = 15 \text{ kHz}\). The third filter is a high-pass filter with a cutoff frequency of \(f_{hp} = 8 \text{ kHz}\). We need to determine the effective frequency range that passes through all three filters in sequence. 1. **First Filter (Low-Pass):** This filter allows frequencies from \(0 \text{ Hz}\) up to \(10 \text{ kHz}\) to pass. The output frequency range is \([0, 10 \text{ kHz})\). 2. **Second Filter (Band-Pass):** This filter allows frequencies between \(5 \text{ kHz}\) and \(15 \text{ kHz}\) to pass. The input to this filter is the output of the first filter, which is \([0, 10 \text{ kHz})\). The intersection of the input range \([0, 10 \text{ kHz})\) and the band-pass filter’s allowed range \([5 \text{ kHz}, 15 \text{ kHz})\) is \([5 \text{ kHz}, 10 \text{ kHz})\). So, the output frequency range after the second filter is \([5 \text{ kHz}, 10 \text{ kHz})\). 3. **Third Filter (High-Pass):** This filter allows frequencies above \(8 \text{ kHz}\) to pass. The input to this filter is the output of the second filter, which is \([5 \text{ kHz}, 10 \text{ kHz})\). The intersection of the input range \([5 \text{ kHz}, 10 \text{ kHz})\) and the high-pass filter’s allowed range \([8 \text{ kHz}, \infty)\) is \([8 \text{ kHz}, 10 \text{ kHz})\). Therefore, the overall frequency range that passes through all three filters is from \(8 \text{ kHz}\) to \(10 \text{ kHz}\). This represents a narrow band of frequencies. The question asks for the range of frequencies that *will not* be attenuated by the system, meaning the frequencies that pass through. The final effective frequency range that passes through all filters is \([8 \text{ kHz}, 10 \text{ kHz})\). This question assesses the understanding of cascaded filter responses, a fundamental concept in signal processing relevant to many engineering disciplines at the National Higher School of Technology. It requires careful consideration of how the passbands and stopbands of sequential filters interact. The ability to determine the composite frequency response of cascaded systems is crucial for designing and analyzing communication systems, audio processing, and control systems, all areas of focus within the National Higher School of Technology’s curriculum. Understanding these interactions allows engineers to precisely shape the spectral content of signals, ensuring that desired information is preserved while unwanted noise or interference is rejected. This problem tests the logical application of filter definitions to a sequential processing chain, emphasizing the importance of understanding the cumulative effect of multiple signal modifications.

The scenario describes a system where a novel material’s response to varying environmental stimuli is being investigated. The core concept being tested is the understanding of feedback loops and their impact on system stability and predictability, particularly in the context of material science and engineering research, which is a key area of focus at the National Higher School of Technology. A positive feedback loop amplifies an initial change. If the material’s conductivity increases with temperature, and this increased conductivity leads to further heat generation (e.g., through Joule heating if a current is applied), the temperature will continue to rise uncontrollably. This is analogous to a runaway reaction. A negative feedback loop counteracts an initial change. If the material’s conductivity decreases with temperature, or if an increase in temperature triggers a mechanism that cools the material, the system will tend towards a stable equilibrium. The question asks about the most likely outcome if the material exhibits a positive feedback mechanism where increased internal energy leads to a further increase in energy absorption rate. This describes a system that is inherently unstable and prone to rapid, escalating changes. Therefore, the material’s properties would likely become unpredictable and potentially lead to a state of rapid degradation or phase transition, making controlled experimentation extremely challenging. The National Higher School of Technology emphasizes rigorous experimental design and understanding of underlying physical principles to ensure reliable research outcomes. A system exhibiting such a positive feedback loop would require significant dampening mechanisms or a re-evaluation of experimental parameters to achieve any meaningful data. The unpredictability and potential for rapid escalation are the defining characteristics of such a positive feedback scenario in a scientific context.

The core concept tested here is the understanding of **algorithmic complexity** and its practical implications in software development, a fundamental area for aspiring technologists. Specifically, it probes the ability to differentiate between various Big O notations and their performance characteristics. Consider two algorithms, Algorithm A and Algorithm B, designed to process a dataset of size \(n\). Algorithm A exhibits a time complexity of \(O(n \log n)\), meaning its execution time grows proportionally to \(n\) multiplied by the logarithm of \(n\). Algorithm B, on the other hand, has a time complexity of \(O(n^2)\), indicating its execution time grows quadratically with \(n\). For small values of \(n\), the difference in performance might be negligible. For instance, if \(n=10\), \(10 \log_{10} 10 = 10\) (using base 10 for simplicity in conceptual illustration, though base 2 is common in computer science) and \(10^2 = 100\). The ratio is 10:1. However, as \(n\) increases significantly, the disparity becomes dramatic. If \(n=1000\), \(1000 \log_2 1000 \approx 1000 \times 10 = 10000\), while \(1000^2 = 1,000,000\). The ratio is now 100:1. For \(n=1,000,000\), \(1,000,000 \log_2 1,000,000 \approx 1,000,000 \times 20 = 20,000,000\), whereas \(1,000,000^2 = 1,000,000,000,000\). The ratio is 50,000:1. This exponential divergence in performance means that an algorithm with \(O(n^2)\) complexity will become prohibitively slow and resource-intensive for large datasets, potentially leading to system unresponsiveness or outright failure. In contrast, an algorithm with \(O(n \log n)\) complexity scales much more gracefully. Therefore, when dealing with potentially large or unbounded datasets, prioritizing algorithms with lower-order complexities like \(O(n \log n)\) over higher-order ones like \(O(n^2)\) is a critical design decision for efficient and scalable software, a principle highly valued at the National Higher School of Technology Entrance Exam. This understanding is crucial for developing robust and performant systems, aligning with the school’s emphasis on practical engineering solutions.

The question probes the understanding of the fundamental principles of data integrity and the role of hashing in ensuring it, particularly within the context of secure digital systems, a core concern at the National Higher School of Technology. The scenario describes a system where data modification is a critical threat. Hashing, specifically cryptographic hashing, is the most robust method for detecting unauthorized alterations. A cryptographic hash function produces a fixed-size output (the hash value or digest) from an input of arbitrary size. Key properties include: determinism (the same input always produces the same output), pre-image resistance (it’s computationally infeasible to find the original input given the hash), second pre-image resistance (it’s computationally infeasible to find a different input that produces the same hash as a given input), and collision resistance (it’s computationally infeasible to find two different inputs that produce the same hash). In this scenario, if the data is altered, even by a single bit, the resulting hash value will change drastically due to the avalanche effect inherent in good cryptographic hash functions. Therefore, by storing the hash of the original data and comparing it with the hash of the data at a later time, any modification can be detected. Let’s consider why other options are less suitable for ensuring data integrity against malicious modification: * **Digital Signatures:** While digital signatures use hashing, they primarily provide authentication (proving the sender’s identity) and non-repudiation (proving the sender cannot deny having sent the message), in addition to integrity. However, the core mechanism for detecting the *alteration* of the data itself, independent of the sender’s identity, is the hash. A digital signature is built *upon* a hash. * **Encryption:** Encryption makes data unreadable to unauthorized parties, ensuring confidentiality. However, if an attacker can modify encrypted data without detection (e.g., by simply flipping bits in the ciphertext, which might result in a different but still valid decryption, or by replacing the entire encrypted block), encryption alone does not guarantee integrity. While authenticated encryption modes (like AES-GCM) combine encryption with integrity checks, the fundamental integrity check is often based on a message authentication code (MAC), which is conceptually similar to a hash but keyed. * **Checksums (e.g., CRC):** Checksums are simpler error detection mechanisms, often used for detecting accidental data corruption during transmission or storage. They are generally not designed to be cryptographically secure and can be relatively easy to manipulate or bypass by an attacker who intentionally modifies the data. An attacker could calculate a new checksum for their modified data that matches the expected checksum, thus evading detection. Therefore, for robust detection of unauthorized data modification, a cryptographic hash function is the most direct and fundamental tool.

The question probes the understanding of the fundamental principles of digital signal processing, specifically concerning the aliasing phenomenon and its mitigation through sampling. Aliasing occurs when a signal is sampled at a rate lower than twice its highest frequency component (Nyquist rate). This leads to the misinterpretation of higher frequencies as lower frequencies. Consider a signal \(x(t)\) with a maximum frequency component \(f_{max}\). According to the Nyquist-Shannon sampling theorem, to perfectly reconstruct \(x(t)\) from its samples, the sampling frequency \(f_s\) must be greater than \(2f_{max}\). If \(f_s \le 2f_{max}\), aliasing will occur. In this scenario, the signal has frequency components up to 5 kHz. Therefore, \(f_{max} = 5 \text{ kHz}\). The Nyquist rate for this signal is \(2 \times f_{max} = 2 \times 5 \text{ kHz} = 10 \text{ kHz}\). The sampling frequency used is \(f_s = 8 \text{ kHz}\). Since \(f_s < 10 \text{ kHz}\), aliasing is inevitable. When a signal with frequency \(f\) is sampled at \(f_s\), the observed frequencies in the sampled signal are \(f \pmod{f_s}\) and \(-f \pmod{f_s}\). For frequencies above \(f_s/2\), they will appear as lower frequencies. Specifically, a frequency \(f > f_s/2\) will be aliased to \(|f – k \cdot f_s|\) where \(k\) is an integer chosen such that the result is within the range \([0, f_s/2]\). In this case, \(f_s/2 = 8 \text{ kHz} / 2 = 4 \text{ kHz}\). The highest frequency component is 5 kHz. This frequency is greater than \(f_s/2 = 4 \text{ kHz}\). To find its aliased frequency, we look for \(|5 \text{ kHz} – k \cdot 8 \text{ kHz}|\) such that the result is in \([0, 4 \text{ kHz}]\). For \(k=1\), we get \(|5 \text{ kHz} – 1 \cdot 8 \text{ kHz}| = |-3 \text{ kHz}| = 3 \text{ kHz}\). Since 3 kHz is within the range \([0, 4 \text{ kHz}]\), the 5 kHz component will be aliased to 3 kHz. Therefore, the highest frequency component of 5 kHz will be incorrectly represented as 3 kHz in the sampled data. This demonstrates a fundamental concept in signal processing crucial for engineers at the National Higher School of Technology, where understanding sampling limitations is vital for designing accurate data acquisition systems and analyzing signals in various technological applications. Proper anti-aliasing filtering before sampling is a standard practice to prevent such distortions, ensuring the integrity of the digital representation of analog signals.

The scenario describes a system where a sensor network is deployed to monitor environmental conditions. The core challenge is to ensure data integrity and timely delivery from distributed nodes to a central processing unit. The question probes the understanding of network protocols and their suitability for such applications. Consider a scenario where a distributed sensor network at the National Higher School of Technology Entrance Exam is tasked with real-time monitoring of atmospheric particulate matter across its campus. Each sensor node has limited processing power and battery life. Data from these nodes needs to be aggregated at a central server for analysis. The network experiences intermittent connectivity due to environmental factors and the sheer number of nodes. The primary objective is to minimize data loss and ensure that critical readings are not delayed beyond a defined threshold for effective environmental response. The question asks to identify the most appropriate communication paradigm for this scenario. Let’s analyze the options: * **Publish-Subscribe (Pub/Sub):** In this model, nodes (publishers) send data to specific topics without knowing who the subscribers are. Subscribers express interest in specific topics and receive messages accordingly. This decouples the sender and receiver, making the system more resilient to node failures and network disruptions. If a central server is temporarily unavailable, publishers can continue to send data, and it will be processed when the server reconnects. It also allows for efficient dissemination of data to multiple interested parties (e.g., different analysis modules). This aligns well with the need for timely delivery and resilience in a sensor network with intermittent connectivity. * **Request-Response:** This model requires a client to explicitly request data from a server. In a large sensor network with intermittent connectivity, this would be highly inefficient. Each node would need to poll the central server, leading to high overhead and potential bottlenecks. Furthermore, if a node needs to send data, it would have to wait for the server to be available to receive the request, which is not ideal for real-time monitoring. * **Peer-to-Peer (P2P):** While P2P can offer decentralization, managing a large-scale sensor network with diverse capabilities and intermittent connectivity using a pure P2P model can be complex. It might require significant overhead for node discovery, data routing, and maintaining network state, which could strain the limited resources of the sensor nodes. While some P2P elements might be incorporated, it’s not the most direct or efficient primary paradigm for this specific problem of data aggregation from many sources to one central point with reliability concerns. * **Client-Server:** This is a more centralized model where clients (sensors) directly communicate with a server. While conceptually simple, it can become a bottleneck if the server is overwhelmed or if connectivity between nodes and the server is unreliable. The publish-subscribe model offers a more robust and scalable solution for this specific distributed sensing application at the National Higher School of Technology Entrance Exam, particularly given the intermittent connectivity and the need for efficient data flow to a central point. Therefore, the Publish-Subscribe model is the most suitable communication paradigm.

The core concept being tested here is the understanding of how different organizational structures impact information flow and decision-making within a technology-focused institution like the National Higher School of Technology Entrance Exam. A highly centralized structure, where decision-making authority is concentrated at the top, can lead to slower response times to localized issues or emerging research opportunities. This is because information must travel up the hierarchy for approval and then back down for implementation. While it ensures consistency, it can stifle innovation and adaptability, which are crucial in rapidly evolving technological fields. Conversely, a decentralized structure empowers lower levels, fostering quicker responses and greater autonomy, but potentially leading to fragmentation or inconsistencies if not managed carefully. A matrix structure, often used in project-based environments, can offer flexibility but may introduce dual reporting lines and potential conflicts. A functional structure, organized by specialization, promotes deep expertise but can create silos between departments. Considering the need for agility, rapid problem-solving, and fostering innovation in a technological education setting, a structure that balances specialized expertise with cross-functional collaboration and distributed decision-making would be most advantageous. This allows for efficient knowledge sharing across disciplines and faster adaptation to new technological trends and student needs. The National Higher School of Technology Entrance Exam, aiming to cultivate future innovators and researchers, would benefit most from an approach that encourages bottom-up input and empowers teams to address challenges directly, while maintaining overarching strategic coherence.

The question probes the understanding of the foundational principles of digital signal processing, specifically concerning the Nyquist-Shannon sampling theorem and its implications for aliasing. 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 continuous-time signal with a maximum frequency component of 15 kHz is being sampled. To avoid aliasing, the sampling frequency must be greater than or equal to twice this maximum frequency. Therefore, the minimum required sampling frequency is \(2 \times 15 \text{ kHz} = 30 \text{ kHz}\). If the signal is sampled at a frequency lower than this Nyquist rate, higher frequency components will masquerade as lower frequencies, a phenomenon called aliasing. This distortion makes accurate reconstruction of the original signal impossible. The National Higher School of Technology Entrance Exam emphasizes a deep understanding of these signal processing fundamentals, as they are critical for various engineering disciplines, including telecommunications, control systems, and data acquisition. Understanding the trade-offs between sampling rate, bandwidth, and reconstruction fidelity is paramount for designing efficient and accurate digital systems. This question assesses the candidate’s ability to apply the core theorem to a practical scenario, demonstrating their grasp of a fundamental concept in digital signal processing.

The question probes the understanding of the scientific method’s core principles, specifically how to establish causality and control for confounding variables in experimental design. The scenario involves investigating the impact of a new pedagogical approach at the National Higher School of Technology Entrance Exam. To isolate the effect of the new method, it’s crucial to compare it against a baseline or alternative. A control group that receives the standard teaching method allows for this comparison. Random assignment of students to either the new method or the standard method ensures that pre-existing differences between students (e.g., prior knowledge, learning styles, motivation) are distributed as evenly as possible across both groups. This minimizes the likelihood that observed differences in learning outcomes are due to these inherent student characteristics rather than the teaching method itself. Without a control group, any observed improvement could be attributed to other factors, such as general curriculum updates, increased student motivation over time, or even the Hawthorne effect (students performing better simply because they are being observed). Therefore, the most robust experimental design to establish causality would involve a control group receiving the standard instruction, with random assignment to both groups.

The scenario describes a system where a user interacts with a digital interface designed for a National Higher School of Technology Entrance Exam. The core of the problem lies in understanding how user input is processed and how the system’s state changes based on that input, particularly concerning the validation of an academic program selection. The system initializes with a default state where no program is selected. The user then attempts to select “Advanced Robotics.” This action triggers a validation process. The validation rule states that a program can only be selected if its prerequisite, “Foundational Engineering,” has been completed. Since “Foundational Engineering” has not been completed (the system state indicates “Foundational Engineering: Not Completed”), the selection of “Advanced Robotics” is deemed invalid. Consequently, the system does not update its state to reflect the selection of “Advanced Robotics.” Instead, it maintains the prior state where no program is selected, and it presents an error message to the user. Therefore, the final state of the system will be: Selected Program: None Prerequisite Status: Foundational Engineering: Not Completed Error Message: “Prerequisite ‘Foundational Engineering’ not met for Advanced Robotics.” This process highlights the importance of state management and conditional logic in user interface design, especially in educational platforms where adherence to academic progression rules is paramount. The National Higher School of Technology Entrance Exam would expect candidates to understand these fundamental principles of system behavior and user interaction.

The core principle tested here is the understanding of how a system’s overall behavior emerges from the interactions of its individual components, particularly in the context of complex systems often studied at institutions like the National Higher School of Technology. The scenario describes a novel bio-integrated sensor network designed for environmental monitoring. The question asks about the most critical factor for the network’s long-term efficacy and adaptability. Let’s analyze why the correct option is superior. The network comprises diverse biological and electronic elements, each with unique lifecycles, failure modes, and environmental sensitivities. For instance, biological components might degrade over time due to natural processes, while electronic components could be susceptible to wear or obsolescence. The interaction and interdependence between these components mean that a failure or degradation in one part can cascade and impact the entire system. Therefore, a robust, adaptive self-repair or self-optimization mechanism that can dynamically reconfigure the network in response to component degradation or environmental shifts is paramount for sustained operation. This aligns with concepts of resilience and fault tolerance crucial in advanced engineering and technology. Consider the incorrect options: A purely centralized control system, while offering initial efficiency, can become a single point of failure and may struggle to adapt to localized, emergent issues within the distributed network. Optimizing for maximum data throughput at all times might lead to premature wear on components or inefficient energy usage, especially if the environmental conditions do not necessitate such high performance, and doesn’t address the fundamental issue of component degradation. Focusing solely on the initial calibration of the biological sensors, while important, is a static measure. Without a mechanism to adapt to changes in biological function or environmental drift, the network’s accuracy will inevitably decline over time. The National Higher School of Technology emphasizes interdisciplinary approaches and the development of robust, intelligent systems. A system that can autonomously manage its own integrity and adapt to the inherent variability of its components and environment directly reflects these values. The ability to maintain functionality despite partial failures or performance degradation, through mechanisms like distributed decision-making and adaptive routing, is a hallmark of advanced system design. This question probes the candidate’s ability to think about system-level properties and the challenges of integrating disparate technologies in a dynamic, real-world setting, a key skill for future technologists.

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 data acquisition at the National Higher School of Technology. The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a 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 sensor is designed to capture phenomena with a maximum frequency of 15 kHz. Therefore, to avoid aliasing and ensure accurate representation of the signal, the sampling frequency must be strictly greater than \(2 \times 15 \text{ kHz}\). This minimum required sampling rate is \(30 \text{ kHz}\). The National Higher School of Technology emphasizes rigorous data integrity in its engineering programs. Selecting a sampling frequency that is precisely twice the maximum frequency (\(2f_{max}\)) is often referred to as the Nyquist rate, but the theorem strictly requires sampling *above* this rate for perfect reconstruction. While sampling at exactly \(30 \text{ kHz}\) might be theoretically sufficient under ideal conditions, in practical engineering scenarios, especially within a research-intensive environment like the National Higher School of Technology, a margin is often incorporated to account for non-ideal filters, signal imperfections, and to ensure robust data acquisition. Therefore, a sampling frequency of 35 kHz is a prudent choice that comfortably exceeds the Nyquist rate, ensuring that the captured data accurately reflects the underlying physical phenomena without introducing distortion due to undersampling. This adherence to sampling principles is crucial for subsequent analysis, modeling, and the development of advanced technological solutions, aligning with the school’s commitment to high-fidelity data and scientific accuracy.

The scenario describes a system where a control signal, \(u(t)\), influences the rate of change of a state variable, \(x(t)\), which is then observed through a measurement, \(y(t)\). The system dynamics are given by \(\frac{dx}{dt} = -ax + bu(t)\) and the measurement equation is \(y(t) = cx + d\). We are given that \(a=2\), \(b=1\), \(c=0.5\), and \(d=3\). The question asks about the steady-state behavior when a constant control input, \(u(t) = U_0\), is applied. In steady-state, the rate of change of the state variable is zero, meaning \(\frac{dx}{dt} = 0\). From the system dynamics equation, we have: \(0 = -ax_{ss} + bu(t)\) where \(x_{ss}\) is the steady-state value of \(x(t)\). Substituting the given values for \(a\) and \(b\), and setting \(u(t) = U_0\): \(0 = -2x_{ss} + 1 \cdot U_0\) \(2x_{ss} = U_0\) \(x_{ss} = \frac{U_0}{2}\) Now, we need to find the steady-state measurement, \(y_{ss}\). The measurement equation is \(y(t) = cx(t) + d\). In steady-state, this becomes: \(y_{ss} = c x_{ss} + d\) Substituting the values for \(c\) and \(d\), and the expression for \(x_{ss}\): \(y_{ss} = 0.5 \cdot \left(\frac{U_0}{2}\right) + 3\) \(y_{ss} = \frac{0.5 U_0}{2} + 3\) \(y_{ss} = 0.25 U_0 + 3\) This result indicates that the steady-state output is directly proportional to the constant control input \(U_0\), with a scaling factor of 0.25, plus a constant offset of 3. This relationship is fundamental in understanding how control systems respond to sustained inputs and how system parameters influence this response, a core concept in control theory relevant to many engineering disciplines at the National Higher School of Technology. The steady-state analysis is crucial for predicting long-term system behavior and designing controllers that achieve desired performance, such as stability and accuracy, which are paramount in the rigorous academic environment of the National Higher School of Technology. Understanding this steady-state gain (\(0.25\)) and offset (\(3\)) allows engineers to anticipate the system’s final output for a given constant input, informing design choices for applications ranging from automated manufacturing to signal processing.

The core principle tested here is the understanding of how different organizational structures impact information flow and decision-making within a technology-focused institution like the National Higher School of Technology. A hierarchical structure, characterized by clear lines of authority and segmented communication channels, often leads to slower decision cycles and potential information bottlenecks. This is because information must traverse multiple levels, and specialized departments may operate with limited cross-functional awareness. In contrast, a flatter, more matrixed, or network-based structure, which emphasizes collaboration and direct communication across teams and disciplines, generally facilitates faster adaptation to emerging technological trends and more agile problem-solving. Such structures are better suited for environments that require rapid innovation and interdisciplinary synergy, aligning with the dynamic nature of technological advancement and research prevalent at the National Higher School of Technology. Therefore, to foster an environment conducive to rapid technological innovation and interdisciplinary collaboration, a less rigid, more networked organizational model would be more effective than a strictly hierarchical one.

The core concept tested here is the understanding of how different organizational structures impact information flow and decision-making within a technology-focused institution like the National Higher School of Technology. A highly centralized structure, where decision-making authority is concentrated at the top, can lead to bottlenecks in communication and slower adaptation to emerging technological trends or student needs. This is because proposals and feedback from various departments or student bodies must traverse multiple hierarchical levels before reaching a decision-maker, and then the decision must be disseminated back down. In contrast, a decentralized or matrix structure, which encourages cross-functional collaboration and distributed decision-making, allows for more agile responses. For the National Higher School of Technology, fostering innovation and rapid adoption of new pedagogical methods or research directions is paramount. Therefore, an organizational model that empowers lower-level units and facilitates direct communication channels between diverse stakeholders (e.g., faculty from different engineering disciplines, research labs, student support services) would be most conducive to achieving these goals. This promotes a culture of shared responsibility and allows for quicker identification and implementation of solutions to complex, interdisciplinary challenges inherent in technological education. The ability to adapt swiftly to the evolving landscape of technology and industry demands is a key performance indicator for such an institution.

The core principle tested here is the understanding of how different organizational structures impact information flow and decision-making within a technology-focused institution like the National Higher School of Technology. A hierarchical structure, characterized by multiple layers of management and clear lines of authority, inherently creates more communication bottlenecks. Each level must process and relay information, leading to potential delays and distortions. In contrast, a flatter, more matrix-based structure, often adopted by innovative tech organizations, promotes direct communication between specialized teams and leadership, facilitating quicker problem-solving and adaptation. The National Higher School of Technology, with its emphasis on cutting-edge research and rapid development cycles, would benefit most from an organizational design that minimizes communication latency and fosters cross-functional collaboration. Therefore, a structure that prioritizes direct access to decision-makers and encourages interdisciplinary project teams, rather than rigid departmental silos, is crucial for its operational efficiency and innovative capacity. This aligns with modern management theories that advocate for agile and responsive organizational frameworks in dynamic technological environments.

The question probes the understanding of the fundamental principles governing the design and operation of a basic resonant circuit, specifically focusing on the relationship between inductance, capacitance, and resonant frequency. The resonant frequency (\(f_r\)) of an LC circuit is determined by the formula \(f_r = \frac{1}{2\pi\sqrt{LC}}\). In this scenario, the National Higher School of Technology Entrance Exam is considering a new experimental setup for their advanced electronics laboratory. They have a fixed inductor with an inductance of \(L = 50 \, \mu\text{H}\) (\(50 \times 10^{-6} \, \text{H}\)) and are evaluating different capacitor values. The goal is to achieve a resonant frequency of \(f_r = 1 \, \text{MHz}\) (\(1 \times 10^{6} \, \text{Hz}\)). To find the required capacitance, we rearrange the resonant frequency formula: \[ f_r = \frac{1}{2\pi\sqrt{LC}} \] \[ f_r^2 = \frac{1}{4\pi^2LC} \] \[ C = \frac{1}{4\pi^2Lf_r^2} \] Now, substitute the given values: \[ C = \frac{1}{4\pi^2 (50 \times 10^{-6} \, \text{H}) (1 \times 10^{6} \, \text{Hz})^2} \] \[ C = \frac{1}{4\pi^2 (50 \times 10^{-6}) (1 \times 10^{12})} \] \[ C = \frac{1}{4\pi^2 (50 \times 10^{6})} \] \[ C = \frac{1}{200\pi^2 \times 10^{6}} \] Using \(\pi^2 \approx 9.87\): \[ C \approx \frac{1}{200 \times 9.87 \times 10^{6}} \] \[ C \approx \frac{1}{1974 \times 10^{6}} \] \[ C \approx 0.0005065 \times 10^{-6} \, \text{F} \] \[ C \approx 0.5065 \times 10^{-9} \, \text{F} \] \[ C \approx 0.5065 \, \text{nF} \] This calculation demonstrates that a capacitance of approximately \(0.5065 \, \text{nF}\) is needed to achieve the target resonant frequency with the given inductor. This understanding is crucial for students at the National Higher School of Technology Entrance Exam as it underpins the design of tuning circuits, oscillators, and filters, which are fundamental components in many areas of electrical engineering and telecommunications, fields of study strongly represented at the institution. The ability to manipulate these formulas and understand the inverse relationship between inductance/capacitance and resonant frequency is a core competency.

The core principle tested here is the understanding of how different organizational structures impact information flow and decision-making, particularly in a technology-focused institution like the National Higher School of Technology. A hierarchical structure, characterized by clear lines of authority and communication flowing primarily vertically, can lead to delays and filtering of information as it moves up and down the chain. This can hinder rapid response to emerging technological challenges or opportunities, which is crucial in fields like advanced engineering and computer science. Conversely, a matrix structure, while complex, allows for cross-functional collaboration and resource sharing, potentially accelerating innovation and problem-solving by bringing diverse expertise together. A flat structure, with fewer management layers, promotes direct communication and faster decision-making, fostering agility. A functional structure, while efficient for specialized tasks, can create silos that impede interdisciplinary projects. Considering the National Higher School of Technology’s emphasis on cutting-edge research and interdisciplinary projects, an organizational model that facilitates rapid information exchange and collaborative problem-solving is paramount. Therefore, a structure that minimizes communication bottlenecks and encourages direct interaction between specialists from different departments, such as a matrix or a highly collaborative, project-based model, would be most conducive to its mission. The question probes the candidate’s ability to connect organizational design principles with the operational needs of a modern technological research and education institution.

The core principle at play here is the concept of **emergent properties** in complex systems, a fundamental idea explored across various technological and scientific disciplines at the National Higher School of Technology. Emergent properties are characteristics of a system that are not present in its individual components but arise from the interactions between those components. In the context of the National Higher School of Technology’s emphasis on interdisciplinary innovation, understanding how novel functionalities and behaviors can arise from the synergistic combination of seemingly disparate elements is crucial. For instance, a network of simple sensors, when interconnected and processing data collectively, can exhibit sophisticated pattern recognition capabilities far beyond what any single sensor could achieve. Similarly, the intricate behaviors of biological systems or the collective intelligence observed in swarm robotics are prime examples of emergence. The question probes the candidate’s ability to recognize this phenomenon in a novel, non-technical scenario, requiring them to abstract the underlying principle of interaction leading to a new quality. The scenario of a symphony orchestra exemplifies this: individual musicians playing their instruments produce sounds, but the coordinated performance, guided by a conductor and the score, creates a unified, emotionally resonant musical experience that is qualitatively different from the sum of individual sounds. This emergent quality – the symphony itself – cannot be found in any single instrument or musician. Therefore, the ability to perceive and articulate this emergent characteristic is key to demonstrating a grasp of complex systems thinking, a vital skill for students at the National Higher School of Technology.

The scenario describes a system where a novel material’s response to varying environmental stimuli is being investigated. The core of the question lies in understanding how to isolate the effect of a single variable when multiple factors are at play, a fundamental principle in experimental design crucial for research at institutions like the National Higher School of Technology. To determine the material’s intrinsic property (its resistance to degradation), we must eliminate the influence of other variables. The experiment involves varying temperature, humidity, and exposure to a specific chemical agent. The goal is to find the condition that isolates the material’s inherent stability. Consider the experimental setup: 1. **Baseline:** Material is kept under standard, controlled conditions (e.g., room temperature, low humidity, no chemical exposure). This establishes a reference point. 2. **Variable Isolation:** To understand the material’s inherent resistance, we need to test it under conditions where only its intrinsic properties are challenged, without confounding environmental factors. This means creating a scenario where the material is subjected to a stress that directly probes its fundamental structure or composition, independent of external fluctuations. 3. **Eliminating Confounding Variables:** * Increasing temperature alone might cause thermal expansion or phase changes, but doesn’t directly test chemical or structural degradation in isolation. * Increasing humidity alone tests hygroscopic properties or susceptibility to hydrolysis, not necessarily intrinsic structural integrity under general stress. * Exposure to the chemical agent tests reactivity with that specific agent. The most effective way to assess the material’s *intrinsic* resistance to degradation, without the influence of specific environmental agents or conditions, is to subject it to a generalized stress that would reveal inherent weaknesses. This is achieved by exposing it to a vacuum at an elevated temperature. A vacuum removes atmospheric components (like oxygen or moisture) that could react with the material, and elevated temperature provides a consistent, non-specific stress that can accelerate any inherent degradation mechanisms (like bond breaking due to thermal energy) without introducing chemical reactivity from the environment. This method allows researchers at the National Higher School of Technology to understand the material’s fundamental thermal stability and structural integrity.

The scenario describes a system where a new technology is being integrated into an existing infrastructure. The core challenge is to ensure that the new system’s operational parameters do not negatively impact the established performance metrics of the legacy components. Specifically, the question probes the understanding of how to manage the introduction of a novel process without causing detrimental interference or degradation to the existing, functional parts of the National Higher School of Technology’s operational framework. This involves considering the principles of system compatibility, resource allocation, and potential emergent behaviors. The correct approach would involve a phased implementation with rigorous monitoring and validation at each stage, focusing on maintaining the integrity of the current system while assessing the benefits of the new one. This aligns with best practices in technological adoption within complex, established environments, emphasizing risk mitigation and iterative validation. The National Higher School of Technology, with its focus on cutting-edge research and practical application, would prioritize methodologies that ensure stability and continuous improvement, rather than disruptive, untested overhauls. Therefore, a strategy that prioritizes controlled integration and performance benchmarking is paramount.

The question probes the understanding of a fundamental concept in digital signal processing, specifically related to the Nyquist-Shannon sampling theorem and its implications for signal reconstruction. The core idea is that to perfectly reconstruct a continuous-time signal from its discrete samples, the sampling frequency (\(f_s\)) must be at least twice the highest frequency component present in the original signal (\(f_{max}\)). This minimum sampling rate is known as the Nyquist rate, \(f_{Nyquist} = 2f_{max}\). In this scenario, the signal is described as having its highest frequency component at 15 kHz. Therefore, to avoid aliasing and ensure faithful reconstruction, the sampling frequency must be greater than or equal to twice this value. Calculation: Minimum required sampling frequency = \(2 \times f_{max}\) Minimum required sampling frequency = \(2 \times 15 \text{ kHz}\) Minimum required sampling frequency = \(30 \text{ kHz}\) The question asks for the *minimum* sampling frequency that guarantees perfect reconstruction. This corresponds to the Nyquist rate. Any sampling frequency below this threshold would result in aliasing, where higher frequencies masquerade as lower frequencies, corrupting the reconstructed signal. The National Higher School of Technology Entrance Exam emphasizes a deep understanding of these foundational principles in signal processing, which are critical for various engineering disciplines, including telecommunications, control systems, and audio/video processing. A thorough grasp of sampling theory is essential for designing efficient and accurate digital systems, ensuring that information is not lost or distorted during the analog-to-digital conversion process. This understanding underpins the ability to analyze and manipulate signals in the digital domain, a core competency for graduates of the National Higher School of Technology.

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 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 rate 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, \(f_{max} = 15 \text{ kHz}\). According to the Nyquist-Shannon sampling theorem, the minimum sampling frequency required to avoid aliasing and ensure perfect reconstruction is \(f_{s,min} = 2 \times f_{max} = 2 \times 15 \text{ kHz} = 30 \text{ kHz}\). The question asks about the consequence of sampling at \(25 \text{ kHz}\), which is below the Nyquist rate of \(30 \text{ kHz}\). When the sampling frequency is less than twice the maximum frequency component of the signal, aliasing occurs. Aliasing is a phenomenon where higher frequencies in the original signal are incorrectly represented as lower frequencies in the sampled signal. Specifically, a frequency \(f\) in the original signal will appear as \(|f – n f_s|\) in the sampled signal, where \(n\) is an integer chosen such that the aliased frequency is within the range \([0, f_s/2]\). For the \(15 \text{ kHz}\) component in the original signal, when sampled at \(f_s = 25 \text{ kHz}\), the aliased frequency would be calculated as follows: The folding frequency is \(f_s/2 = 25 \text{ kHz} / 2 = 12.5 \text{ kHz}\). The original frequency \(f = 15 \text{ kHz}\) is greater than the folding frequency. To find the aliased frequency, we subtract multiples of \(f_s\) until the result falls within the range \([0, f_s/2]\). \(15 \text{ kHz} – 1 \times 25 \text{ kHz} = -10 \text{ kHz}\). The absolute value is \(10 \text{ kHz}\). Since \(10 \text{ kHz}\) is within the range \([0, 12.5 \text{ kHz}]\), the \(15 \text{ kHz}\) component will be aliased to \(10 \text{ kHz}\). This means that after sampling at \(25 \text{ kHz}\), the signal will appear to have a \(10 \text{ kHz}\) component that was not present in the original signal’s intended frequency band, and the original \(15 \text{ kHz}\) information is lost or distorted. This distortion is a direct consequence of violating the Nyquist criterion. The ability to correctly reconstruct the original signal is compromised because the higher frequency has folded back into the lower frequency range, making it indistinguishable from genuine lower frequency components. This is a fundamental concept tested in signal processing, crucial for understanding digital communication, audio, and image processing systems, all areas of study at the National Higher School of Technology.

The scenario describes a situation where a new material’s tensile strength is being evaluated under varying environmental conditions. The core concept being tested is the understanding of how external factors can influence material properties and the importance of controlled experimentation in validating these influences. Specifically, the question probes the most critical aspect of ensuring the observed changes in tensile strength are attributable to the environmental variations and not to inherent inconsistencies in the material itself or the testing methodology. To address this, a robust experimental design is paramount. The most crucial step is to establish a baseline. This involves testing a representative sample of the new material under identical, stable, and controlled laboratory conditions *before* introducing any environmental variables. This baseline measurement serves as the reference point against which all subsequent tests under varying conditions will be compared. Without this initial, unadulterated data, it becomes impossible to definitively attribute any observed changes in tensile strength to the specific environmental factors being investigated. The other options, while potentially part of a comprehensive study, do not address this foundational requirement for establishing causality. For instance, testing multiple batches is good for generalizability but doesn’t establish the baseline for *this specific* material’s response. Testing under extreme conditions without a baseline is meaningless for determining the *impact* of those conditions. Finally, simply recording data without a controlled comparison point renders the data insufficient for drawing valid conclusions about the material’s behavior under stress. Therefore, establishing a controlled baseline is the indispensable first step in this scientific inquiry, aligning with the rigorous empirical standards expected at the National Higher School of Technology.

The question probes the understanding of the fundamental principles of data integrity and the role of hashing in ensuring it, particularly in the context of software development and digital security, which are core to many programs at the National Higher School of Technology. A cryptographic hash function takes an input (or ‘message’) and returns a fixed-size string of bytes, typically a hexadecimal number. This output is called a hash value, message digest, or simply hash. Key properties of cryptographic hash functions include: 1. **Determinism:** The same input will always produce the same output hash. 2. **Pre-image resistance (one-way):** It is computationally infeasible to determine the original input message given only the hash value. 3. **Second pre-image resistance:** It is computationally infeasible to find a different input message that produces the same hash value as a given input message. 4. **Collision resistance:** It is computationally infeasible to find two different input messages that produce the same hash value. In the scenario presented, the developer is concerned about unauthorized modifications to the source code of a critical application deployed by the National Higher School of Technology. If the source code is altered, even slightly, the resulting hash value will change drastically due to the avalanche effect inherent in good hash functions. By storing the original hash of the verified source code, the developer can later re-calculate the hash of the deployed code and compare it. A mismatch indicates that the code has been tampered with or corrupted. Option (a) correctly identifies the use of cryptographic hashing for detecting unauthorized modifications. This is a standard security practice for verifying the integrity of digital assets. Option (b) is incorrect because while encryption secures data confidentiality, it doesn’t directly address the integrity of the code itself in the way hashing does. Encrypted code would need to be decrypted before its integrity could be verified, and the decryption key itself would need protection. Option (c) is incorrect. Digital signatures use hashing as a component, but they also involve asymmetric cryptography (public/private keys) to provide authentication (proving the origin of the data) and non-repudiation (preventing the sender from denying they sent it). While related, the primary mechanism for detecting *unauthorized modification* of the code itself, without necessarily knowing the original author, is hashing. Option (d) is incorrect. Data obfuscation aims to make code harder to understand for reverse engineering, not to verify its integrity against accidental or malicious changes. Obfuscated code can still be modified, and its integrity would still need to be checked using methods like hashing. Therefore, the most direct and effective method for the developer to ensure the integrity of the source code against unauthorized modifications is by employing cryptographic hashing.

The question probes the understanding of the fundamental principles of **systems thinking** and **feedback loops** as applied to complex technological and societal challenges, a core area of study at the National Higher School of Technology. The scenario describes a common issue in urban development and resource management. To effectively address the problem of increasing traffic congestion and its associated environmental impact in a rapidly growing metropolitan area, a systems approach is paramount. This involves identifying the interconnected elements and understanding how they influence each other through various feedback mechanisms. The core of the problem lies in the interconnectedness of urban sprawl, increased car dependency, and the resulting pollution and infrastructure strain. Simply building more roads (a linear, reductionist solution) often leads to induced demand, where the new capacity attracts more vehicles, ultimately exacerbating congestion and pollution in the long run. This is a classic example of a **reinforcing loop** where increased road capacity leads to more driving, which then necessitates more road capacity. A more effective approach, aligned with the National Higher School of Technology’s emphasis on sustainable and integrated solutions, would involve understanding and manipulating **balancing loops** and **system leverage points**. For instance, investing in and promoting efficient public transportation systems, encouraging mixed-use development to reduce travel distances, and implementing smart urban planning policies that prioritize pedestrian and cycling infrastructure create balancing forces. These interventions aim to reduce car dependency, thereby alleviating congestion and pollution. Furthermore, understanding the **delays** inherent in implementing such changes (e.g., construction of new transit lines, shifts in public behavior) is crucial for realistic planning. Therefore, the most effective strategy involves a multi-faceted approach that addresses the root causes by altering the underlying system dynamics, rather than just treating the symptoms. This requires a deep understanding of how different interventions interact within the complex urban system. The correct option reflects this holistic, systems-oriented perspective, recognizing that technological solutions must be integrated with policy, behavioral, and planning considerations to achieve sustainable outcomes.