8.4 Practice Question

Duration: 1 min

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Module outline

Course Overview: About the Course
Paper - 1 | Unit - 1 | Teaching Aptitude: शिक्षण की अवधारणा एवं उद्देश्य / Concept and Objectives of Teaching, शिक्षण के स्तर / Levels of Teaching, शिक्षार्थी की विशेषताएँ / Learner's Characteristics, अधिगम: प्रकृति एवं सिद्धांत / Learning: Nature and Theories, संज्ञान, स्मृति एवं अधिसंज्ञान / Cognition, Memory and Metacognition, शिक्षण को प्रभावित करने वाले कारक / Factors Affecting Teaching, प्रभावी शिक्षण एवं शिक्षक / Effective Teaching and the Teacher, अनुदेशनात्मक उद्देश्य एवं पाठ नियोजन / Instructional Objectives and Lesson Planning, शिक्षण विधियाँ / Methods of Teaching, ऑफ़लाइन एवं ऑनलाइन शिक्षण विधियाँ / Offline and Online Teaching Methods, शिक्षण सहायक प्रणाली / Teaching Support System, मूल्यांकन प्रणाली / Evaluation Systems, Sāṃkhya, व्यक्तिगत व्यवहार / Individual Behaviour, मानव संसाधन प्रबंधन / Human Resource Management, बाल्यावस्था में विकास के क्षेत्र / Domains of Child Development, संवेग का जैविक आधार / Biological Basis of Emotion, उपनिषद और भगवद्गीता / Upanishads and Bhagavad Gita, केन्द्रीय और परिधीय तंत्रिका तंत्र / Central and Peripheral Nervous Systems
Paper - 1 | Unit - 2 | Research Aptitude: अनुसंधान: अर्थ, लक्षण व वैज्ञानिक विधि / Research: Meaning, Features and Scientific Method, अनुसंधान के प्रतिमान एवं उपागम / Research Paradigms and Approaches, अनुसंधान के प्रकार / Types of Research, चर एवं मापन / Variables and Measurement, अनुसंधान की विधियाँ / Methods of Research, अनुसंधान के चरण / Steps of Research, प्रतिचयन / Sampling, आँकड़ा संग्रह के उपकरण एवं विधियाँ / Tools and Methods of Data Collection, आँकड़ा विश्लेषण एवं शोध सांख्यिकी / Data Analysis and Statistics in Research, शोध-प्रबंध एवं लेख लेखन / Thesis and Article Writing, अनुसंधान में ICT का अनुप्रयोग / Application of ICT in Research, शोध नैतिकता / Research Ethics
Paper - 1 | Unit - 3 | Comprehension: प्रत्यक्ष बोध / Literal Comprehension, गद्यांश में शब्दावली और भाषा / Vocabulary and Language in Context, निष्कर्षात्मक बोध / Inferential Comprehension, आलोचनात्मक बोध / Critical Comprehension, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Restoration and Eighteenth-Century Drama, Modern British Fiction, William Shakespeare, Mid-Twentieth-Century and Contemporary British Fiction, American Drama
Paper - 1 | Unit - 4 | Communication: संचार: अर्थ, प्रकृति एवं प्रक्रिया / Communication: Meaning, Nature and Process, संचार के प्रकार एवं स्तर / Types and Levels of Communication, मौखिक एवं अमौखिक संचार / Verbal and Non-verbal Communication, संकेत विज्ञान एवं अर्थ / Semiotics and Meaning, संचार के मॉडल एवं सिद्धांत / Models and Theories of Communication, प्रभावी संचार / Effective Communication, संचार की बाधाएँ / Barriers to Communication, कक्षा संचार / Classroom Communication, जनसंचार माध्यम: प्रकार एवं विकास / Mass Media: Types and Evolution, जनसंचार एवं समाज / Mass Media and Society, डिजिटल एवं नव माध्यम / Digital and New Media, Static General Knowledge, Morphology and Syntax, जन स्वास्थ्य पोषण / Public Health Nutrition, Newtonian Motion and Stability, GK- Current Affairs, Indian Economy, Art and Architecture, India after Independence
Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: संख्या पद्धति एवं सरलीकरण / Number System and Simplification, बीजगणित एवं आयु / Algebra and Ages, प्रतिशतता / Percentage, अनुपात, समानुपात, साझेदारी एवं मिश्रण / Ratio, Proportion, Partnership and Mixtures, औसत / Averages, लाभ, हानि एवं बट्टा / Profit, Loss and Discount, साधारण एवं चक्रवृद्धि ब्याज / Simple and Compound Interest, समय एवं कार्य / Time and Work, चाल, समय एवं दूरी / Speed, Time and Distance, क्षेत्रमिति एवं ज्यामिति / Mensuration and Geometry, श्रेणी / Series, कूटलेखन-कूटवाचन / Coding-Decoding, संबंध, दिशा एवं क्रम / Relationships, Directions and Ranking, व्यवस्था, पहेलियाँ, घड़ी एवं कैलेंडर / Arrangements, Puzzles, Clock and Calendar, Mathematical Foundations, Polity, जीवनी, Deconstruction, Gender and Queer Theory, Modern British and Irish Poetry, Central Force and Scattering, Chemical thermodynamics, Microscopic techniques, संविधान का दर्शन / Philosophy of the Constitution, Waves, Optics and Charged-Particle Motion, Membrane structure and function, Analysis
Paper - 1 | Unit - 6 | Logical Reasoning: युक्ति की संरचना / Structure of Arguments, पद, परिभाषा एवं भाषा के उपयोग / Terms, Definitions and Uses of Language, निरुपाधिक प्रतिज्ञप्तियाँ / Categorical Propositions, निरुपाधिक न्यायवाक्य / Categorical Syllogism, वेन आरेख / Venn Diagrams, निगमन, आगमन एवं सादृश्यता / Deduction, Induction and Analogy, तर्कदोष / Fallacies, भारतीय तर्कशास्त्र: प्रमाण / Indian Logic: Pramanas, अनुमान एवं व्याप्ति / Anumana and Vyapti, हेत्वाभास / Hetvabhasa, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Aristotle, पाश्चात्य दर्शन की विचारधाराएँ / Western Schools of Philosophy, Kant, Sadhana Paada, Vaiśeṣika
Paper - 1 | Unit - 7 | Data Interpretation: आँकड़े एवं आलेखीय निरूपण / Data and Graphical Representation, आँकड़ा निर्वचन: तालिका / Data Interpretation: Tables
Paper - 1 | Unit - 8 | Information and Communication Technology: कंप्यूटर की मूल बातें और हार्डवेयर / Computer Fundamentals and Hardware, मेमोरी, भंडारण और डेटा निरूपण / Memory, Storage and Data Representation, कंप्यूटर सॉफ्टवेयर / Computer Software, ऑफिस अनुप्रयोग / Office Applications, मल्टीमीडिया और फ़ाइल प्रारूप / Multimedia and File Formats, कंप्यूटर नेटवर्क / Computer Networks, इंटरनेट और वर्ल्ड वाइड वेब / Internet and World Wide Web, ई-मेल और ऑनलाइन संचार / Email and Online Communication, साइबर सुरक्षा / Cyber Security, डिजिटल नैतिकता, बौद्धिक संपदा और समाज / Digital Ethics, IPR and Society, क्लाउड और वितरित कंप्यूटिंग / Cloud and Distributed Computing, उभरती प्रौद्योगिकियाँ / Emerging Technologies, शिक्षा और शासन में ICT / ICT in Education and Governance, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Electronic Data Interchange and E-Commerce, Internet Fundamentals, Web Design & Development, Web Publishing & Hosting, Emerging Technologies, Terms & Abbreviations, Society, Law & Ethics, Keyboard Shortcuts, Website, Browser & Services, भौगोलिक संकेतों का संरक्षण / Protection of Geographical Indications
Paper - 1 | Unit - 9 | People Development and Environment: पारितंत्र और जैव विविधता / Ecosystems and Biodiversity, मानव और पर्यावरण की अंतःक्रिया / Human and Environment Interaction, विकास और पर्यावरण / Development and Environment, प्राकृतिक संसाधन: वन, जल और मृदा / Natural Resources – Forests, Water and Soil, ऊर्जा संसाधन / Energy Resources, वायु प्रदूषण / Air Pollution, जल प्रदूषण और उपचार / Water Pollution and Treatment, ध्वनि प्रदूषण / Noise Pollution, अपशिष्ट प्रबंधन / Waste Management, पर्यावरणीय स्वास्थ्य और विषविज्ञान / Environmental Health and Toxicology, जलवायु परिवर्तन और वैश्विक पर्यावरणीय समस्याएँ / Climate Change and Global Environmental Issues, प्राकृतिक प्रकोप और आपदा प्रबंधन / Natural Hazards and Disaster Management, भारतीय पर्यावरण कानून और नीतियाँ / Indian Environmental Laws and Policies, अंतर्राष्ट्रीय पर्यावरण समझौते / International Environmental Agreements, Environment, Geography, कारखाना और उद्योग व्यवस्थाएँ / Factory and Industry Systems, Earth Materials, Surface Features and Processes, संक्रामक रोग और प्रतिरक्षण / Communicable Diseases and Immunization
Paper - 1 | Unit - 10 | Higher Education System: प्राचीन भारत में शिक्षा / Education in Ancient India, प्राचीन भारत के उच्च शिक्षा केंद्र / Ancient Centres of Higher Learning, औपनिवेशिक काल की शिक्षा नीतियाँ और आयोग / Colonial Education Policies and Commissions, औपनिवेशिक कॉलेज, विश्वविद्यालय व सुधारक / Colonial Colleges, Universities and Reformers, स्वतंत्र भारत में शिक्षा आयोग और नीतियाँ / Education Commissions and Policies after Independence, राष्ट्रीय शिक्षा नीति 2020 / National Education Policy 2020, उच्च शिक्षा संस्थानों के प्रकार / Types of Higher Education Institutions, अधिगम कार्यक्रम और अकादमिक क्रेडिट / Learning Programmes and Academic Credits, व्यावसायिक, तकनीकी और कौशल आधारित शिक्षा / Professional, Technical and Skill-Based Education, मूल्य शिक्षा और पर्यावरण शिक्षा / Value Education and Environmental Education, शासन, प्रशासन और वित्तपोषण / Governance, Administration and Financing, उच्च शिक्षा का नियमन, प्रत्यायन और रैंकिंग / Regulation, Accreditation and Ranking
Paper 2 | Unit 1 | Discrete Structures and Optimization: Propositional and Predicate Logic, Set Theory, Relations, Functions, क्रमचय, संचय एवं प्रायिकता / Permutation, Combination and Probability, Graph Theory, Group Theory, Digital Systems & Boolean Basics, Boolean Expression, Boolean Minimization, Optimization, Markov Chains
Paper 2 | Unit 2 | Computer System Architecture: Logic Gates & Hardware, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Basics of COA, Register Transfer and Microoperations, Programming the Basic Computer, Instr Formats & Modes, Control Unit Design, Pipelining, Input Output Organisation, Cache Memory Organization, Multiprocessors
Paper 2 | Unit 3 | Programming Languages and Computer Graphics: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, HTML Basics, XML, JavaScript-Basics, Java, Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, OOPS with C++, Java Fundamentals, Array, String, IO & References, OOPS with Java
Paper 2 | Unit 4 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
Paper 2 | Unit 5 | System Software and Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
Paper 2 | Unit 6 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
Paper 2 | Unit 7 | Data Structures and Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
Paper 2 | Unit 8 | Theory of Computation and Compilers: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
Paper 2 | Unit 9 | Data Communication and Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Mobile Technology, Cloud Computing and IoT, Cloud Computing
Paper 2 | Unit 10 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
Live Classes: NTA UGC NET 2025 Live Class
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AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This instructional segment focuses on graph theory applications involving the Handshaking Lemma to calculate vertex counts based on edge and degree information. The instructor presents a specific problem where the graph contains exactly twenty-four edges, and every vertex maintains a uniform degree of four throughout the structure. The core mathematical principle demonstrated relies on the fundamental formula stating that the sum of degrees equals twice the number of edges. This relationship allows students to derive unknown variables by balancing the total degree sum against the known edge count multiplied by two. The lesson emphasizes algebraic manipulation to isolate the vertex variable, ensuring accurate calculation of graph properties without visual enumeration. By applying this lemma, learners understand how local vertex connections aggregate to define global graph characteristics efficiently within discrete mathematics contexts and theoretical frameworks.

Chapters

0:00 – 1:16 00:00-01:16
This comprehensive instructional segment covers a practice question involving graph theory principles and detailed mathematical problem solving techniques. The primary focus is applying the Handshaking Lemma to determine vertex counts within a simple non-directed graph structure. The instructor carefully systematically breaks down the problem by identifying given values such as edge counts and uniform vertex degrees before setting up the necessary algebraic equation for solution. This process highlights standard techniques used in discrete mathematics education to solve network problems precisely and accurately.

The teaching progression moves from problem identification to formula application and finally algebraic resolution. Initially, the instructor defines the graph parameters explicitly, stating twenty-four edges exist with a uniform degree of four per vertex. This establishes the known variables required for calculation. Subsequently, the lesson transitions to theoretical justification by invoking the Handshaking Lemma, which links local vertex degrees to global edge counts. The instructor demonstrates how to equate the sum of all vertex degrees against twice the total edges, creating a solvable linear equation. This segment answers student doubts regarding how to calculate unknown vertex quantities when only edge counts and degree regularity are provided. It clarifies the relationship between graph topology and numerical constraints, ensuring learners can derive vertex counts without visual enumeration or complex traversal algorithms. The method reinforces algebraic skills within discrete structures, addressing confusion about when to apply degree sums versus edge counts directly in network analysis.