Practice Questions

Duration: 33 min

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Inside: a video lesson and guided study material.

Module outline

  1. Course Overview: About the Course
  2. 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 / सांख्य, Individual Behaviour / व्यक्तिगत व्यवहार, Human Resource Management / मानव संसाधन प्रबंधन, बाल्यावस्था में विकास के क्षेत्र / Domains of Child Development, Biological Basis of Emotion / संवेग का जैविक आधार, Upanishads and Bhagavad Gita / उपनिषद और भगवद्गीता, Central and Peripheral Nervous Systems / केन्द्रीय और परिधीय तंत्रिका तंत्र
  3. 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
  4. 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
  5. 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, Public Health Nutrition / जन स्वास्थ्य पोषण, Newtonian Motion and Stability, GK- Current Affairs, Indian Economy, Art and Architecture / कला और स्थापत्य, India after Independence
  6. 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, Philosophy of the Constitution / संविधान का दर्शन, Waves, Optics and Charged-Particle Motion, Membrane structure and function, Analysis
  7. 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 / अरस्तू, पाश्चात्य दर्शन की विचारधाराएँ / Western Schools of Philosophy, Kant / कांट, Sadhana Paada, Vaiśeṣika / वैशेषिक
  8. Paper - 1 | Unit - 7 | Data Interpretation: आँकड़े एवं आलेखीय निरूपण / Data and Graphical Representation, आँकड़ा निर्वचन: तालिका / Data Interpretation: Tables
  9. Paper - 1 | Unit - 8 | Information and Communication Technology: Computer Fundamentals and Hardware, Memory, Storage and Data Representation, Computer Software, Office Applications, Multimedia and File Formats, Computer Networks, Internet and World Wide Web, Email and Online Communication, Cyber Security, Digital Ethics, IPR and Society, Cloud and Distributed Computing, Emerging Technologies, 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
  10. 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, Factory and Industry Systems / कारखाना और उद्योग व्यवस्थाएँ, Earth Materials, Surface Features and Processes, Communicable Diseases and Immunization / संक्रामक रोग और प्रतिरक्षण
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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, Mobile Computing
  21. 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
  22. Live Classes: NTA UGC NET 2025 Live Class
  23. Paper 1 | Full Mock Tests:
  24. Paper 2 | Full Mock Tests:
  25. Paper 1 | Previous Year Papers:
  26. Paper 2 | Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive walkthrough of asymptotic analysis problems, focusing on comparing the growth rates of various functions using logarithmic transformations. The instructor systematically solves ten distinct problems, demonstrating how to apply Big-O, Omega, and Theta notations. Key techniques include taking logarithms of functions to simplify complex exponential and factorial expressions, utilizing properties like log(a^b) = b*log(a), and applying Stirling's approximation for factorial growth. The progression moves from basic comparisons of logarithmic and polynomial functions to more advanced analyses involving factorials, power towers, and iterated logarithms. Each problem is solved step-by-step on screen, with the instructor writing out derivations and final conclusions regarding asymptotic relationships.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with the instructor introducing a problem to compare two functions asymptotically: f(n) = log n and g(n) = √n. The instructor begins the solution process by writing down the logarithm of each function, specifically log(f(n)) and log(g(n)), indicating a strategy to simplify the comparison. On-screen text displays the problem statement 'Compare the following functions asymptotically' along with the function definitions. The instructor writes log(f(n)) under the first function and log(g(n)) under the second, starting to substitute f(n) into the logarithm expression. This initial setup establishes the core technique of using logarithmic transformation to make growth rates easier to analyze and compare.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues the asymptotic comparison by simplifying log(f(n)) to log(log n) and transforming g(n) = sqrt(n) into n^(1/2), then taking the log to get (1/2)log n. The on-screen text shows 'sqrt(n) = n^(1/2)' and the derived forms 'log(log n)' versus '(1/2) log n'. The instructor compares these two resulting expressions to determine which grows faster. By analyzing the simplified logarithmic forms, it becomes evident that (1/2)log n grows faster than log(log n). This section demonstrates the practical application of logarithmic identities and radical simplification in asymptotic notation analysis, setting up the final conclusion for this problem.

  3. 5:00 – 10:00 05:00-10:00

    The instructor concludes the asymptotic comparison of f(n) = log n and g(n) = sqrt(n), demonstrating that the logarithm of the square root function simplifies to a linear term in log n, which grows faster than log(log n). He writes the final conclusion that g(n) is asymptotically bigger than f(n), establishing Big-O and Omega relationships. The on-screen text explicitly states 'log(f(n)) < log(g(n))' and 'g(n) asymptotically bigger than f(n)', along with the formal notation 'f(n) = O(g(n))'. The video then transitions to a new problem comparing exponential functions f(n) = 2^n and g(n) = 2^(2n), marking a shift from polynomial-logarithmic comparisons to exponential growth analysis.

  4. 10:00 – 15:00 10:00-15:00

    The instructor is comparing two functions, f(n) = 2^n and g(n) = 2^(2n), to determine their asymptotic relationship. By taking the logarithm of both functions, he simplifies them to n log 2 and 2n log 2 respectively. The on-screen text shows 'log(f(n)) = n log 2' and 'log(g(n)) = 2n log 2'. He then equates the logarithmic forms to show that both simplify to a linear relationship with n, indicating they belong to the same complexity class. The instructor demonstrates that despite the different exponents, the logarithmic transformation reveals a proportional relationship between n and 2n, which is crucial for understanding exponential growth rates in algorithm analysis.

  5. 15:00 – 20:00 15:00-20:00

    The instructor is solving a problem comparing the asymptotic complexity of two functions, f(n) = 2^n and g(n) = 2^(2n). He applies logarithms to both functions to simplify the comparison, showing that log(f(n)) simplifies to n and log(g(n)) also simplifies to n, leading to the conclusion that f(n) = O(g(n)). The on-screen text displays 'log(f(n)) = log(g(n))' and 'n = n', confirming the relationship. The video then transitions to a new example comparing f(n) = 2^n and g(n) = 2^(n+1). This segment reinforces the technique of using logarithms to simplify exponential comparisons and identifies constant versus exponential terms, verifying Big-O notation through simplification.

  6. 20:00 – 25:00 20:00-25:00

    The instructor transitions from analyzing exponential functions to comparing polynomial and logarithmic growth rates. He introduces a new problem set involving f(n) = n^2 and g(n) = n log n to determine their asymptotic relationship. The instructor begins applying logarithmic properties, specifically the product rule log(xy) = log x + log y, to simplify the expressions for analysis. On-screen text shows 'log(xy) = log x + log y' and the expansion of 'log(n^2)' to '2log n'. This section demonstrates how to break down composite functions for Big O analysis, using logarithmic identities to simplify complexity and compare growth rates of different function types.

  7. 25:00 – 30:00 25:00-30:00

    The instructor is solving asymptotic notation problems by taking logarithms of both functions to compare their growth rates. In the first problem, he compares n^100 and 2^n by applying log rules to simplify them into 100logn and n. In the second problem, he analyzes f(n) = n! against g(n) = 2^n, deriving the logarithmic form of factorial. A third problem is shown where he compares n^2 and n log n, utilizing the logarithmic identity log(xy) = log x + log y. The on-screen text lists problems 4, 5, and 3 with their respective functions. This segment applies logarithm rules to simplify complex factorial expressions and uses Stirling's approximation for asymptotic analysis, breaking down products inside logarithms into sums.

  8. 30:00 – 32:45 30:00-32:45

    The instructor is analyzing the asymptotic relationship between two functions: f(n) = log(n!) and g(n) = n log n. The process involves simplifying f(n) using logarithmic properties to show it is equivalent to log(n^n), which further simplifies to n log n. The on-screen text shows 'f(n) = Θ(g(n))' and the derivation steps including 'log(x^y)' and 'n log n'. The instructor concludes that f(n) and g(n) are asymptotically equivalent, denoted as f(n) = Θ(g(n)). This final segment demonstrates the use of log(ab) = log a + log b property and approximating n! with n^n for asymptotic analysis, completing the series of practice problems.

The video systematically teaches asymptotic analysis through a sequence of ten practice problems, each building upon fundamental logarithmic properties and transformation techniques. The instructor consistently applies the strategy of taking logarithms to simplify complex functions, making growth rates comparable. Key mathematical tools include log(a^b) = b*log(a), log(xy) = log x + log y, and Stirling's approximation for factorial growth. The progression moves from simple polynomial-logarithmic comparisons to more complex exponential and factorial analyses, demonstrating how logarithmic transformations can reveal underlying relationships between functions. Students learn to identify dominant terms, apply Big-O and Theta notations correctly, and understand the relative growth rates of common algorithmic complexities. The visual presentation of derivations on screen reinforces the step-by-step logical process required for rigorous asymptotic analysis.

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