Short Tricks to Find Unit Digit of an Expression (1)

Duration: 15 min

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  1. Course Overview: About the Course
  2. Paper - 1 | Unit - 1 | Teaching Aptitude: Nature, Objectives & Characteristics of Teaching, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Teaching-Learning Aids & ICT Integration, Evaluation, Assessment & Measurement
  3. Paper - 1 | Unit - 2 | Research Aptitude: Introduction to Research, Validity & Reliability, Research Paradigms & Types of Research, Research Process Steps, Research Ethics, Writing & Publication
  4. Paper - 1 | Unit - 3 | Comprehension: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions)
  5. Paper - 1 | Unit - 4 | Communication: Communication Basics, Language and Semiotics, Types of Communication, Communication Models, Mass Communication, Mass Media, Journalism, General Knowledge and General Studies related to Communication
  6. Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Number System, Percentage, Ratio and Proportion (Ratios), Simple Interest and Compound Interest, Speed Time and Distance, Powers and Exponents (Surds and Indices), Profit and Loss, Average, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Verbal Analogy (Word Based Analogy), Divisibility Rules, Calendar, Miscellaneous, Time and Work, Algebra
  7. Paper - 1 | Unit - 6 | Logical Reasoning: Syllogisms, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Venn Diagram, School Of Thoughts, Fallacy, Western Logic
  8. Paper - 1 | Unit - 7 | Data Interpretation: Data Interpretation
  9. Paper - 1 | Unit - 8 | Information and Communication Technology: MS Office Applications, 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, Artificial Intelligence, Society, Law & Ethics, Keyboard Shortcuts, Website, Browser & Services
  10. Paper - 1 | Unit - 9 | People Development and Environment: Ecosystem, Biomes & Environmental Issues, MDG & SDG, Air Pollution, Water Pollution, Soil, Noise Pollution and Waste Management, Natural Resources, Energy & Disaster Management, Global Environmental Conventions – COP, Protocols & ISA
  11. Paper - 1 | Unit - 10 | Higher Education System: Vedic Education, Jainism & Buddhism, Ancient Universities, Pre-Independence Commissions, Post-Independence Policy, Higher Education Structure & Accreditation, Universities & Learning Programmes, Types of Education & NEP 2020
  12. Paper 2 | Unit 1 | Discrete Structures and Optimization: Propositional and Predicate Logic, Set Theory, Relations, Functions, Permutation and Combination, Probability, Graph Theory, Group Theory, Digital Systems & Boolean Basics, Boolean Expression, Boolean Minimization, Optimization
  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
  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
  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 is a comprehensive lecture on the concept of 'Unit Digit' in number systems, presented by an instructor from Knowledge Gate Eduventures. The video begins with an introduction to the topic, emphasizing its importance for various competitive exams such as CAT, XAT, GMAT, and government tests, where it is a crucial part of the aptitude section. The core of the lecture focuses on a method to find the unit digit of large numbers raised to high powers. The instructor explains that this is achieved by identifying the cyclicity of the unit digit of the base number. The method involves observing the pattern of unit digits as the base is raised to successive powers. The video provides a classification of single-digit numbers (0-9) into three categories based on their cyclicity: numbers with a fixed unit digit (0, 1, 5, 6), numbers with a two-number cycle (4, 9), and numbers with a four-number cycle (2, 3, 7, 8). The instructor demonstrates this concept with several examples, including 185^563, 271^6987, and 156^25369, showing how to determine the unit digit by finding the remainder when the exponent is divided by the cycle length. The video concludes with a summary of the method and a list of practice problems for the viewer.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for 'NUMBER SYSTEM' and a subtitle 'The mysterious world of numbers...'. The instructor, Yash Jain, introduces the topic, stating that it is a fundamental concept for various competitive exams. A slide titled 'Why Study This Topic?' lists numerous exams including CAT, XAT, CMAT, NMAT, SNAP, MAT, IIFT, GMAT, GATE, and others, emphasizing that number system is a crucial part of the aptitude section, with at least two questions appearing in every exam. The instructor is visible in a small window in the bottom right corner, speaking to the camera.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to explain the importance of the topic, with a list of exams on the screen. He emphasizes that the number system is a key area for aptitude tests. The slide lists exams such as Placements, Government Exams, Civil Services Exams, Banking Exams, Railway Exams, College Entrance Exams, and others. The instructor's voiceover explains that this topic is essential for students preparing for these competitive exams. The visual focus remains on the list of exams, with the instructor's video feed in the corner.

  3. 5:00 – 10:00 05:00-10:00

    The video transitions to a new slide titled 'Concept of Unit Digit'. The instructor explains that to find the unit digit of a number raised to a power, one must understand the concept of cyclicity. He states that the unit digit of a number repeats in a pattern when the number is raised to successive powers. The slide shows an example: 'Unit Digit of 3547^153 x 251^72'. The instructor then moves to a new slide with a question: 'Q: Find the unit digit of the following:', followed by a list of 11 problems, including 185^563, 271^6987, and 154^258741369. The instructor begins to solve the first problem, 185^563, by focusing on the unit digit of the base, which is 5.

  4. 10:00 – 14:35 10:00-14:35

    The instructor explains the rule for numbers ending in 0, 1, 5, or 6: their unit digit remains the same regardless of the power. He demonstrates this with 185^563, stating the unit digit is 5. He then moves to 271^6987, noting the unit digit of the base is 1, so the answer is 1. For 156^25369, the unit digit is 6. The instructor then explains the cyclicity of 4 and 9, which have a cycle of 2. He demonstrates with 154^258741369, where the unit digit of the base is 4, and the exponent is odd, so the unit digit is 4. He then explains the cycle of 2, 3, 7, and 8, which have a cycle of 4. He demonstrates with 190^654789321, where the unit digit of the base is 0, so the answer is 0. The video ends with a 'Thank You for Watching' screen.

The video provides a structured and practical guide to solving unit digit problems, a common type of question in competitive exams. It begins by establishing the relevance of the topic, then systematically introduces the core concept of cyclicity. The instructor uses a clear, step-by-step approach, first explaining the rules for numbers with fixed unit digits (0, 1, 5, 6), then for those with a two-number cycle (4, 9), and finally for those with a four-number cycle (2, 3, 7, 8). The method is demonstrated through a series of worked examples, showing how to determine the cycle length and use the remainder of the exponent divided by the cycle length to find the correct unit digit. This logical progression from theory to application makes the concept accessible and provides a reliable method for students to solve similar problems under time pressure.

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