Short Tricks to Find Unit Digit of an Expression (2)

Duration: 19 min

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Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, Logarithm, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, अनुक्रम, श्रेणी और संयोजन / Sequences, Series and Combinatorics, समय, चाल और दूरी / Time, Speed and Distance, प्रतिशत / Percentage, औसत / Average, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, Statistics, Probability, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समय और कार्य / Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Paper-1 & 2 | Data Interpretation: आँकड़ा निर्वचन / Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Data Arrangement, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making
  7. Paper-1 | General Science: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, समसामयिकी / Current Affairs
  9. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits
  10. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Calculus, Relational Algebra, SQL, NoSQL
  11. Paper-2 | Data Structures & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Algorithm Analysis, Sorting Algorithms, Intro to Compilers, Hashing
  12. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, Data Link Layer - Ethernet, DLL: Error Control, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Application Layer, Hardware basics, Network Security, Ethical Hacking
  13. Paper-2 | Operating Systems: Introduction to OS, Process Management, Memory Management, File Management, Deadlock
  14. Paper-2 | Computer Organization and Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer, Number System, Number Representation
  15. Paper 2 | System Analysis and Design: Fundamentals of Systems and Information Systems, Fundamentals of Software Engineering, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance, Software Testing
  16. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Paper 2 | OOPS , C++ , JAVA: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  18. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  19. Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection
  20. Paper-2 | Data Processing (Ms-Office): MS Office Applications, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), प्रेज़ेंटेशन (MS PowerPoint) / Presentation Software (MS PowerPoint)
  21. Paper-2 | Internet and Web Technologies: HTML Basics, CSS, XML, JavaScript-Basics, Internet Fundamentals, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, Terms & Abbreviations, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर नेटवर्क / Computer Networks
  22. Paper 2 | Pedagogy: वृद्धि और विकास / Growth and Development, विकास के सिद्धांत / Theories of Development, Concept of Pedagogy, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, आकलन और मूल्यांकन / Assessment and Evaluation, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  23. Live Classes: RSSB Live Sessions
  24. Paper 1 - Full Mock Tests:
  25. Paper 2 - Full Mock Tests:
  26. BCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive tutorial on finding the unit digit of large exponential numbers, a common problem in competitive exams. The instructor begins by introducing the concept of unit digit cyclicity, explaining that the unit digit of a number raised to a power follows a repeating pattern. The lesson systematically breaks down the behavior of digits 0 through 9. It first establishes that digits 0, 1, 5, and 6 have a cyclicity of 1, meaning their unit digit remains unchanged regardless of the power. Next, it covers digits 4 and 9, which have a cyclicity of 2, with their unit digits alternating between two values based on whether the exponent is odd or even. The core of the lesson focuses on digits 2, 3, 7, and 8, which all have a cyclicity of 4, meaning their unit digits cycle through four different values. The instructor demonstrates this by calculating the first few powers of each digit (e.g., 2^1=2, 2^2=4, 2^3=8, 2^4=16) to identify the repeating cycle. The video concludes by presenting a summary table that consolidates the cyclicity and power cycles for all digits 0-9, providing a quick reference for students. The entire explanation is supported by on-screen text, handwritten calculations, and a clear, step-by-step teaching approach.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide for a lesson on the 'NUMBER SYSTEM' by Yash Jain of Knowledge Gate Eduventures. The instructor introduces the topic, which is to find the unit digit of large exponential numbers. The first concept presented is that digits 0, 1, 5, and 6 have a cyclicity of 1, meaning their unit digit remains the same when raised to any power. For example, the text on screen states: '0^n = 0, 1^n = 1, 5^n = 5, 6^n = 6.' This establishes the foundation for the lesson.

  2. 2:00 – 5:00 02:00-05:00

    The instructor explains the cyclicity of digits 4 and 9, which have a cycle of 2. The on-screen text states: 'Digits 4 & 9: Both these numbers have a cyclicity of only two different digits as their unit digit.' The instructor demonstrates this by calculating the powers of 4: 4^1 = 4 (unit digit 4), 4^2 = 16 (unit digit 6), 4^3 = 64 (unit digit 4), and 4^4 = 256 (unit digit 6). This shows a repeating pattern of 4 and 6. The same logic is applied to 9, where 9^1 = 9, 9^2 = 81, 9^3 = 729, etc., showing a cycle of 9 and 1. The key takeaway is that for these digits, the unit digit depends on whether the exponent is odd or even.

  3. 5:00 – 10:00 05:00-10:00

    The lesson progresses to the most complex case: digits 2, 3, 7, and 8, which have a cyclicity of 4. The on-screen text states: 'Digits 2, 3, 7 & 8: These numbers have a power cycle of 4 different numbers.' The instructor demonstrates this by showing the power cycles. For digit 2: 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, and then the cycle repeats (2, 4, 8, 6). For digit 3: 3^1 = 3, 3^2 = 9, 3^3 = 27, 3^4 = 81, and then the cycle repeats (3, 9, 7, 1). The same pattern is shown for 7 and 8. The method to solve a problem is to find the remainder when the exponent is divided by 4, which determines the position in the 4-step cycle.

  4. 10:00 – 15:00 10:00-15:00

    The instructor applies the learned concepts to solve a specific problem: finding the unit digit of 287^562581. The on-screen text shows the problem statement. The solution involves identifying the unit digit of the base, which is 7. The instructor then refers to the previously established rule that the unit digit of 7 follows a cycle of 4: 7, 9, 3, 1. To find the unit digit of 7^562581, the exponent 562581 is divided by 4. The remainder is 1 (since 562581 = 4*140645 + 1). This means the unit digit corresponds to the first number in the cycle, which is 7. The instructor also shows a list of other problems for practice, such as 185^563 and 271^6987, to reinforce the method.

  5. 15:00 – 18:33 15:00-18:33

    The video concludes with a summary table that consolidates all the concepts. The table, titled 'Cyclicity Table', lists the digits 0-9, their cyclicity (1, 2, or 4), and their power cycle. For example, it shows that digit 2 has a cyclicity of 4 and a power cycle of 2, 4, 8, 6. The instructor reviews the table, circling the key values. The final frame is a 'Thank You for Watching' message, indicating the end of the lesson.

The video presents a structured and logical progression for solving unit digit problems. It begins with the simplest cases (digits with cyclicity 1) and builds complexity by introducing digits with cyclicity 2 and then the most common case (cyclicity 4). The core method is to identify the unit digit of the base, determine its cyclicity, and then use the remainder of the exponent divided by the cyclicity to find the corresponding digit in the cycle. This systematic approach, reinforced by a summary table, provides students with a reliable and efficient strategy for tackling these types of questions in exams.

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