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

Duration: 19 min

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  1. About the course: About the Course
  2. Mathematical Aptitude / गणितीय अभिक्षमता: Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Divisibility Rules / विभाज्यता के नियम, Percentage / प्रतिशत, Ratio and Proportion / अनुपात और समानुपात, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time, Speed and Distance / समय, चाल और दूरी, Age Problems / आयु संबंधी प्रश्न, Mixture and Alligation / मिश्रण और एलिगेशन, Algebra / बीजगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Pipe and Cistern / नल और टंकी, Trigonometry / त्रिकोणमिति, Statistics / सांख्यिकी, Data Interpretation / आँकड़ा निर्वचन, Arithmetic / अंकगणित, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
  3. Logical Reasoning / तार्किक तर्कशक्ति: Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Order and Ranking / क्रम एवं रैंकिंग, Non-Verbal Reasoning / अशाब्दिक तर्क, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Syllogisms / न्यायवाक्य, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Alphabet and Number Test / वर्णमाला एवं संख्या परीक्षण, Statement-Based Reasoning / कथन आधारित तार्किक विवेचन, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी
  4. General Knowledge / सामान्य ज्ञान: Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Chemistry / रसायन विज्ञान, Biology / जीव विज्ञान, History / इतिहास, Geography / भूगोल, Polity / राजव्यवस्था, Indian Economy / भारतीय अर्थव्यवस्था, Current Affairs / समसामयिकी, Static General Knowledge / स्थैतिक सामान्य ज्ञान, State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान
  5. Art of Teaching / शिक्षण कला: Teaching-Learning Process and Classroom Management / शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन, Learners & Learning Process / अधिगमकर्ता और अधिगम प्रक्रिया, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Teaching Methods and Approaches / शिक्षण विधियाँ एवं उपागम, Microteaching and Classroom Communication / सूक्ष्म शिक्षण एवं कक्षा संप्रेषण, Teaching Aids and Educational Technology / शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी, Assessment and Evaluation / आकलन एवं मूल्यांकन, Teacher: Qualities, Professional Ethics and Development / शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास, Educational Policies, Acts and Administration / शैक्षिक नीतियाँ, अधिनियम एवं प्रशासन, Curriculum, Arts and Co-curricular Areas / पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र, Guidance and Counselling / निर्देशन एवं परामर्श, Education of Children with Disabilities / दिव्यांग बच्चों की शिक्षा, Micro-Teaching & Teaching Skills / सूक्ष्म शिक्षण और शिक्षण कौशल, Lesson Planning / पाठ योजना
  6. Environmental Science / पर्यावरण विज्ञान: Environment / पर्यावरण
  7. Unit 1 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  8. Unit 2 | COA: 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
  9. Unit 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  10. Unit 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  11. Unit 4 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  12. Unit 5 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  13. Unit 6 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Transaction Management, Concurrency Control
  14. Unit 7 | 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
  15. Unit 8 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  16. Unit 9 | Object Oriented Programming: OOPS with C++
  17. Unit 10 | Web Development: HTML Basics, CSS, JavaScript-Basics, XML, Node.js, Git & Github, PHP
  18. Unit 11 | Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines
  19. Unit 12 | IoT: Emerging Tech Trends, Cloud Computing, Computer Networks, Internet of Things
  20. Unit 13 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  21. Unit 14 | E-Commerce: Electronic Data Interchange and E-Commerce, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Physical Security and Cryptography Basics, Cyber Safety and Security
  22. Unit 15 | Multimedia: Multimedia
  23. Unit 16 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  24. Full Length Mock Tests — General Paper:
  25. Full Length Mock Tests — Computer Science (Paper II):
  26. Full Length Mock Test – General + Computer Science:
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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