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

Duration: 15 min

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Inside: a video lesson and guided study material.

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, Sequence and Series (Series), 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 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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