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

Duration: 19 min

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Module outline

  1. Paper - 1 | Unit - 1 | Teaching Aptitude: Concept and Objectives of Teaching / शिक्षण की अवधारणा एवं उद्देश्य, Levels of Teaching / शिक्षण के स्तर, Learner's Characteristics / शिक्षार्थी की विशेषताएँ, Learning: Nature and Theories / अधिगम: प्रकृति एवं सिद्धांत, Cognition, Memory and Metacognition / संज्ञान, स्मृति एवं अधिसंज्ञान, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Effective Teaching and the Teacher / प्रभावी शिक्षण एवं शिक्षक, Instructional Objectives and Lesson Planning / अनुदेशनात्मक उद्देश्य एवं पाठ नियोजन, Methods of Teaching / शिक्षण विधियाँ, Offline and Online Teaching Methods / ऑफ़लाइन एवं ऑनलाइन शिक्षण विधियाँ, Teaching Support System / शिक्षण सहायक प्रणाली, Evaluation Systems / मूल्यांकन प्रणाली, Sāṃkhya / सांख्य, Individual Behaviour / व्यक्तिगत व्यवहार, Human Resource Management / मानव संसाधन प्रबंधन, Domains of Child Development / बाल्यावस्था में विकास के क्षेत्र, 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
  2. Paper - 1 | Unit - 2 | Research Aptitude: Research: Meaning, Features and Scientific Method / अनुसंधान: अर्थ, लक्षण व वैज्ञानिक विधि, Research Paradigms and Approaches / अनुसंधान के प्रतिमान एवं उपागम, Types of Research / अनुसंधान के प्रकार, Variables and Measurement / चर एवं मापन, Methods of Research / अनुसंधान की विधियाँ, Steps of Research / अनुसंधान के चरण, Sampling / प्रतिचयन, Tools and Methods of Data Collection / आँकड़ा संग्रह के उपकरण एवं विधियाँ, Data Analysis and Statistics in Research / आँकड़ा विश्लेषण एवं शोध सांख्यिकी, Thesis and Article Writing / शोध-प्रबंध एवं लेख लेखन, Application of ICT in Research / अनुसंधान में ICT का अनुप्रयोग, Research Ethics / शोध नैतिकता
  3. Paper - 1 | Unit - 3 | Comprehension: Literal Comprehension, Vocabulary and Language in Context, Inferential Comprehension, 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
  4. Paper - 1 | Unit - 4 | Communication: Communication: Meaning, Nature and Process / संचार: अर्थ, प्रकृति एवं प्रक्रिया, Types and Levels of Communication / संचार के प्रकार एवं स्तर, Verbal and Non-verbal Communication / मौखिक एवं अमौखिक संचार, Semiotics and Meaning / संकेत विज्ञान एवं अर्थ, Models and Theories of Communication / संचार के मॉडल एवं सिद्धांत, Effective Communication / प्रभावी संचार, Barriers to Communication / संचार की बाधाएँ, Classroom Communication / कक्षा संचार, Mass Media: Types and Evolution / जनसंचार माध्यम: प्रकार एवं विकास, Mass Media and Society / जनसंचार एवं समाज, Digital and New Media / डिजिटल एवं नव माध्यम, Static General Knowledge / स्थैतिक सामान्य ज्ञान, Morphology and Syntax, Public Health Nutrition / जन स्वास्थ्य पोषण, Newtonian Motion and Stability, GK- Current Affairs / GK- समसामयिकी, Indian Economy / भारतीय अर्थव्यवस्था, Art and Architecture / कला और स्थापत्य, India after Independence / स्वतंत्रता के बाद भारत
  5. Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: Number System and Simplification / संख्या पद्धति एवं सरलीकरण, Algebra and Ages / बीजगणित एवं आयु, Percentage / प्रतिशतता, Ratio, Proportion, Partnership and Mixtures / अनुपात, समानुपात, साझेदारी एवं मिश्रण, Averages / औसत, Profit, Loss and Discount / लाभ, हानि एवं बट्टा, Simple and Compound Interest / साधारण एवं चक्रवृद्धि ब्याज, Time and Work / समय एवं कार्य, Speed, Time and Distance / चाल, समय एवं दूरी, Mensuration and Geometry / क्षेत्रमिति एवं ज्यामिति, Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता, Series / श्रेणी, Coding-Decoding / कूटलेखन-कूटवाचन, Relationships, Directions and Ranking / संबंध, दिशा एवं क्रम, Arrangements, Puzzles, Clock and Calendar / व्यवस्था, पहेलियाँ, घड़ी एवं कैलेंडर, Mathematical Foundations, Polity / राजव्यवस्था, 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, Markov Chains, Univariate and Joint Distributions
  6. Paper - 1 | Unit - 6 | Logical Reasoning: Structure of Arguments / युक्ति की संरचना, Terms, Definitions and Uses of Language / पद, परिभाषा एवं भाषा के उपयोग, Categorical Propositions / निरुपाधिक प्रतिज्ञप्तियाँ, Categorical Syllogism / निरुपाधिक न्यायवाक्य, Venn Diagrams / वेन आरेख, Deduction, Induction and Analogy / निगमन, आगमन एवं सादृश्यता, Fallacies / तर्कदोष, Indian Logic: Pramanas / भारतीय तर्कशास्त्र: प्रमाण, Anumana and Vyapti / अनुमान एवं व्याप्ति, Hetvabhasa / हेत्वाभास, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Aristotle / अरस्तू, Western Schools of Philosophy / पाश्चात्य दर्शन की विचारधाराएँ, Kant / कांट, Sadhana Paada, Vaiśeṣika / वैशेषिक
  7. Paper - 1 | Unit - 7 | Data Interpretation: Data and Graphical Representation / आँकड़े एवं आलेखीय निरूपण, Data Interpretation: Tables / आँकड़ा निर्वचन: तालिका
  8. 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, Basics of COA, Introduction to OS, Introduction to CN, Data Communication, Net Layer: IP Addressing, Network Security, Number System, Number Representation, Society, Law & Ethics, Keyboard Shortcuts, Website, Browser & Services, Protection of Geographical Indications / भौगोलिक संकेतों का संरक्षण
  9. Paper - 1 | Unit - 9 | People Development and Environment: Ecosystems and Biodiversity / पारितंत्र और जैव विविधता, Human and Environment Interaction / मानव और पर्यावरण की अंतःक्रिया, Development and Environment / विकास और पर्यावरण, Natural Resources – Forests, Water and Soil / प्राकृतिक संसाधन: वन, जल और मृदा, Energy Resources / ऊर्जा संसाधन, Air Pollution / वायु प्रदूषण, Water Pollution and Treatment / जल प्रदूषण और उपचार, Noise Pollution / ध्वनि प्रदूषण, Waste Management / अपशिष्ट प्रबंधन, Environmental Health and Toxicology / पर्यावरणीय स्वास्थ्य और विषविज्ञान, Climate Change and Global Environmental Issues / जलवायु परिवर्तन और वैश्विक पर्यावरणीय समस्याएँ, Natural Hazards and Disaster Management / प्राकृतिक प्रकोप और आपदा प्रबंधन, Indian Environmental Laws and Policies / भारतीय पर्यावरण कानून और नीतियाँ, International Environmental Agreements / अंतर्राष्ट्रीय पर्यावरण समझौते, Environment / पर्यावरण, Geography / भूगोल, Factory and Industry Systems / कारखाना और उद्योग व्यवस्थाएँ, Earth Materials, Surface Features and Processes, Communicable Diseases and Immunization / संक्रामक रोग और प्रतिरक्षण
  10. Paper - 1 | Unit - 10 | Higher Education System: Education in Ancient India / प्राचीन भारत में शिक्षा, Ancient Centres of Higher Learning / प्राचीन भारत के उच्च शिक्षा केंद्र, Colonial Education Policies and Commissions / औपनिवेशिक काल की शिक्षा नीतियाँ और आयोग, Colonial Colleges, Universities and Reformers / औपनिवेशिक कॉलेज, विश्वविद्यालय व सुधारक, Education Commissions and Policies after Independence / स्वतंत्र भारत में शिक्षा आयोग और नीतियाँ, National Education Policy 2020 / राष्ट्रीय शिक्षा नीति 2020, Types of Higher Education Institutions / उच्च शिक्षा संस्थानों के प्रकार, Learning Programmes and Academic Credits / अधिगम कार्यक्रम और अकादमिक क्रेडिट, Professional, Technical and Skill-Based Education / व्यावसायिक, तकनीकी और कौशल आधारित शिक्षा, Value Education and Environmental Education / मूल्य शिक्षा और पर्यावरण शिक्षा, Governance, Administration and Financing / शासन, प्रशासन और वित्तपोषण, Regulation, Accreditation and Ranking / उच्च शिक्षा का नियमन, प्रत्यायन और रैंकिंग
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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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