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

Duration: 19 min

This video lesson is available to enrolled students.

Return to /learn/NTA-UGC-NET-PAPER---1/paper-1-unit-5-mathematical-reasoning-and-aptitude/number-system-bff2d7/unit-digit-last-digit-concepts/asset-short-tricks-to-find-unit-digit-of-an-expression-2 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Paper - 1 | Unit - 1 | Teaching Aptitude: शिक्षण की अवधारणा एवं उद्देश्य / Concept and Objectives of Teaching, शिक्षण के स्तर / Levels of Teaching, शिक्षार्थी की विशेषताएँ / Learner's Characteristics, अधिगम: प्रकृति एवं सिद्धांत / Learning: Nature and Theories, संज्ञान, स्मृति एवं अधिसंज्ञान / Cognition, Memory and Metacognition, शिक्षण को प्रभावित करने वाले कारक / Factors Affecting Teaching, प्रभावी शिक्षण एवं शिक्षक / Effective Teaching and the Teacher, अनुदेशनात्मक उद्देश्य एवं पाठ नियोजन / Instructional Objectives and Lesson Planning, शिक्षण विधियाँ / Methods of Teaching, ऑफ़लाइन एवं ऑनलाइन शिक्षण विधियाँ / Offline and Online Teaching Methods, शिक्षण सहायक प्रणाली / Teaching Support System, मूल्यांकन प्रणाली / Evaluation Systems, Nature, Objectives & Characteristics of Teaching, Learners & Learning Process, Teaching-Learning Aids & ICT Integration
  2. Paper - 1 | Unit - 2 | Research Aptitude: अनुसंधान: अर्थ, लक्षण व वैज्ञानिक विधि / Research: Meaning, Features and Scientific Method, अनुसंधान के प्रतिमान एवं उपागम / Research Paradigms and Approaches, अनुसंधान के प्रकार / Types of Research, चर एवं मापन / Variables and Measurement, अनुसंधान की विधियाँ / Methods of Research, अनुसंधान के चरण / Steps of Research, प्रतिचयन / Sampling, आँकड़ा संग्रह के उपकरण एवं विधियाँ / Tools and Methods of Data Collection, आँकड़ा विश्लेषण एवं शोध सांख्यिकी / Data Analysis and Statistics in Research, शोध-प्रबंध एवं लेख लेखन / Thesis and Article Writing, अनुसंधान में ICT का अनुप्रयोग / Application of ICT in Research, शोध नैतिकता / Research Ethics, Introduction to Research, Validity & Reliability, Research Paradigms & Types of Research, Research Ethics, Writing & Publication
  3. Paper - 1 | Unit - 3 | Comprehension: प्रत्यक्ष बोध / Literal Comprehension, गद्यांश में शब्दावली और भाषा / Vocabulary and Language in Context, निष्कर्षात्मक बोध / Inferential Comprehension, आलोचनात्मक बोध / Critical Comprehension, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions)
  4. Paper - 1 | Unit - 4 | Communication: संचार: अर्थ, प्रकृति एवं प्रक्रिया / Communication: Meaning, Nature and Process, संचार के प्रकार एवं स्तर / Types and Levels of Communication, मौखिक एवं अमौखिक संचार / Verbal and Non-verbal Communication, संकेत विज्ञान एवं अर्थ / Semiotics and Meaning, संचार के मॉडल एवं सिद्धांत / Models and Theories of Communication, प्रभावी संचार / Effective Communication, संचार की बाधाएँ / Barriers to Communication, कक्षा संचार / Classroom Communication, जनसंचार माध्यम: प्रकार एवं विकास / Mass Media: Types and Evolution, जनसंचार एवं समाज / Mass Media and Society, डिजिटल एवं नव माध्यम / Digital and New Media, Communication Basics, Language and Semiotics, Mass Communication, Mass Media, Journalism, General Knowledge and General Studies related to Communication
  5. Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: संख्या पद्धति एवं सरलीकरण / Number System and Simplification, बीजगणित एवं आयु / Algebra and Ages, प्रतिशतता / Percentage, अनुपात, समानुपात, साझेदारी एवं मिश्रण / Ratio, Proportion, Partnership and Mixtures, औसत / Averages, लाभ, हानि एवं बट्टा / Profit, Loss and Discount, साधारण एवं चक्रवृद्धि ब्याज / Simple and Compound Interest, समय एवं कार्य / Time and Work, चाल, समय एवं दूरी / Speed, Time and Distance, क्षेत्रमिति एवं ज्यामिति / Mensuration and Geometry, क्रमचय, संचय एवं प्रायिकता / Permutation, Combination and Probability, श्रेणी / Series, कूटलेखन-कूटवाचन / Coding-Decoding, संबंध, दिशा एवं क्रम / Relationships, Directions and Ranking, व्यवस्था, पहेलियाँ, घड़ी एवं कैलेंडर / Arrangements, Puzzles, Clock and Calendar, Series (Number and Letter Series) (Numerical Relations and Reasoning), Ratio and Proportion (Ratios), Powers and Exponents (Surds and Indices), Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Verbal Analogy (Word Based Analogy), Divisibility Rules, Miscellaneous, Probability
  6. Paper - 1 | Unit - 6 | Logical Reasoning: युक्ति की संरचना / Structure of Arguments, पद, परिभाषा एवं भाषा के उपयोग / Terms, Definitions and Uses of Language, निरुपाधिक प्रतिज्ञप्तियाँ / Categorical Propositions, निरुपाधिक न्यायवाक्य / Categorical Syllogism, वेन आरेख / Venn Diagrams, निगमन, आगमन एवं सादृश्यता / Deduction, Induction and Analogy, तर्कदोष / Fallacies, भारतीय तर्कशास्त्र: प्रमाण / Indian Logic: Pramanas, अनुमान एवं व्याप्ति / Anumana and Vyapti, हेत्वाभास / Hetvabhasa, 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, Western Logic
  7. Paper - 1 | Unit - 7 | Data Interpretation: आँकड़े एवं आलेखीय निरूपण / Data and Graphical Representation, आँकड़ा निर्वचन: तालिका / Data Interpretation: Tables
  8. Paper - 1 | Unit - 8 | Information and Communication Technology: कंप्यूटर की मूल बातें और हार्डवेयर / Computer Fundamentals and Hardware, मेमोरी, भंडारण और डेटा निरूपण / Memory, Storage and Data Representation, कंप्यूटर सॉफ्टवेयर / Computer Software, ऑफिस अनुप्रयोग / Office Applications, मल्टीमीडिया और फ़ाइल प्रारूप / Multimedia and File Formats, कंप्यूटर नेटवर्क / Computer Networks, इंटरनेट और वर्ल्ड वाइड वेब / Internet and World Wide Web, ई-मेल और ऑनलाइन संचार / Email and Online Communication, साइबर सुरक्षा / Cyber Security, डिजिटल नैतिकता, बौद्धिक संपदा और समाज / Digital Ethics, IPR and Society, क्लाउड और वितरित कंप्यूटिंग / Cloud and Distributed Computing, उभरती प्रौद्योगिकियाँ / Emerging Technologies, शिक्षा और शासन में ICT / 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, Artificial Intelligence, 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
  9. Paper - 1 | Unit - 9 | People Development and Environment: पारितंत्र और जैव विविधता / Ecosystems and Biodiversity, मानव और पर्यावरण की अंतःक्रिया / Human and Environment Interaction, विकास और पर्यावरण / Development and Environment, प्राकृतिक संसाधन: वन, जल और मृदा / Natural Resources – Forests, Water and Soil, ऊर्जा संसाधन / Energy Resources, वायु प्रदूषण / Air Pollution, जल प्रदूषण और उपचार / Water Pollution and Treatment, ध्वनि प्रदूषण / Noise Pollution, अपशिष्ट प्रबंधन / Waste Management, पर्यावरणीय स्वास्थ्य और विषविज्ञान / Environmental Health and Toxicology, जलवायु परिवर्तन और वैश्विक पर्यावरणीय समस्याएँ / Climate Change and Global Environmental Issues, प्राकृतिक प्रकोप और आपदा प्रबंधन / Natural Hazards and Disaster Management, भारतीय पर्यावरण कानून और नीतियाँ / Indian Environmental Laws and Policies, अंतर्राष्ट्रीय पर्यावरण समझौते / International Environmental Agreements, Ecosystem, Biomes & Environmental Issues, Noise Pollution and Waste Management, Natural Resources, Energy & Disaster Management
  10. Paper - 1 | Unit - 10 | Higher Education System: प्राचीन भारत में शिक्षा / Education in Ancient India, प्राचीन भारत के उच्च शिक्षा केंद्र / Ancient Centres of Higher Learning, औपनिवेशिक काल की शिक्षा नीतियाँ और आयोग / Colonial Education Policies and Commissions, औपनिवेशिक कॉलेज, विश्वविद्यालय व सुधारक / Colonial Colleges, Universities and Reformers, स्वतंत्र भारत में शिक्षा आयोग और नीतियाँ / Education Commissions and Policies after Independence, राष्ट्रीय शिक्षा नीति 2020 / National Education Policy 2020, उच्च शिक्षा संस्थानों के प्रकार / Types of Higher Education Institutions, अधिगम कार्यक्रम और अकादमिक क्रेडिट / Learning Programmes and Academic Credits, व्यावसायिक, तकनीकी और कौशल आधारित शिक्षा / Professional, Technical and Skill-Based Education, मूल्य शिक्षा और पर्यावरण शिक्षा / Value Education and Environmental Education, शासन, प्रशासन और वित्तपोषण / Governance, Administration and Financing, उच्च शिक्षा का नियमन, प्रत्यायन और रैंकिंग / Regulation, Accreditation and Ranking, Jainism & Buddhism, Pre-Independence Commissions, Post-Independence Policy, Higher Education Structure & Accreditation, Universities & Learning Programmes, Types of Education & NEP 2020
  11. Live Classes: NTA UGC NET 2025 Live Class
  12. Full Mock Tests:
  13. 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.

Loading lesson…