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

Duration: 19 min

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Module outline

  1. Child Development and Pedagogy / बाल विकास एवं शिक्षाशास्त्र: Concept of Development / विकास की अवधारणा, Psychological Theories of Development / विकास के मनोवैज्ञानिक सिद्धांत, Individual Differences, Personality and Gender / व्यक्तिगत भिन्नताएँ, व्यक्तित्व एवं जेंडर, Intelligence and Creativity / बुद्धि एवं सृजनात्मकता, Learning and Its Theories / अधिगम एवं इसके सिद्धांत, How Children Think and Learn / बालक कैसे सोचते एवं सीखते हैं, Emotion, Motivation, Mental Health and Guidance / संवेग, अभिप्रेरणा, मानसिक स्वास्थ्य एवं निर्देशन, Inclusive Education / समावेशी शिक्षा, Teaching-Learning Process / शिक्षण-अधिगम प्रक्रिया, Teaching Methods and Strategies / शिक्षण विधियाँ एवं रणनीतियाँ, Assessment and Evaluation / आकलन एवं मूल्यांकन, Curriculum and School Activities / पाठ्यचर्या और विद्यालयी गतिविधियाँ, Lesson Planning and Teaching Skills / पाठ योजना और शिक्षण कौशल, Teaching Resources and Educational Technology / शिक्षण संसाधन और शैक्षिक प्रौद्योगिकी, Classroom Management and Communication / कक्षा प्रबंधन और सम्प्रेषण, Teacher Identity and Professional Development / शिक्षक पहचान और व्यावसायिक विकास, Educational Thinkers, Aims and National Policies / शैक्षिक विचारक, उद्देश्य एवं राष्ट्रीय नीतियाँ, School Leadership and Administration / विद्यालय नेतृत्व और प्रशासन, Life Skills, Values, Peace and Environmental Education / जीवन कौशल, मूल्य, शांति एवं पर्यावरण शिक्षा, Pedagogy of Environmental Studies / पर्यावरण अध्ययन का शिक्षणशास्त्र, Science Pedagogy / विज्ञान शिक्षण शास्त्र, Constitution, Commissions, Acts and Schemes in Education / संविधान, आयोग, अधिनियम एवं योजनाएँ, Computer Hardware and Peripherals / कंप्यूटर हार्डवेयर एवं परिधीय उपकरण
  2. Language I — हिंदी / Hindi: भाषा, लिपि और वर्ण-विचार, संधि, शब्द-स्रोत और शब्द-रचना, समास, शब्द-भेद: विकारी और अविकारी, लिंग, वचन, कारक, काल और वाच्य, वाक्य-विचार और शुद्ध लेखन, शब्द-भंडार, रस, छंद, अलंकार और शब्द-शक्ति, हिंदी साहित्य, अपठित बोध, हिंदी शिक्षणशास्त्र
  3. Language II — English: Sounds, Spelling and Word Formation, Parts of Speech, Nouns and Pronouns, Articles, Determiners and Adjectives, Verbs and Modals, Tenses and Subject–Verb Agreement, Adverbs, Prepositions and Conjunctions, Sentence Structure, Voice and Narration, Vocabulary, Sentence Correction and Writing Skills, Poetry and English Literature, Reading Comprehension, Pedagogy of English Language
  4. Language II — اردو / Urdu: رسم الخط، املا اور تلفظ, ذخیرۂ الفاظ, قواعد, محاورے اور ضرب الامثال, شعر و سخن, اردو ادب کی تاریخ, تفہیمِ عبارت, اردو کی تدریس
  5. Language II — संस्कृत / Sanskrit: वर्णविचारः एवं संज्ञाप्रकरणम्, सन्धिप्रकरणम्, शब्दरूपाणि, धातुरूपाणि, कारकाणि एवं विभक्तयः, उपसर्गाः एवं अव्ययानि, प्रत्ययप्रकरणम्, समासप्रकरणम्, वाच्यप्रकरणम्, संख्याज्ञानम्, शब्दज्ञानम् एवं अनुवादः, अपठितावबोधनम्, संस्कृतसाहित्यम् एवं काव्यशास्त्रम्, संस्कृतशिक्षणशास्त्रम्
  6. Mathematics / गणित: Number System & Place Value / संख्या पद्धति एवं स्थानीय मान, Basic Operations, Simplification & Patterns / मूलभूत संक्रियाएँ, सरलीकरण एवं पैटर्न, Factors, Divisibility, HCF & LCM / गुणनखंड, विभाज्यता, म.स.प. एवं ल.स.प., Fractions & Decimals / भिन्न एवं दशमलव, Squares, Cubes, Exponents & Surds / वर्ग, घन, घातांक एवं करणी, Measurement: Length, Mass, Capacity, Time & Money / मापन: लंबाई, भार, धारिता, समय एवं मुद्रा, Algebra / बीजगणित, Ratio, Proportion, Average & Ages / अनुपात, समानुपात, औसत एवं आयु, Percentage, Profit–Loss & Interest / प्रतिशत, लाभ-हानि एवं ब्याज, Time & Work and Speed–Distance / समय-कार्य एवं चाल-दूरी, Lines, Angles, Shapes & Coordinates / रेखाएँ, कोण, आकृतियाँ एवं निर्देशांक, Triangles, Quadrilaterals, Circles & Trigonometry / त्रिभुज, चतुर्भुज, वृत्त एवं त्रिकोणमिति, Mensuration: Perimeter, Area & Volume / क्षेत्रमिति: परिमाप, क्षेत्रफल एवं आयतन, Data Handling, Statistics & Probability / आँकड़ा प्रबंधन, सांख्यिकी एवं प्रायिकता, Mathematics Pedagogy / गणित शिक्षणशास्त्र
  7. Science / विज्ञान: Technology, Measurement and Motion / प्रौद्योगिकी, मापन एवं गति, Force, Pressure, Work and Energy / बल, दाब, कार्य एवं ऊर्जा, Heat and Sound / ऊष्मा एवं ध्वनि, Light / प्रकाश, Electricity and Magnetism / विद्युत एवं चुंबकत्व, Universe and Natural Phenomena / ब्रह्मांड एवं प्राकृतिक परिघटनाएँ, Matter and Its Structure / पदार्थ एवं उसकी संरचना, Chemical Reactions, Acids, Bases and Salts / रासायनिक अभिक्रियाएँ, अम्ल, क्षार एवं लवण, Metals, Non-metals and Materials of Daily Use / धातु, अधातु एवं दैनिक उपयोग की सामग्री, Living World: Classification, Cell and Tissues / सजीव जगत: वर्गीकरण, कोशिका एवं ऊतक, Plants: Nutrition, Transport and Reproduction / पादपों में पोषण, परिवहन एवं जनन, Human Body and Organ Systems / मानव शरीर एवं अंग तंत्र, Food, Nutrition and Health / भोजन, पोषण एवं स्वास्थ्य, Environment and Ecology / पर्यावरण एवं पारिस्थितिकी, Environment, Ecology and Wildlife / पर्यावरण, पारिस्थितिकी और वन्यजीव, Natural Resources, Pollution and Climate Change / प्राकृतिक संसाधन, प्रदूषण और जलवायु परिवर्तन
  8. Social Studies/Social Science / सामाजिक अध्ययन/सामाजिक विज्ञान: Ancient Indian History / प्राचीन भारत का इतिहास, Medieval Indian History / मध्यकालीन भारत का इतिहास, Colonial India and Social Reform / औपनिवेशिक भारत एवं समाज सुधार, Indian National Movement and Independent India / भारतीय राष्ट्रीय आंदोलन एवं स्वतंत्र भारत, World History and International Relations / विश्व इतिहास एवं अंतरराष्ट्रीय संबंध, Earth, Globe and Maps / पृथ्वी, ग्लोब एवं मानचित्र, Physical Geography / भौतिक भूगोल, Natural Vegetation, Wildlife and World Regions / प्राकृतिक वनस्पति, वन्य जीवन एवं विश्व के प्रदेश, Geography of India / भारत का भूगोल, Resources and Development / संसाधन एवं विकास, Social and Political Life / सामाजिक एवं राजनीतिक जीवन, Indian Constitution / भारतीय संविधान, Government: Union, State and Local / सरकार: केंद्र, राज्य एवं स्थानीय, Economics and Indian Economy / अर्थशास्त्र एवं भारतीय अर्थव्यवस्था, Social Science Pedagogy / सामाजिक विज्ञान शिक्षणशास्त्र, Earth, Sky and Disasters / पृथ्वी, आकाश और आपदाएँ, Uttar Pradesh GK / उत्तर प्रदेश सामान्य ज्ञान
  9. Extra Practice (beyond syllabus) / अतिरिक्त अभ्यास (पाठ्यक्रम से बाहर): Indian Economy: Data & Current Affairs / भारतीय अर्थव्यवस्था: आँकड़े एवं समसामयिकी, Indian Art & Culture / भारतीय कला एवं संस्कृति, Science & Technology / विज्ञान एवं प्रौद्योगिकी, Environment & Climate Affairs / पर्यावरण एवं जलवायु समसामयिकी, Defence & Security / रक्षा एवं सुरक्षा, Static General Knowledge / स्थिर सामान्य ज्ञान, Awards & Honours / पुरस्कार एवं सम्मान, Government Schemes, Governance & Infrastructure / सरकारी योजनाएँ, शासन एवं आधारभूत संरचना, Dice & Cubes / पासा एवं घन
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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