Important Practice Questions on Divisibility Rules

Duration: 15 min

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Module outline

  1. Child Development and Pedagogy: विकास की अवधारणा / Concept of Development, विकास के मनोवैज्ञानिक सिद्धांत / Psychological Theories of Development, व्यक्तिगत भिन्नताएँ, व्यक्तित्व एवं जेंडर / Individual Differences, Personality and Gender, बुद्धि एवं सृजनात्मकता / Intelligence and Creativity, अधिगम एवं इसके सिद्धांत / Learning and Its Theories, बालक कैसे सोचते एवं सीखते हैं / How Children Think and Learn, संवेग, अभिप्रेरणा, मानसिक स्वास्थ्य एवं निर्देशन / Emotion, Motivation, Mental Health and Guidance, समावेशी शिक्षा / Inclusive Education, शिक्षण-अधिगम प्रक्रिया / Teaching-Learning Process, शिक्षण विधियाँ एवं रणनीतियाँ / Teaching Methods and Strategies, आकलन एवं मूल्यांकन / Assessment and Evaluation, पाठ्यचर्या और विद्यालयी गतिविधियाँ / Curriculum and School Activities, पाठ योजना और शिक्षण कौशल / Lesson Planning and Teaching Skills, शिक्षण संसाधन और शैक्षिक प्रौद्योगिकी / Teaching Resources and Educational Technology, शैक्षिक विचारक, उद्देश्य एवं राष्ट्रीय नीतियाँ / Educational Thinkers, Aims and National Policies, कक्षा प्रबंधन और सम्प्रेषण / Classroom Management and Communication, शिक्षक पहचान और व्यावसायिक विकास / Teacher Identity and Professional Development, सामाजिक विज्ञान शिक्षणशास्त्र / Social Science Pedagogy, सामाजिक एवं राजनीतिक जीवन / Social and Political Life, विज्ञान शिक्षण शास्त्र / Science Pedagogy, जीवन कौशल, मूल्य, शांति एवं पर्यावरण शिक्षा / Life Skills, Values, Peace and Environmental Education, संविधान, आयोग, अधिनियम एवं योजनाएँ / Constitution, Commissions, Acts and Schemes in Education
  2. Mathematics: संख्या पद्धति एवं स्थानीय मान / Number System & Place Value, मूलभूत संक्रियाएँ, सरलीकरण एवं पैटर्न / Basic Operations, Simplification & Patterns, गुणनखंड, विभाज्यता, म.स.प. एवं ल.स.प. / Factors, Divisibility, HCF & LCM, भिन्न एवं दशमलव / Fractions & Decimals, वर्ग, घन, घातांक एवं करणी / Squares, Cubes, Exponents & Surds, मापन: लंबाई, भार, धारिता, समय एवं मुद्रा / Measurement: Length, Mass, Capacity, Time & Money, बीजगणित / Algebra, अनुपात, समानुपात, औसत एवं आयु / Ratio, Proportion, Average & Ages, प्रतिशत, लाभ-हानि एवं ब्याज / Percentage, Profit–Loss & Interest, समय-कार्य एवं चाल-दूरी / Time & Work and Speed–Distance, रेखाएँ, कोण, आकृतियाँ एवं निर्देशांक / Lines, Angles, Shapes & Coordinates, त्रिभुज, चतुर्भुज, वृत्त एवं त्रिकोणमिति / Triangles, Quadrilaterals, Circles & Trigonometry, क्षेत्रमिति: परिमाप, क्षेत्रफल एवं आयतन / Mensuration: Perimeter, Area & Volume, आँकड़ा प्रबंधन, सांख्यिकी एवं प्रायिकता / Data Handling, Statistics & Probability, गणित शिक्षणशास्त्र / Mathematics Pedagogy, वर्णमाला एवं संख्या परीक्षण / Alphabet & Number Test, अशाब्दिक तर्क / Non-Verbal Reasoning, पासा एवं घन / Dice & Cubes, गणितीय संक्रियाएँ एवं अंकगणितीय तर्क / Mathematical Operations & Arithmetical Reasoning, क्रम, बैठक व्यवस्था एवं पहेली / Ranking, Seating Arrangement & Puzzles, कैलेंडर एवं घड़ी / Calendar & Clock, वेन आरेख एवं तार्किक निगमन / Venn Diagrams & Logical Deduction
  3. Environmental Studies: परिवार, मित्र और समुदाय / Family, Friends and Community, पौधे / Plants, जंतु / Animals, खेती और पशुपालन / Farming and Animal Husbandry, भोजन और पोषण / Food and Nutrition, शरीर और स्वास्थ्य / Body and Health, जल / Water, आवास / Shelter, यात्रा, परिवहन और संचार / Travel, Transport and Communication, मानचित्र, दिशाएँ और भारत / Maps, Directions and India, हम क्या बनाते और करते हैं / Things We Make and Do, पृथ्वी, आकाश और आपदाएँ / Earth, Sky and Disasters, पर्यावरण, पारिस्थितिकी और वन्यजीव / Environment, Ecology and Wildlife, प्राकृतिक संसाधन, प्रदूषण और जलवायु परिवर्तन / Natural Resources, Pollution and Climate Change, पर्यावरण अध्ययन का शिक्षणशास्त्र / Pedagogy of Environmental Studies, भौतिक भूगोल / Physical Geography, संसाधन एवं विकास / Resources and Development, बल, दाब, कार्य एवं ऊर्जा / Force, Pressure, Work and Energy, पर्यावरण एवं पारिस्थितिकी / Environment and Ecology, विज्ञान एवं प्रौद्योगिकी / Science & Technology, ऊष्मा एवं ध्वनि / Heat and Sound, प्रकाश / Light, ब्रह्मांड एवं प्राकृतिक परिघटनाएँ / Universe and Natural Phenomena, रासायनिक अभिक्रियाएँ, अम्ल, क्षार एवं लवण / Chemical Reactions, Acids, Bases and Salts, प्राकृतिक वनस्पति, वन्य जीवन एवं विश्व के प्रदेश / Natural Vegetation, Wildlife and World Regions, पर्यावरण एवं जलवायु समसामयिकी / Environment & Climate Affairs
  4. Language I/II — 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
  5. Language I/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
  6. Language I/II — 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
  7. Language I/II — 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
  8. Language I/II — Bengali: ভাষা, ধ্বনি ও বর্ণ, সন্ধি ও বানান, শব্দের উৎস ও গঠন, সমাস, পদ পরিচয়, কারক ও বিভক্তি, ক্রিয়া ও কাল, বাক্যতত্ত্ব, শব্দার্থ ও বাগর্থ, পাঠ অনুধাবন ও সাহিত্য, নির্মিতি ও পত্রলিখন, বাংলা শিক্ষণবিদ্যা
  9. अतिरिक्त अभ्यास / Extra Practice (beyond syllabus): कंप्यूटर हार्डवेयर एवं परिधीय उपकरण / Computer Hardware and Peripherals, अंतरराष्ट्रीय संबंध एवं संगठन / International Relations & Organisations, भारतीय अर्थव्यवस्था: आँकड़े एवं समसामयिकी / Indian Economy: Data & Current Affairs
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a lecture on divisibility rules, presented by an instructor named Yash Jain Sir from Knowledge Gate Eduventures. The video begins with an introduction to the topic, using a colorful circular diagram that outlines the divisibility rules for numbers 2 through 10. The main content consists of a series of practice problems. The first problem asks to find the value of K in the number K35624 so that it is divisible by 11. The instructor applies the rule for 11, which involves the alternating sum of digits, and solves the resulting equation to find K=6. The second problem involves the number 42573K being divisible by 72. The instructor factors 72 into 8 and 9, then applies the divisibility rules for 8 (last three digits) and 9 (sum of digits) to determine that K=6. The final problem asks for the value of K in 97215K6 to make it divisible by 11, again using the alternating sum rule to find K=3. The video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide displaying 'DIVISIBILITY RULES' over a background of scattered numbers. This transitions to a colorful, hand-drawn circular diagram titled 'DIVISIBILITY RULES' which visually explains the rules for divisibility by 2, 3, 4, 5, 6, 8, 9, and 10. The instructor, Yash Jain Sir, is visible in a small window, introducing the topic. The next slide, with a space theme, is titled 'Questions on Divisibility' and sets the stage for the problem-solving session.

  2. 2:00 – 5:00 02:00-05:00

    The first problem is presented: 'Find the value of K if K35624 is divisible by 11?'. The instructor begins the solution by writing the number K35624 and applying the divisibility rule for 11, which states that the difference between the sum of the digits in odd positions and the sum of the digits in even positions must be a multiple of 11. He writes the equation: (K + 5 + 2) - (3 + 6 + 4) = 0 or 11. This simplifies to (K + 7) - 13 = 0 or 11, leading to K - 6 = 0 or 11. He concludes that K=6 is the only valid single-digit solution.

  3. 5:00 – 10:00 05:00-10:00

    The second problem is introduced: 'If 42573K is divisible by 72, then the value of K is:'. The instructor explains that 72 = 8 x 9, so the number must be divisible by both 8 and 9. For divisibility by 8, the last three digits, 73K, must be divisible by 8. He tests values and finds that 736 is divisible by 8, so K=6. For divisibility by 9, the sum of the digits (4+2+5+7+3+K) must be divisible by 9. The sum is 21+K, and for K=6, this is 27, which is divisible by 9. He confirms K=6 satisfies both conditions.

  4. 10:00 – 15:00 10:00-15:00

    The third problem is presented: 'Find the value of K if 97215K6 is divisible by 11?'. The instructor applies the alternating sum rule for 11. He writes the equation: (9 + 2 + 5 + 6) - (7 + 1 + K) = 0 or 11. This simplifies to 22 - (8 + K) = 0 or 11. He then solves the equation 22 - 8 - K = 0, which gives 14 - K = 0, so K=14. Since K must be a single digit, he considers the other possibility: 22 - 8 - K = 11, which gives 14 - K = 11, so K=3. He concludes K=3 is the correct answer.

  5. 15:00 – 15:05 15:00-15:05

    The video concludes with a final screen that displays the text 'THANKS FOR WATCHING' in white letters against a dark, gradient background. This is the end of the lecture.

The video provides a structured and practical lesson on divisibility rules. It begins with a conceptual overview using a visual aid, then progresses to a series of progressively challenging problems. The core teaching method is the application of specific rules: the alternating sum for 11, the last three digits for 8, and the sum of digits for 9. The instructor demonstrates a systematic approach to solving each problem, showing the step-by-step derivation of equations and the logical elimination of invalid solutions, particularly when dealing with the constraint that K must be a single digit. The progression from a single rule (11) to a composite rule (72) and back to a single rule (11) effectively reinforces the concepts and problem-solving strategies.

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