Important Practice Questions on Divisibility Rules

Duration: 15 min

This video lesson is available to enrolled students.

Return to /learn/UPTET-PAPER-2/mathematics-science/divisibility-rules/mathematics-problems-on-divisibility/asset-important-practice-questions-on-divisibility-rules after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Child Development and Pedagogy: Concept of Pedagogy, Psychology, Child Development, Theories, Personality Development, Individual Differences, Learning and Motivation, Understanding Diverse Learners, Inclusive Education, Mental Health & Life Skills, Teaching-Learning Process, Teaching Methods & Strategies, Experiential Pedagogy, Assessment & Evaluation, National Education Policy (NEP) 2020, Curriculum Framework & Reforms, Miscellaneous Topics, Nature, Objectives & Characteristics of Teaching, Learners & Learning Process, Factors Affecting Teaching, Classroom Management & Communication, Teaching-Learning Aids & ICT Integration, Curriculum & School Environment, Lesson Planning, Evaluation, Assessment & Measurement, Inclusive Education & Special Needs, Guidance, Counselling & Mental Health, Policies, Acts & Contemporary Issues
  2. Language I — 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 Pedagogy (Language I and II): Language Pedagogy (Hindi/English/Sanskrit/Urdu learning & teaching)
  4. Language II — English: Parts of Speech, Nouns and Pronouns, Pronoun, Determiner, Articles, Determiners and Adjectives, Adjectives, Verbs and Modals, Adverb, Adverbs, Prepositions and Conjunctions, Conjunction, Sentence Structure, Phrases & Clauses, Tenses and Subject–Verb Agreement, Subject Verb Agreement (Verb Noun Agreement), Modals, Sentence Structure, Voice and Narration, Direct and Indirect Speech, Vocabulary, Verbal Analogy (Word Based Analogy), Sentence Construction, Sentence Correction and Writing Skills, Sentence Completion (Fill in the blanks), Reading Comprehension, Cloze Test (Cloze Passage), Sounds, Spelling and Word Formation, Pedagogy of English Language, Poetry and English Literature
  5. Language II — Urdu: املا اور اعراب, ذخیرۂ الفاظ, قواعد, محاورے اور ضرب الامثال, اصنافِ شاعری, مصنفین، نثر اور ادبی تصانیف, تفہیم, رسم الخط اور آوازیں, جملہ سازی, بلاغت, اصنافِ نثر, اردو زبان اور ادبی تاریخ, تحریری اظہار, اردو کی تدریس
  6. Language II — Sanskrit: वर्ण, उच्चारण, सन्धि, शब्दरूप, धातुरूप, कारक-विभक्ति, समासप्रकरणम्, प्रत्यय, उपसर्गाः एवं अव्ययानि, वाच्य, सङ्ख्या, अव्यय, अपठित अवबोधन, संस्कृत साहित्य-कवि-ग्रन्थ, वर्णविचारः एवं संज्ञाप्रकरणम्, सन्धिप्रकरणम्, शब्दरूपाणि, धातुरूपाणि, कारकाणि एवं विभक्तयः, संख्याज्ञानम्, शब्दज्ञानम् एवं अनुवादः, प्रत्ययप्रकरणम्, वाच्यप्रकरणम्, संस्कृतसाहित्यम् एवं काव्यशास्त्रम्, अपठितावबोधनम्, संस्कृतशिक्षणशास्त्रम्
  7. Mathematics: Number System & Place Value, Whole Numbers & Four Operations, Factors, Multiples, Divisibility, HCF & LCM, Fractions & Decimals, Integers & Rational Numbers, Exponents, Powers, Squares, Cubes & Roots, Patterns, Algebra — Expressions, Identities & Linear Equations, Ratio, Proportion & Percentage, Measurement — Length, Mass, Capacity, Time, Money, Commercial Arithmetic (Profit-Loss-Discount, SI & CI), Average, Ages & Mixtures, Time & Work, Speed-Time-Distance, Geometry — Shapes, Lines & Angles, Symmetry, Spatial Understanding, Geometry — Triangles, Quadrilaterals, Circles, Congruence & Constructions, Mensuration — Perimeter, Area, Surface Area, Volume, Data Handling, Graphs & Probability, Coordinates & Graphs, Mathematics Pedagogy, संख्या पद्धति एवं अंकगणितीय आधार / Number System & Arithmetic Foundations, गुणनखंड, विभाज्यता एवं HCF–LCM / Factors, Divisibility & HCF–LCM, अनुपात, समानुपात एवं प्रतिशत / Ratio, Proportion & Percentage, व्यावसायिक अंकगणित / Commercial Arithmetic, औसत, आयु एवं मिश्रण / Averages, Ages & Mixtures, समय, कार्य एवं गति / Time, Work & Motion, बीजगणित एवं समीकरण / Algebra & Equations, ज्यामिति एवं स्थानिक बोध / Geometry & Spatial Understanding, मापन एवं क्षेत्रमिति / Measurement & Mensuration, डेटा प्रबंधन, सांख्यिकी एवं प्रायिकता / Data Handling, Statistics & Probability, निर्देशांक, त्रिकोणमिति एवं उच्चतर गणित / Coordinates, Trigonometry & Higher Mathematics, गणित शिक्षाशास्त्र / Mathematics Pedagogy
  8. Science: Food, Nutrition & Components of Food, Plants — Nutrition, Transport, Reproduction, Animals & Human Body — Systems, Organs, Nutrition, Health, Diseases, Microorganisms & Hygiene, Cell, Tissues & Classification of Living Beings, Reproduction & Adolescence, Materials, Matter, Mixtures & Separation, Elements, Compounds, Acids-Bases-Salts, Metals & Non-metals, Physical & Chemical Changes, Combustion, Fuels, Motion, Force, Pressure & Friction, Heat & Temperature, Light, Shadows, Mirrors & Lenses, Sound, Electricity & Magnetism, Earth, Universe & Solar System, Natural Resources, Environment, Ecosystem & Pollution, Science & Technology in Daily Life (inventions, space, defence), Science Pedagogy, वैज्ञानिक आधार, मापन और प्रौद्योगिकी / Scientific Foundations, Measurement & Technology, भोजन, पोषण एवं स्वास्थ्य / Food, Nutrition and Health, पदार्थ और दैनिक उपयोग की सामग्री / Matter & Materials of Daily Use, रासायनिक अभिक्रियाएँ, अम्ल, क्षार एवं लवण / Chemical Reactions, Acids, Bases and Salts, बल, दाब, कार्य एवं ऊर्जा / Force, Pressure, Work and Energy, प्रकाश / Light, विद्युत एवं चुंबकत्व / Electricity and Magnetism, सजीव जगत: वर्गीकरण, कोशिका एवं ऊतक / Living World: Classification, Cell and Tissues, पादपों में पोषण, परिवहन एवं जनन / Plants: Nutrition, Transport and Reproduction, मानव शरीर एवं अंग तंत्र / Human Body and Organ Systems, पर्यावरण एवं पारिस्थितिकी / Environment and Ecology, विज्ञान शिक्षण और शिक्षाशास्त्र / Science Pedagogy
  9. Social Studies/Social Science: History — Sources, Prehistory & Harappan Civilisation, History — Vedic Age, Mahajanapadas, Religions (Buddhism/Jainism), History — Mauryas, Guptas & Post-Gupta Kingdoms, History — Medieval India (Sultanate, Mughals, Regional Kingdoms, Bhakti-Sufi), History — Modern India & Colonial Rule, History — Indian National Movement (1857–1947), History — India Since Independence, Geography — Earth, Globe, Maps, Latitudes-Longitudes, Geography — Landforms, Atmosphere, Hydrosphere, Climate, Natural Vegetation & Biomes, Geography — Physical & Political India (rivers, mountains, soils, vegetation, climate), Geography — Resources, Agriculture, Industries, Transport, Geography — World (continents, countries, oceans), Geography — Population, Settlements & Census, Polity — Democracy, Diversity, Social Justice & Gender, Polity — Constitution, Preamble, Fundamental Rights & Duties, DPSP, Polity — Union & State Government, Parliament, Judiciary, Elections, Polity — Local Government (Panchayati Raj, Urban bodies), Polity — International Relations & Organisations, Economy — Basic Concepts, Money, Banking, Budget, Schemes, Social Studies Pedagogy, Uttar Pradesh, उत्तर प्रदेश / Uttar Pradesh
  10. Mathematics & Science (Video Lessons & Notes): Number System, Divisibility Rules, HCF LCM, Powers and Exponents (Surds and Indices), Algebra, Sequence and Series (Series), Ratio and Proportion (Ratios), Percentage, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Partnership, Statistics, Data Interpretation, Probability, Biology, Chemistry, Physics
  11. Social Studies (Video Lessons & Notes): Geography, History, Polity, Environment, Static General Knowledge, State Wise GK
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.

Loading lesson…