Series with combination

Duration: 12 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. About the course: About the Course
  2. Mathematical Aptitude / गणितीय अभिक्षमता: Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Divisibility Rules / विभाज्यता के नियम, Percentage / प्रतिशत, Ratio and Proportion / अनुपात और समानुपात, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time, Speed and Distance / समय, चाल और दूरी, Age Problems / आयु संबंधी प्रश्न, Mixture and Alligation / मिश्रण और एलिगेशन, Algebra / बीजगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Pipe and Cistern / नल और टंकी, Trigonometry / त्रिकोणमिति, Statistics / सांख्यिकी, Data Interpretation / आँकड़ा निर्वचन, Arithmetic / अंकगणित, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
  3. Logical Reasoning / तार्किक तर्कशक्ति: Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Order and Ranking / क्रम एवं रैंकिंग, Non-Verbal Reasoning / अशाब्दिक तर्क, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Syllogisms / न्यायवाक्य, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Alphabet and Number Test / वर्णमाला एवं संख्या परीक्षण, Statement-Based Reasoning / कथन आधारित तार्किक विवेचन, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी
  4. General Knowledge / सामान्य ज्ञान: Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Chemistry / रसायन विज्ञान, Biology / जीव विज्ञान, History / इतिहास, Geography / भूगोल, Polity / राजव्यवस्था, Indian Economy / भारतीय अर्थव्यवस्था, Current Affairs / समसामयिकी, Static General Knowledge / स्थैतिक सामान्य ज्ञान, State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान
  5. Art of Teaching / शिक्षण कला: Teaching-Learning Process and Classroom Management / शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन, Learners & Learning Process / अधिगमकर्ता और अधिगम प्रक्रिया, Factors Affecting Teaching / शिक्षण को प्रभावित करने वाले कारक, Teaching Methods and Approaches / शिक्षण विधियाँ एवं उपागम, Microteaching and Classroom Communication / सूक्ष्म शिक्षण एवं कक्षा संप्रेषण, Teaching Aids and Educational Technology / शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी, Assessment and Evaluation / आकलन एवं मूल्यांकन, Teacher: Qualities, Professional Ethics and Development / शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास, Educational Policies, Acts and Administration / शैक्षिक नीतियाँ, अधिनियम एवं प्रशासन, Curriculum, Arts and Co-curricular Areas / पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र, Guidance and Counselling / निर्देशन एवं परामर्श, Education of Children with Disabilities / दिव्यांग बच्चों की शिक्षा, Micro-Teaching & Teaching Skills / सूक्ष्म शिक्षण और शिक्षण कौशल, Lesson Planning / पाठ योजना
  6. Environmental Science / पर्यावरण विज्ञान: Environment / पर्यावरण
  7. Unit 1 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  8. Unit 2 | COA: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer
  9. Unit 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  10. Unit 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  11. Unit 4 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  12. Unit 5 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  13. Unit 6 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Transaction Management, Concurrency Control
  14. Unit 7 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer
  15. Unit 8 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  16. Unit 9 | Object Oriented Programming: OOPS with C++
  17. Unit 10 | Web Development: HTML Basics, CSS, JavaScript-Basics, XML, Node.js, Git & Github, PHP
  18. Unit 11 | Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines
  19. Unit 12 | IoT: Emerging Tech Trends, Cloud Computing, Computer Networks, Internet of Things
  20. Unit 13 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  21. Unit 14 | E-Commerce: Electronic Data Interchange and E-Commerce, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Physical Security and Cryptography Basics, Cyber Safety and Security
  22. Unit 15 | Multimedia: Multimedia
  23. Unit 16 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  24. Full Length Mock Tests — General Paper:
  25. Full Length Mock Tests — Computer Science (Paper II):
  26. Full Length Mock Test – General + Computer Science:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The lecture introduces number and letter series, focusing on a difference-based trick for solving sequences. It presents three example series: 2, 5, 10, 17, 26, 37; 2, 6, 12, 20, 30, 42; and 0, 2, 6, 12, 20, 30. The instructor calculates first differences (e.g., +3, +5, +7 for the first series) and second differences to identify patterns. A key rule '±1 ±n' is highlighted, relating terms to index positions and base powers. The lesson then transitions to combination patterns like n²+1, n³-1, and cube-square combinations. A worked example shows 2, 5, 10, 17, 26, 37 as n²+1 (base squares 1,4,9,16,25,36 plus constant 1), yielding next term 7²+1=50. Another example works out 2, 9, 28, 65, 126 using cube gaps (1,8,27,64) with next value 125. The video concludes with a 'Series with Combination' slide listing ten patterns from Square+1 to Cube-Square, ending with 'THANKS FOR WATCHING'.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card 'NUMBER SERIES - LETTER SERIES' displaying the alphabet and digits, then transitions to a slide titled 'An Important Trick'. Three number series are presented: 2, 5, 10, 17, 26, 37; 2, 6, 12, 20, 30, 42; and 0, 2, 6, 12, 20, 30. A red check mark appears under the leading '2' of the middle series, followed by red difference values 4, 6, 8, 10, 12, 14 written beneath it with connecting check marks. The value '56' is handwritten in red into the middle series blank, and partial differences 2, 4, 6, 8 appear under the bottom series.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the difference method across all three series. For the first series, differences 3, 5, 7, 9, 11, 13 are written; for the second, 4, 6, 8, 10, 12; for the third, 2, 4, 6, 8, 10. A boxed rule '±1 ±n' is highlighted to guide pattern recognition. Index numbers 1, 2, 3, 4, 5, 6 are written below the first series, and a formula involving '±n' is applied to relate terms to their positions. Second-order differences of 2, 2, 2, 2 are calculated for both the first and third series, confirming constant second differences.

  3. 5:00 – 10:00 05:00-10:00

    The lesson shifts to combination patterns. Formulas such as n²+1, n³-1, and cube+square are listed. The series 2, 5, 10, 17, 26, 37 is broken into base squares (1, 4, 9, 16, 25, 36) with a constant +1 added to each, yielding the next term as 7²+1=50. The slide 'Series with Combination' lists ten patterns from 'Square + 1' to 'Cube - Square' alongside formulas like n²+1, n³-n, and n³-n². Red handwriting works out the series 2, 9, 28, 65, 126 with gaps 1, 8, 27, 64 and a next value 125.

  4. 10:00 – 12:09 10:00-12:09

    The final segment revisits the 'An Important Trick' slide, showing 2, 5, 10, 17, 26, 37 annotated in red with square-based differences and the form 'n² + (n)'. A drawing tool palette is visible on the left. The 'Series with Combination' slide reappears, listing ten patterns and formulas. A second row 0, 4, 18, 48, 106 is worked out alongside the cube-gap example. The video concludes with 'THANKS FOR WATCHING' on screen.

The lecture teaches a systematic approach to number series using first and second differences, then extends to combination patterns involving squares and cubes. The core method: compute consecutive differences; if first differences form an arithmetic progression (odd or even numbers), the second difference is constant. The '±1 ±n' rule connects terms to index positions, enabling formula-based solutions like n²+1. Worked examples demonstrate both the difference method (yielding 56 for the middle series) and the combination approach (yielding 50 for n²+1 and 125 for cube-gap series). The ten-pattern reference list provides a quick lookup for common combination types.

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