Some Important Observations and Short Tricks

Duration: 22 min

This video lesson is available to enrolled students.

Return to /learn/NTA-UGC-NET-PAPER-2/paper-1-unit-5-mathematical-reasoning-and-aptitude/series-number-and-letter-series-numerical-relations-and-reasoning/number-series/asset-some-important-observations-and-short-tricks after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Course Overview: About the Course
  2. Paper - 1 | Unit - 1 | Teaching Aptitude: Nature, Objectives & Characteristics of Teaching, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Teaching-Learning Aids & ICT Integration, Evaluation, Assessment & Measurement
  3. Paper - 1 | Unit - 2 | Research Aptitude: Introduction to Research, Validity & Reliability, Research Paradigms & Types of Research, Research Process Steps, Research Ethics, Writing & Publication
  4. Paper - 1 | Unit - 3 | Comprehension: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions)
  5. Paper - 1 | Unit - 4 | Communication: Communication Basics, Language and Semiotics, Types of Communication, Communication Models, Mass Communication, Mass Media, Journalism, General Knowledge and General Studies related to Communication
  6. Paper - 1 | Unit - 5 | Mathematical Reasoning and Aptitude: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Number System, Percentage, Ratio and Proportion (Ratios), Simple Interest and Compound Interest, Speed Time and Distance, Powers and Exponents (Surds and Indices), Profit and Loss, Average, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Verbal Analogy (Word Based Analogy), Divisibility Rules, Calendar, Miscellaneous, Time and Work, Algebra
  7. Paper - 1 | Unit - 6 | Logical Reasoning: 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, Fallacy, Western Logic
  8. Paper - 1 | Unit - 7 | Data Interpretation: Data Interpretation
  9. Paper - 1 | Unit - 8 | Information and Communication Technology: MS Office Applications, 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, Society, Law & Ethics, Keyboard Shortcuts, Website, Browser & Services
  10. Paper - 1 | Unit - 9 | People Development and Environment: Ecosystem, Biomes & Environmental Issues, MDG & SDG, Air Pollution, Water Pollution, Soil, Noise Pollution and Waste Management, Natural Resources, Energy & Disaster Management, Global Environmental Conventions – COP, Protocols & ISA
  11. Paper - 1 | Unit - 10 | Higher Education System: Vedic Education, Jainism & Buddhism, Ancient Universities, Pre-Independence Commissions, Post-Independence Policy, Higher Education Structure & Accreditation, Universities & Learning Programmes, Types of Education & NEP 2020
  12. Paper 2 | Unit 1 | Discrete Structures and Optimization: Propositional and Predicate Logic, Set Theory, Relations, Functions, Permutation and Combination, Probability, Graph Theory, Group Theory, Digital Systems & Boolean Basics, Boolean Expression, Boolean Minimization, Optimization
  13. Paper 2 | Unit 2 | Computer System Architecture: Logic Gates & Hardware, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Basics of COA, Register Transfer and Microoperations, Programming the Basic Computer, Instr Formats & Modes, Control Unit Design, Pipelining, Input Output Organisation, Cache Memory Organization, Multiprocessors
  14. Paper 2 | Unit 3 | Programming Languages and Computer Graphics: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, HTML Basics, XML, JavaScript-Basics, Java, Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, OOPS with C++, Java Fundamentals
  15. Paper 2 | Unit 4 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  16. Paper 2 | Unit 5 | System Software and Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  17. Paper 2 | Unit 6 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  18. Paper 2 | Unit 7 | Data Structures and Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  19. Paper 2 | Unit 8 | Theory of Computation and Compilers: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  20. Paper 2 | Unit 9 | Data Communication and 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, Hardware basics, Network Security, Mobile Technology, Cloud Computing and IoT, Cloud Computing
  21. Paper 2 | Unit 10 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  22. Live Classes: NTA UGC NET 2025 Live Class
  23. Paper 1 | Full Mock Tests:
  24. Paper 2 | Full Mock Tests:
  25. Paper 1 | Previous Year Papers:
  26. Paper 2 | Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture teaches foundational shortcuts for solving number and letter series, emphasizing pattern recognition over brute-force calculation. The instructor introduces three core operation types—addition, multiplication, and mixed (A+m)—and applies them to sequences like 5, 15, 45, 135, 405 (×3 pattern) and large powers of two. Reference tables for squares (1–50), cubes (1–20), and primes (1–200) are used to quickly identify missing terms in sequences such as 961, 1024, 1089, __, 1225 (answer 1156 = 34²) and 6, 15, 35, __, 143 (consecutive prime products). A difference-based method using the formula (a × p) + m is demonstrated on 2, 6, 14, 30 (answer 62). The final section covers miscellaneous series with alternating patterns and Fibonacci-like sums, concluding with a pair-based rule yielding 4 + 1 = 5.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lesson opens with a title slide 'NUMBER SERIES - LETTER SERIES' showing the alphabet and numbers, followed by a 'Back To Basics' card with wooden letter blocks. The instructor presents the first puzzle: 5, 15, 45, 135, 405, ____, and a second: 524288, 65536, 8192, 1024, 128, 16, ____. On-screen text also shows 'Find the Next Number in this series: 5, 7, 12, 19, 31, 50, ?' as a teaser. The teaching cue is to return to foundational pattern recognition before solving.

  2. 2:00 – 5:00 02:00-05:00

    The instructor writes 'addition', 'multiplication', and 'mix (A+m)' as candidate patterns for 5, 15, 45, 135, 405. Arrows above the sequence show differences +10, +30, +90, and a calculation '(5x2)+5' illustrates the mixed method. The instructor then crosses out 'add x', writes 'inc ↑↑', and labels arrows between terms with 'x3'. A vertical calculation 405 × 3 = 1215 confirms the answer. For the second sequence, 'Sub. X' is crossed out while 'div.' and 'div + sub.' are checked; 128/16 = 2³ is written, and the exponent rule a^m/a^n = a^(m-n) explains the power-of-two division pattern.

  3. 5:00 – 10:00 05:00-10:00

    A slide titled 'Some Important Points' displays a table 'Squares 1 to 50' (1²=1 through 50²=2500). The row '961 1024 1089 __ 1225' is solved by filling the blank in red as '1156', with arrows labeling 31², 32², 33², 34², 35² and red circles marking the matching entries. A second slide 'Cubes 1 to 20' (1³=1 through 20³=8000) shows '729 1000 1331 1728 2197' annotated with arrows for 9³ through 13³ and a circle around 1728. The final frame in this window shows the halving sequence '360 180 90 __ 22.5' with a red arrow and handwritten cue 'dec', indicating division by 2.

  4. 10:00 – 15:00 10:00-15:00

    The instructor demonstrates a difference-based shortcut on 2, 6, 14, 30, __. Differences below the sequence are 4, 8, 16. The general formula '(a x p) + m' is written with p=2 and m=2. Verification: (14 × 2) + 2 = 30 confirms the pattern; the next difference is (30 × 2) + 2 = 62, which is added to the last term. The window then transitions to a prime-number table (1–200) and the sequence '6 15 35 __ 143'. The instructor writes '2x3=6' and '3x5=15', circles the first four primes (2, 3, 5, 7), and highlights 31, 37, 41, 43, 47 in the table to show consecutive prime products.

  5. 15:00 – 20:00 15:00-20:00

    Continuing the prime-product sequence, the instructor applies 5×7=35 and 11×13=143 to confirm the pattern, so the missing term is 7×11=77. The lecture then shifts to 'Miscellaneous Series'. The first example '1 10 2 9 3 8 4 7' is analyzed as an alternating pattern with the on-screen cue 'even', pairing terms that sum to 11. A second example '2 4 6 10 16 26 42' is shown as Fibonacci-like, with on-screen text '2+4=6, 4+6=10, 6+10=16, 10+16=26' confirming each term is the sum of the two preceding terms.

  6. 20:00 – 21:51 20:00-21:51

    The final example is the pair-based series '96 15 71 8 37 10 41'. The instructor applies a rule to adjacent pairs, and the on-screen calculation '4+1=5' gives the final answer. This closes the miscellaneous section, reinforcing that series may combine alternating patterns, adjacent-term sums, or pair-based rules rather than a single uniform operation.

The lecture builds a systematic toolkit for number-series problems. First, it classifies operations into addition, multiplication, and mixed (A+m), using the ×3 sequence 5→1215 as a clean multiplication example and the power-of-two division sequence to introduce exponent rules. Second, it provides reference tables (squares 1–50, cubes 1–20, primes 1–200) so students can spot missing terms by matching values rather than computing from scratch—e.g., 1156=34² and the prime-product gap 7×11=77. Third, it teaches a difference-based formula (a × p) + m for sequences where first differences themselves follow a pattern, as in 2, 6, 14, 30 → 62. Finally, it covers miscellaneous series with alternating pairs (1+10=11), Fibonacci-like sums (2, 4, 6, 10, 16, 26, 42), and pair rules (96, 15, 71, 8, 37, 10, 41 → 5). The central idea is to test simple operations first, use reference tables for recognition, and only then move to mixed or multi-step rules.

Loading lesson…