Arithmetic - Part 2

Duration: 27 min

This video lesson is available to enrolled students.

Return to /learn/IOCL-ENGINEERS-OFFICERS-GRADE-A-PAPER-2/quantitative-aptitude/arithmetic/basic-arithmetic/asset-arithmetic-part-2 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper 1 | Quantitative Aptitude: Speed Mathematics and Basic Mathematics, Percentage, Ratio and Proportion (Ratios), Powers and Exponents (Surds and Indices), Logarithm, Sequence and Series (Series), Mensuration and Geometry, Data Interpretation, Average, Arithmetic
  3. Paper 1 | Logical Reasoning: Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Analogy, Cubes & Dices, Syllogisms
  4. Paper 1 | English Language: Vocabulary, Noun, Pronoun, Verb, Adjectives, Adverb, Preposition, Conjunction, Interjection, Articles, Tenses, Subject Verb Agreement (Verb Noun Agreement), Modals, Determiner, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Construction
  5. Paper 1 | Unit Tests:
  6. Paper 1 | Full-Length Mock Tests:
  7. Paper 2 | Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Permutation and Combination, Probability, Statistics
  8. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  9. Paper 2 | Computer Architecture: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design
  10. Paper 2 | Programming and Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  11. Paper 2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  12. Paper 2 | Theory Of Computation/Automata Theory: 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
  13. Paper 2 | Compiler Design: 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
  14. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  15. Paper 2 | DataBase Management System/DBMS: 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
  16. Paper 2 | Computer Networks: Introduction to CN, 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
  17. Paper 2 | CS/IT Sectional Mock Tests:
  18. Complete Paper Full Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a lecture on solving a problem related to finding the number of common terms between two arithmetic progressions (APs). The instructor, Yash Jain Sir from Knowledge Gate Eduventures, begins by presenting a question from the TCS NQT 2020 exam: "Find the number of common terms" between the sequences A) 17, 21, 25, 29, ..., 417 and B) 16, 21, 26, 31, ..., 466. The core of the lesson is a step-by-step algorithm. First, the common difference (d) of each sequence is identified: d1 = 4 for sequence A and d2 = 5 for sequence B. The first common term is found to be 21. The key insight is that the common terms form a new arithmetic progression with a common difference equal to the Least Common Multiple (LCM) of the original two differences, which is LCM(4, 5) = 20. The final step is to use the formula for the nth term of an AP, n = (l - a) / d + 1, where 'l' is the last common term, 'a' is the first common term, and 'd' is the common difference of the new sequence. The instructor demonstrates this by calculating the last common term as 417, then applying the formula: n = (417 - 21) / 20 + 1 = 396 / 20 + 1 = 19.8 + 1, which is not an integer, indicating a need to find the actual last common term. The video also includes a brief, unrelated segment on a different topic, 'THE BADMAAASH BACCHHA', which appears to be a mnemonic or a separate example, but the main focus remains on the AP problem.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide showing a man writing on a green chalkboard filled with mathematical equations, with the word "ARITHMETIC" at the bottom. This transitions to a black screen with the title "PLAYING WITH AP/GP" in red text. The instructor, Yash Jain Sir, is introduced in a small window, and the video is identified as copyrighted content from Knowledge Gate Eduventures.

  2. 2:00 – 5:00 02:00-05:00

    The main problem is presented on a blackboard: "QUE: FIND THE NUMBER OF COMMON TERMS". The two sequences are given as A) 17 21 25 29 .... 417 and B) 16 21 26 31 .... 466. The instructor states the question was asked in TCS NQT 2020. The video shows the sequences being written out, with the first common term, 21, being highlighted.

  3. 5:00 – 10:00 05:00-10:00

    The instructor begins to solve the problem. He identifies the common difference of sequence A as 4 (21-17) and sequence B as 5 (21-16). He explains that the common terms will form a new AP with a common difference equal to the LCM of 4 and 5, which is 20. He writes the formula for the nth term of an AP: a_n = a + (n-1)d. He then identifies the first common term as 21 and the last common term as 417, which is the last term of sequence A.

  4. 10:00 – 15:00 10:00-15:00

    The instructor writes the formula for the number of terms: n = (l - a) / d + 1. He substitutes the values: l = 417, a = 21, d = 20. He calculates (417 - 21) / 20 + 1 = 396 / 20 + 1 = 19.8 + 1 = 20.8. He notes that this is not an integer, which is a problem. He then realizes that 417 might not be a common term and needs to find the actual last common term that is less than or equal to 417.

  5. 15:00 – 20:00 15:00-20:00

    The instructor corrects the approach. He states that the last common term must be a multiple of 20, starting from 21. He calculates the last common term by finding the largest multiple of 20 that is less than or equal to 417. He finds that 400 is the largest such number. He then applies the formula: n = (400 - 21) / 20 + 1 = 379 / 20 + 1 = 18.95 + 1 = 19.95. He realizes this is still not an integer. He then correctly identifies that the last common term is 401, which is 21 + 19*20. He calculates n = (401 - 21) / 20 + 1 = 380 / 20 + 1 = 19 + 1 = 20. The number of common terms is 20.

  6. 20:00 – 25:00 20:00-25:00

    The video transitions to a different topic, titled "THE BADMAAASH BACCHHA". The instructor draws a circle and writes numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 inside it. He then writes a formula: (a+b)-1, and applies it to the numbers 2 and 3, getting (2+3)-1 = 4. He then writes (5+1)-1 = 5, and 6-1-1 = 4. This appears to be a separate example or a mnemonic for a different concept, possibly related to counting or combinations.

  7. 25:00 – 26:42 25:00-26:42

    The video ends with a final slide that says "THANKS FOR WATCHING" over a blue, abstract background with mathematical symbols. The instructor's video window is still visible in the corner, and the copyright notice for Knowledge Gate Eduventures remains at the bottom.

The video provides a clear, step-by-step solution to a common problem in arithmetic progression. It begins by identifying the key components of the two given sequences: their first terms, common differences, and last terms. The central concept is that the common terms of two APs form a new AP, whose common difference is the LCM of the original two differences. The instructor correctly identifies the first common term and then applies the standard formula for the number of terms in an AP. The video demonstrates a common pitfall: assuming the last term of the original sequence is also a common term, and shows the correct method of finding the actual last common term by checking the sequence of common terms. The final answer is 20. The latter part of the video, on 'THE BADMAAASH BACCHHA', seems to be an unrelated example or a mnemonic, but the core lesson on APs is well-structured and pedagogically sound.

Loading lesson…