Gate CS 2013 - 1 Mark Question

Duration: 3 min

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Module outline

  1. About Course: About the Course
  2. Paper-2 | Programming & 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
  3. Paper-2 | Databases / DBMS & SQL: 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
  4. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  5. Paper-2 | Computer Networks & Security: 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 Access Technologies, Network Security
  6. Paper-2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  7. 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
  8. Paper-2 | 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
  9. Paper-2 | Computer Organization & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  10. 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
  11. Paper-1 | General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, GK- Current Affairs, History, Geography, Indian Economy, Environment
  12. Paper-1 | Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Data Interpretation, Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Clock, Calendar, Cubes & Dices, Directions (Direction Test), Analogy, Seating Arrangements, Analytical Reasoning (Counting Figures Reasoning)
  13. Paper-1 | Quantitative Aptitude: Ratio and Proportion (Ratios), Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Speed Time and Distance, Average, Age Problems, Percentage, Profit and Loss, Time and Work, Pipe and Cistern, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Mensuration and Geometry, Probability, Statistics, Arithmetic, Algebra
  14. Paper-1 | English: Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Cloze Test (Cloze Passage)
  15. Coal India Previous Year Paper:
  16. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus
  17. Coal India Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video is an educational lecture on Calculus, specifically focusing on the continuity of functions. It begins with a title card displaying 'CALCULUS' over a background of mathematical formulas. The main content is a multiple-choice question from GATE CS 2013 asking to identify which function is continuous at x=3. The instructor, Yash Jain Sir, systematically evaluates four options (A, B, C, D) defined as piecewise functions. He explains the condition for continuity: the left-hand limit (LHL), right-hand limit (RHL), and the function value at the point must be equal.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card and then presents the problem statement. The instructor begins by analyzing Option A, a piecewise function defined as 2 if x=3, x-1 if x>3, and (x+3)/3 if x<3. To verify continuity, he writes annotations 'value', 'right', and 'left' next to the respective parts of the function. He calculates the function value at x=3 as 2. He then computes the right-hand limit (RHL) by substituting x=3 into (x-1), yielding 2. Similarly, he calculates the left-hand limit (LHL) by substituting x=3 into (x+3)/3, which equals 2. Seeing that LHL = RHL = Value, he circles the number 2 three times and places a checkmark next to Option A, confirming it is the correct answer. He then analyzes Option B, noting f(3)=4 but the limit is 5, leading him to cross it out. He moves to Option C, calculating LHL=6 and RHL=-1, and crosses it out due to inequality.

  2. 2:00 – 2:35 02:00-02:35

    In the final segment, the instructor addresses Option D, which is defined as 1/(x^3 - 27) for x != 3. He points out that at x=3, the denominator becomes zero, implying the limit does not exist or is infinite. He marks this option as discontinuous, likely with an 'X' or by crossing it out, although the specific marking is brief. The instructor concludes the problem-solving session. The video ends with a black screen displaying the text 'THANKS FOR WATCHING' in a stylized white font. This final section reinforces the method of checking continuity by comparing limits and function values for all given options.

The lecture demonstrates a systematic approach to determining the continuity of piecewise functions at a specific point. By calculating the left-hand limit, right-hand limit, and the function value, the instructor verifies the condition LHL = RHL = f(c). The video effectively uses visual annotations to track these calculations for each option, eliminating incorrect choices until the correct function is identified.

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