GATE CS 2016 - Set 2 - 1 Mark Question

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/DSSSB-TGT-COMPUTER-SCIENCE-PAPER-2/mathematics-i-ii-iii-iv/calculus/differentiability-and-differentiation/asset-gate-cs-2016-set-2-1-mark-question after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Programming, Data Structures, OOP & Java: 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, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  3. Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Access Technologies, Network Security, Society, Law & Ethics, Cloud Computing, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  4. Teaching Methodology: Child Development, Concept of Pedagogy, Theories, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Curriculum Framework & Reforms, National Education Policy (NEP) 2020, Psychology, Teaching-Learning Process, Personality Development, Teaching Methods & Strategies, Learning and Motivation, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Nature, Objectives & Characteristics of Teaching, Teaching-Learning Aids & ICT Integration, Classroom Management & Communication, Evaluation, Assessment & Measurement, Curriculum & School Environment, Inclusive Education & Special Needs, Professional Development & Ethics
  5. Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  6. Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  7. Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  8. Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  9. Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep, Artificial Intelligence, साइबर सुरक्षा / Cyber Safety and Security, कंप्यूटर सॉफ़्टवेयर / Computer Software, ऑपरेटिंग सिस्टम / Operating System, वर्ड प्रोसेसिंग (MS Word) / Word Processing (MS Word), कंप्यूटर नेटवर्क / Computer Networks
  10. Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  11. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  12. Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  13. Mathematics - I, II, III, IV: Permutation and Combination, Logarithm, Linear Algebra, Algebra, Calculus, Trigonometry, Vectors, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps, Graph Theory, Number System & Place Value, Factors, Multiples, Divisibility, HCF & LCM, Mensuration — Perimeter, Area, Surface Area, Volume, Data Handling, Graphs & Probability, Coordinates & Graphs, Higher Mathematics — Trigonometry, Quadratics, Polynomials, Progressions, Statistics, Logarithms, समतल क्षेत्रमिति / Plane Mensuration, प्रतिचयन / Sampling
  14. Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  15. Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing
  16. Statistical Techniques: Probability, Statistics
  17. Interpolation - DI: Data Interpretation
  18. Basis of Physics: Physics
  19. Previous Year Paper:
  20. Business Studies and Management: Business Communication, Business Organization and Management, Financial Accounting, Business Economics, Management Information System (MIS), Knowledge Management & New Economy
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video solves a calculus problem from the GATE CS 2016 exam regarding polynomial degrees and derivatives. The instructor demonstrates a practical method using a specific example function to determine the degree of a derived expression involving f(x) and g(x). The lesson covers properties of even and odd functions and how differentiation affects polynomial degrees.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a blackboard background displaying the word "CALCULUS" and various equations like cos x and sin x. The main problem is displayed in red text: "Let f(x) be a polynomial and g(x) = f'(x) be its derivative. If the degree of (f(x) + f(-x)) is 10, then the degree of (g(x) - g(-x)) is _______." The text indicates this is from "(GATE CS 2016) (SET-2) (1 MARK)". The instructor, Yash Jain Sir, wearing a blue polo shirt with a "KG" logo, begins solving by assuming a specific polynomial to simplify the logic. He writes f(x) = x^10 on the digital whiteboard. He then calculates f(-x) = (-x)^10, simplifying it to x^10. He sums them to show f(x) + f(-x) = x^10 + x^10 = 2x^10, confirming the degree is 10. He then differentiates to find g(x), writing g(x) = 10x^9.

  2. 2:00 – 3:08 02:00-03:08

    The instructor continues by evaluating g(-x). He writes g(-x) = 10(-x)^9, which simplifies to -10x^9. He then substitutes these into the expression g(x) - g(-x), resulting in 10x^9 - (-10x^9). This simplifies to 20x^9. He circles the exponent 9 and writes the final answer "9" in the blank space. The video concludes with a slide titled "Correct Answer: Option C". The solution text explains that f(x) must be an even function because f(x) + f(-x) has a degree. It derives that g(x) = -g(-x), leading to g(x) - g(-x) = 2f'(x). Since f(x) is degree 10, f'(x) is degree 9, making the final degree 9. The slide explicitly shows the step g(x) - g(-x) = f'(x) - (-f'(-x)).

The lesson progresses from a specific example to a general theoretical proof. By assuming f(x) = x^10, the instructor shows that g(x) becomes 10x^9. The final slide reinforces that if f(x) is even, its derivative g(x) is odd, meaning g(x) - g(-x) effectively doubles g(x), preserving the degree of 9.

Loading lesson…