GATE CS 2016 - Set 2 - 1 Mark Question

Duration: 3 min

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Module outline

  1. About Course: About the Course
  2. General Aptitude & Reasoning: Number System, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Speed Time and Distance, Mixture and Alligation, Data Interpretation, Algebra, Probability, Permutation and Combination, Venn Diagram, HCF LCM, Divisibility Rules, Age Problems, Pipe and Cistern, Partnership, Linear Algebra, Sequence and Series (Series), Statistics, Powers and Exponents (Surds and Indices), Arithmetic, Mensuration and Geometry, Calculus, Trigonometry, Vectors, Speed Mathematics and Basic Mathematics, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analogy, Series (Number and Letter Series) (Numerical Relations and Reasoning), Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Calendar, Seating Arrangements, Coding Decoding, Blood Relations, Directions (Direction Test), Clock, Analytical Reasoning (Counting Figures Reasoning), Ranking, Order and Sequence, Logical Sequence Of Words, Inequality, Data Sufficiency, Cubes & Dices
  3. Computer Networks & Cybersecurity: 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
  4. Programming, Data Structures & Algorithms: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, 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
  5. AI, Machine Learning, Big Data & Cloud: Emerging Tech Trends, Artificial Intelligence, Big Data Systems, Approaches to AI, Search Algorithms, Knowledge Representation, Cloud Computing
  6. Digital Logic & Computer Organization: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
  7. TOC & Compiler: 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
  8. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  9. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Distributed Systems
  10. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Object Oriented Technology, HTML Basics, JavaScript-Basics, Java, XML
  11. 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, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Data Warehousing & Mining, Enhanced Data Models, NoSQL
  12. Other Recurring CS Topics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, Multimedia
  13. Live Classes: ISRO Live classes
  14. Full Mock Test:
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.

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