GATE CS 2016 - Set 2 - 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.

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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