GATE CS 2014 - Set 1 - 2 Marks Question

Duration: 2 min

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Inside: a video lesson and guided study material.

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 a tutorial solving a calculus problem from the GATE CS 2014 exam. The problem asks to find the value of 't' given that the function f(x) = x * sin(x) satisfies the differential equation f''(x) + f(x) + t cos(x) = 0. The instructor systematically differentiates the function twice to find the second derivative, substitutes the expressions back into the original equation, simplifies the terms, and solves for the unknown constant 't'. The final answer is identified as -2. This is a classic example of verifying a function against a differential equation, a common topic in engineering mathematics.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    This window covers the core problem-solving process. It begins with the problem statement visible on screen: "Q. The function f(x) = x * sin(x) satisfies the following equation f''(x) + f(x) + t cosx = 0." The instructor writes the function f(x) = x sin x on the whiteboard. He then calculates the first derivative f'(x) = x cos x + sin x using the product rule. Next, he computes the second derivative f''(x) = -x sin x + cos x + cos x, which simplifies to 2 cos x - x sin x. He substitutes these values into the given equation: (2 cos x - x sin x) + (x sin x) + t cos x = 0. The x sin x terms cancel out, leaving 2 cos x + t cos x = 0. He factors this to (2 + t) cos x = 0, leading to the conclusion that t = -2. Finally, he circles option B on the multiple-choice list.

  2. 2:00 – 2:19 02:00-02:19

    This short window shows the conclusion of the video. The instructor has finished solving the problem and is likely wrapping up the explanation. He points to the correct option B. -2 on the screen. The screen then transitions to a black background with the text "THANKS FOR WATCHING" in white, stylized font, signaling the end of the lecture segment.

The lecture demonstrates a standard application of differentiation rules, specifically the product rule, to solve a differential equation problem. By finding the second derivative of the given function and substituting it into the provided equation, the variable 't' is isolated and solved algebraically. This reinforces the connection between function properties and differential equations. The step-by-step derivation ensures clarity for students preparing for competitive exams like GATE.

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