Practice Question

Duration: 5 min

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Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): Spelling & Diacritics, Grammar (اسم, فعل, صفت, ضمیر), Vocabulary, Idioms & Proverbs, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): Bangla Script and Sounds, Bangla Grammar and Usage, Bangla Word Formation and Vocabulary, Reading and Text Interpretation
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Verb, Adverb, Preposition, Articles, Determiner, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Mensuration and Geometry, Age Problems, Arithmetic, Powers and Exponents (Surds and Indices), Algebra, Probability, Trigonometry, Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, Indian Economy, Environment, GK- Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow 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
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Artificial Intelligence, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The lecture provides a step-by-step derivation for calculating the memory space of a tridiagonal matrix. It begins by defining the matrix condition where elements are zero if they are more than one position away from the main diagonal. Using a 4x4 example, the instructor visualizes the non-zero elements forming a band around the main diagonal. He counts the elements in the main diagonal (n), upper diagonal (n-1), and lower diagonal (n-1). By summing these, he derives the total count of non-zero elements as 3n-2. Finally, he calculates the total space by multiplying this count by the size of an element (4 bytes), demonstrating an efficient storage method for sparse matrices.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with a question displayed on the screen: "Consider a n*n square matrix A, such that A[i][j] = 0 if |i-j| > 1. find the space required to store the array in memory". The instructor underlines key phrases like "n*n square matrix", "A[i][j] = 0", and "space required" to emphasize the problem constraints. He decides to use a concrete example with n=4 to visualize the matrix structure. He draws a 4x4 grid on the whiteboard. He explains the condition |i-j| > 1, meaning if the absolute difference between row index i and column index j is greater than 1, the element is zero. He fills the first row (i=0) by checking j=0, 1, 2, 3. He calculates |0-0|=0, |0-1|=1, |0-2|=2, |0-3|=3. Since 2 and 3 are greater than 1, he writes 0 in those positions. He fills the first two positions with 'a' and 'b'. He continues this process for the entire matrix, filling it with letters like 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j' to represent non-zero values. He circles the non-zero elements to highlight the pattern, showing that non-zero values only exist on the main diagonal and the diagonals immediately above and below it.

  2. 2:00 – 5:00 02:00-05:00

    The instructor proceeds to count the non-zero elements to determine the storage requirement. He writes "Main Diagonal = n" in green ink, circling the elements a, d, g, j. He then identifies the upper diagonal elements (b, e, h) and writes "Upper Diagonal = n-1" in red ink. He counts the lower diagonal elements (c, f, i) and writes "Lower Diagonal = n-1". He sums these values: n + (n-1) + (n-1). He simplifies the expression to 3n - 2. He writes "(3n-2) * 4B" on the board, explaining that if each element requires 4 bytes of memory, the total space is the number of non-zero elements multiplied by 4. He emphasizes that since the matrix is sparse, we do not store the zero elements, only the non-zero ones.

  3. 5:00 – 5:24 05:00-05:24

    The instructor concludes the problem by summarizing the result. He points to the final formula 3n-2, which represents the total number of non-zero elements. He reiterates that this is the number of elements that need to be stored in memory. He confirms that the space required is (3n-2) * 4 bytes. He wraps up the explanation, having successfully derived the space complexity for this specific type of sparse matrix. He concludes the lesson by ensuring the student understands that the space is proportional to the number of non-zero elements.

The video demonstrates space optimization for sparse matrices. It starts with the definition of a tridiagonal matrix where non-zero elements are restricted to the main diagonal and adjacent diagonals. By using a 4x4 example, the instructor visualizes the pattern. He then counts the elements in each diagonal band (n, n-1, n-1) to derive the total count of 3n-2. Finally, he calculates the memory space by multiplying this count by the size of an element (4 bytes), showing how to efficiently store such matrices.

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