SOE Archive

Question Papers

• 2023
• CIE

Notes

• Calculus of complex functions: Review of function of a complex variables, limits, continuity, and differentiability. Analytic functions: Cauchy-Riemann equations in Cartesian and polar forms and consequences.
  
  Construction of analytic functions: Milne-Thomson method Problems.

  Module 1

• Conformal transformations: Introduction. Discussion of transformations: w = z² , w = z + 1/z , (z ≠ 0). Bilinear transformations- Problems.
  
  Complex integration: Line integral of a complex function Cauchy’s theorem and Cauchy’s integral formula and problems.

  Module 2

• Numerical Solutions of Ordinary Differential Equations (ODE’s): Numerical solution of ODE’s of first order and first degree- Taylor’s series method, Modified Euler’s method. Runge -Kutta method of fourth order, Milne’s predictor and corrector method (No derivations of formulae)-Problems. Numerical Solution of Second Order ODE’s - Runge-Kutta method and Milne’s predictor and corrector method. (No derivations of formulae).

  Module 3

• Probability Distributions: Review of basic probability theory. Random variables (discrete and continuous), probability mass/density functions. Binomial, Poisson, exponential and normal distributions- problems (No derivation for mean and standard deviation)-Illustrative examples.

  Module 4

• Joint probability distribution: Joint Probability distribution for two discrete random variables, expectation and covariance.
  
  Sampling Theory: Introduction to sampling distributions, standard error, Type-I and Type-II errors. Test of hypothesis for means, student’s t-distribution, Chi-square distribution as a test of goodness of fit.

  Module 5

Question Papers

• 2023
• CIE

Notes

• Introduction to Algorithm, Algorithm Specification, Analysis Framework, Performance Analysis: Space complexity, Time complexity. Asymptotic Notations: Mathematical analysis of non-recursive and recursive Algorithms with Examples. Important Problem Types: Sorting, Searching, String processing, Graph Problems, Combinatorial Problems.
  
  Fundamental Data Structures: Stacks, Queues, Graphs, Trees, Sets and Dictionaries.

  Module 1

• Divide and Conquer: General method, Binary search, Recurrence equation for divide and conquer, Finding the maximum and minimum, Merge sort, Quick sort, Strassen’s matrix multiplication, Advantages and Disadvantages of divide and conquer. Decrease and Conquer Approach: Topological Sort.

  Module 2

• Greedy Method: General method, Coin Change Problem, Knapsack Problem, Job sequencing with deadlines. Minimum cost spanning trees: Prim’s Algorithm, Kruskal’s Algorithm. Single source shortest paths: Dijkstra's Algorithm. Optimal Tree problem: Huffman Trees and Codes. Transform and Conquer Approach: Heaps and Heap Sort.

  Module 3

• Dynamic Programming: General method with Examples, Multistage Graphs. Transitive Closure: Warshall’s Algorithm, All Pairs Shortest Paths: Floyd's Algorithm, Optimal Binary Search Trees, Knapsack problem, Bellman-Ford Algorithm, Travelling Sales Person problem, Reliability design.

  Module 4

• Backtracking: General method, N-Queens problem, Sum of subsets problem, Graph coloring, Hamiltonian cycles. Branch and Bound: Assignment Problem, Travelling Sales Person problem, 0/1 Knapsack problem: LC Branch and Bound solution, FIFO Branch and Bound solution. NP Complete and NP-Hard problems: Basic concepts, nondeterministic algorithms, P, NP, NP-Complete, and NP Hard classes.

  Module 5

Question Papers

• 2023
• CIE

Notes

• Introduction to operating systems, System structures: What operating systems do; Computer System organization; Computer System architecture; Operating System structure; Operating System operations; Process management; Memory management; Storage management; Protection and Security; Distributed system; Special-purpose systems; Computing environments. Operating System Services; User - Operating System interface; System calls; Types of system calls; System programs; Operating system design and implementation; Operating System structure; Virtual machines; Operating System generation; System boot.
  
  Process Management: Process concept, Process scheduling; Operations on processes; Inter process communication

  Module 1

• Multi-threaded Programming: Overview; Multithreading models; Thread Libraries; Threading issues. Process Scheduling: Basic concepts; Scheduling Criteria; Scheduling Algorithms; Multiple-processor scheduling; Thread scheduling.
  Process Synchronization: Synchronization: The critical section problem; Peterson’s solution; Synchronization hardware; Semaphores; Classical problems of synchronization; Monitors.

  Module 2

• Deadlocks: Deadlocks; System model; Deadlock characterization; Methods for handling deadlocks; Deadlock prevention; Deadlock avoidance; Deadlock detection and recovery from deadlock. Memory Management: Memory management strategies: Background; Swapping; Contiguous memory allocation; Paging; Structure of page table; Segmentation.

  Module 3

• Virtual Memory Management: Background; Demand paging; Copy-on-write; Page replacement; Allocation of frames; Thrashing. File System, Implementation of File System: File system: File concept; Access methods; Directory structure; File system mounting; File sharing; Protection: Implementing File system: File system structure; File system implementation; Directory implementation; Allocation methods; Free space management.

  Module 4

• Secondary Storage Structures, Protection: Mass storage structures; Disk structure; Disk attachment; Disk scheduling; Disk management; Swap space management. Protection: Goals of protection, Principles of protection, Domain of protection, Access matrix, Implementation of access matrix, Access control, Revocation of access rights, Capability- Based systems. Case Study: The Linux Operating System: Linux history; Design principles; Kernel modules; Process management; Scheduling; Memory Management; File systems, Input and output; Inter process communication.

  Module 5

Question Papers

• 2023
• CIE

Notes

• Introduction: Data Communications, Networks, Network Types, Networks Models: Protocol Layering, TCP/IP Protocol suite, The OSI model, Introduction to Physical Layer-1: Data and Signals, Digital Signals, Transmission Impairment, Data Rate limits, Performance. SLE: Internet History, Standards and Administration

  Module 1

• Digital Transmission: Digital to digital conversion: Line coding- Polar, Bipolar, Manchester coding, AMI, Pseudo ternary, Physical Layer-2: Analog to digital conversion, Pulse Code Modulation, Delta Modulation, Transmission Modes, Analog Transmission: Digital to analog conversion. SLE: Bandwidth Utilization: Multiplexing

  Module 2

• Transmission Media: Introduction, Guided Media: Twisted Pair Cable, Coaxial Cable, Fiber Optics Cable, switching: Introduction, Circuit Switched Networks and Packet switching, Data Link Layer: Error Detection and Correction: Introduction, Block Coding, Cyclic Code. SLE: Checksum

  Module 3

• Data link control: DLC Services: Framing, Flow Control, Error Control, Connectionless and Connection Oriented, Data link layer protocols, High Level Data Link Control (HDLC), Media Access control: Random Access, Controlled Access. SLE: Channelization

  Module 4

• Introduction to Network Layer: Network Layer Services, Packet Switching, Network Layer Performance, IPv4 Addresses. SLE: IPv6

  Module 5

Question Papers

• 2023
• CIE

Notes

• Introduction to C++: Introduction to Procedure-oriented programming vs. object-oriented programming, concepts of object-oriented programming.
  
  Overview of C++, Sample C++ program, Different data types, operators, expressions, and statements, arrays and strings, pointers & user-defined types Function Components, argument passing, inline functions, function overloading, recursive functions.

  Module 1

• Classes, Objects and Polymorphism: Class Specification, Class Objects, Scope resolution operator, Access members, Defining member functions, Data hiding, Constructors, Destructors, Static data members and functions. Constant data members and functions, mutable data members.
  
  Friend functions, Passing objects as arguments, Returning objects, Arrays of objects, Dynamic objects, Pointers to objects, Generic functions and classes, Operator overloading and their applications such as +, - , pre-increment, post increment, [ ] etc.

  Module 2

• Inheritance: Introduction to Inheritance, Different types of Inheritances, Inheritance and protected members, protected base class inheritance, Constructors and Destructors in Inheritance, Granting access, Virtual base classes.

  Module 3

• Run-time polymorphism and Exception handling: Virtual functions and Polymorphism: Introduction to Virtual functions, calling a Virtual function through a base class reference, Inheritance of virtual attributes, Hierarchy of virtual functions, Pure virtual functions and Abstract classes, Early and late binding.
  
  Exception Handling: Exception handling fundamentals, Catching Class Types, Using Multiple catch Statements, Handling Derived-Class Exceptions, Exception handling options: Catching All Exceptions, Restricting Exceptions & Re-throwing an Exception, user defined exceptions, Applying Exception Handling.

  Module 4

• I/O System Basics and Standard template library:
  I/O System Basics: The C++ I/O system basics: C++ stream classes, Formatted I/O, I/O manipulators; C++ file I/O: fstream and the File classes, File operations. STL: An overview, the container classes, general theory of operations, vectors, lists, maps.

  Module 5

Question Papers

• 2023
• CIE

Notes

• Introduction to Graph Theory: Definitions and Examples, Subgraphs, Complements, and Graph Isomorphism, Vertex Degree, Euler Trails and Circuits.

  Module 1

• Introduction to Graph Theory contd.: Planar Graphs, Hamilton Paths and Cycles, Graph Colouring, and Chromatic Polynomials

  Module 2

• Trees: Definitions, Properties, and Examples, Routed Trees, Trees and Sorting, Weighted Trees and Prefix Codes

  Module 3

• Optimization and Matching: Dijkstra‟s Shortest Path Algorithm, Minimal Spanning Trees – The algorithms of Kruskal and Prim, Transport Networks – Max-flow, Min-cut Theorem, Matching Theory

  Module 4

• The Principle of Inclusion and Exclusion: The Principle of Inclusion and Exclusion, Generalizations of the Principle, Derangements – Nothing is in its Right Place, Rook Polynomials.

  Module 5

• Module 1
  

  Introduction to Indian Constitution: Definition of Constitution, Necessity of the Constitution, Societies before and after the Constitution adoption. Introduction to the Indian constitution, Making of the Constitution, Role of the Constituent Assembly. Preamble of Indian Constitution & Key concepts of the Preamble. Salient features of India Constitution.

• Module 2
  

  Fundamental Rights (FR’s), Directive Principles of State Policy (DPSP’s) and Fundamental Duties (FD’s): Fundamental Rights and its Restriction and limitations in different Complex Situations. DPSP’s and its present relevance in Indian society. Fundamental Duties and its Scope and significance in Nation building.

• Module 3
  

  Union Executive: Parliamentary System, Union Executive – President, Prime Minister, Union Cabinet, Parliament - LS and RS, Parliamentary Committees, Important Parliamentary Terminologies. Supreme Court of India, Judicial Reviews and Judicial Activism.

• Module 4
  

  State Executive & Elections, Amendments and Emergency Provisions: State Executive, Election Commission, Elections & Electoral Process. Amendment to Constitution (Why and How) and Important Constitutional Amendments till today. Emergency Provisions.

• Module 5
  

  Professional Ethics: Definition of Ethics & Values. Professional & Engineering Ethics. Positive and Negative aspects of Engineering Ethics.
  
  Cyber Laws: Salient features of the IT Act, 2000, various authorities under IT Act and their powers. ; Penalties & Offences, amendments.
  
  Computer & Cyber Security: (a) Types of Attacks, (b) Network Security (c) Overview of Security threats, (d) Hacking Techniques, (e) Password cracking (f) Insecure Network connections, (g) Malicious code (h) Concept of Fire wall Security