Vellore Institute of Technology (VIT)

Pattern of the Question Paper

• The computer based test (CBT) objective question Paper consists of 100 questions with a maximum of 100 marks.

• Of these, 80 will be from the chosen technical subject and 20 will be from English communication. There are no negative marks for wrong answers.

Syllabus

MATHEMATICS :

Algebra :  Fundamental operations in Algebra, Expansion, factorization, quadratic equations, indices, logarithms, arithmetic, geo-metric and harmonic progressions, binomial theorem, permutations and combinations.

Calculus :  Functions of single variable, limit, continuity and differentiability, Mean value theorems, indeterminate forms and L’Hos-pital rule, Maxima and minima, Taylor’s series, Fundamental and mean value-theorems of integral calculus, total derivatives, La-grange method of multipliers.

Differential Equations :  Differential equations of first order and their solutions, linear differential equations with constant coeffi-cients, homogenous linear differential equations.

Algorithms :  Analysis, Asymptotic notation, Notions of space and time complexity, Worst and average case analysis; Design: Greedy approach, Dynamic programming, Divide-and conquer; Connected components, Spanning trees, Shortest paths. Asymptotic analy-sis (best, worst, average cases) of time and space, upper and lower bounds.

Probability :  Probability theory, Dependent and independent events, frequency distributions, and measures of dispersions, Skew-ness and Kurtosis, random variable and distribution functions, mathematical expectations, Binomial, Poisson, normal distributions.

Algebra and Complex Analysis :  Algebra of matrices, rank and determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem. Matrix representation of linear transformations. Canonical forms, diagonal forms, triangular forms, Quadratic forms, reduction and classification of quadratic forms Analytic func-tions, Cauchy-Riemann equations. Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius transformations—Fourier series—harmonics.

Calculus and its Applications :  Linear ordinary differential equations (ODEs), variation of parameters, Sturm-Liouville problem. Partial differential equations (PDEs) – Classification of second order PDEs, General solution of higher or-der PDEs with constant coefficients, Method of separation of variables for Laplace, Heat and Wave equations. Transformation techniques—Laplace transformation—Fourier transforms—z—transformation to solve differential and difference equations.

Numerical Methods :  Numerical solutions of algebraic and transcendental equations iteration methods and Newton—Raphson method, Solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods-Numerical differentiation and integration, Numerical solutions of ODEs and PDEs.

Descriptive statistics,  Exploratory  Data Analysis :  Sample space, discrete probability, independent events, Bayes theorem. Random variables and distribution functions (univariate and multivariate) – expectation and moments. Independ-ent random variables, marginal and conditional distributions. Characteristic functions. Standard discrete and con-tinuous univariate distributions. Correlation and simple and multiple linear regression. Test of hypotheses—Large and small sample tests confidence intervals. Chi-square test goodness of fit. Simple non parametric tests for one and two sample problems, rank correlation and test for independence. ANOVA.

COMPUTER  AWARENESS :

Data Structures :  Arrays, Stacks, Queues, linked Lists. Sorting techniques, Searching Techniques, Trees and Graph terminology and representation in memory, binary  search tree, traversal techniques of graphs and Trees.

Computer Networks  :  Network models, Internet model, OSI model, Physical Layer – Analog and Digital Signals, Analog and Digital Transmission, Coding, Sampling. Data Link Layer – Error detection and correction, Data link control and Protocols, Stop and wait, Go-back-n, Selective repeat. Network Layer – Inter-networks, Addressing, unicast and multicast routing, Presentation Layer.

Programming in C :  Data types, Declarations, Expressions, statements and symbolic constants, input-Output functions. Operators and expressions: Arithmetic, unary, logical, bit-wise, assignment and conditional operators. Control statements: While, do-while, for state-ments, nested loops, if else, switch, break, Continue, comma operators. Storage types: Automatic, external, register and static variables. Functions: Defining and accessing, passing arguments, Recursion.

Database Management Systems :  DBMS architecture, Data models, data independence, E-R model, normalization, Relational Model: concepts, constraints, languages. Data storage, indexing, query processing, design and programming SQL.

Operating  Systems  :  Process management, Process States, Process Control Block, Process and Threads, CPU Scheduling, Schedul-ing algorithm, Process Synchronization and Deadlock, Memory management, Virtual memory concepts paging and segmentation File organization, Blocking and buffering, file descriptor, File and Directory structures, I/O Devices.

Computer Architecture :  Boolean algebra and computer arithmetic, flip-flops, design of combinational and sequential circuits, in-struction formats, addressing modes, interfacing peripheral devices, types of memory and their organization, interrupts and excep-tions. Von Neumann Computer, System Bus. Instruction Cycle, Data Representation, Machine instruction and Assembly Language.

ENGLISH COMMUNICATION  (20 Questions) :

1- Grammar

Subject , Verb Agreement,  Tense forms, Voices,  Articles  and Preposition,  Use of Conjunctions

2- Writing Technical Instructions

3- Writing Memos &  Writing Minutes

4- Transcoding

5- Preparing  Questionnaire

6- Proof  Reading

7- General vocabulary (words often confused)