## Syllabus of LPUNEST (MCA)

Databases: Keys, Normalization, SQL Basic commands and basics of backup and recovery,

Programming: Basics of C-Language, Basics of OOPS, Arrays, Stacks, Pointers, Inorder, Preorder, Postorder, Binary Trees, Linked Lists, Searching and sorting,

System Architecture: Number conversions, Microprocessor architecture, Register, ALU, RISC/CISC, Hardware Knowledge,

Software Engineering: Basics of OS, Basics of UML, Prototyping, Deadlocks, RAD Model, SDLC, Complexity, Testing and Maintenance,

Networks: OSI, TCP/IP, Networking devices, IPv4/IPv6, Error detection and correction

Sequences and Series of Real Numbers: Sequence of real numbers, Convergence of sequences, Bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences, Subsequences, Bolzano-Weierstrass theorem. Series of real numbers, Absolute convergence, Tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibniz test for convergence of alternating series.

Functions of One Real Variable: Limit, Continuity, Intermediate value property, Differentiation, Rolle’s Theorem, Mean value theorem, L’Hospital rule, Taylor’s theorem, Maxima and minima.

Functions of Two or Three Real Variables:
Limit, Continuity, Partial derivatives, Differentiability, Maxima and minima.

Integral Calculus: Integration as the inverse process of differentiation, Definite integrals and their properties, Fundamental theorem of calculus. Double and triple integrals, Change of order of integration, Calculating surface areas and volumes using double integrals, Calculating volumes using triple integrals.

Differential Equations: Ordinary differential equations of the first order of the form y’=f(x,y), Bernoulli’s equation, Exact differential equations, Integrating factor, Orthogonal trajectories, Homogeneous differential equations, Variable separable equations, Linear Differential equations of second order with constant coefficients, Method of variation of parameters, Cauchy-Euler equation.

Vector Calculus:
Scalar and vector fields, Gradient, Divergence, Curl, Line integrals, Surface integrals, Green, Stokes and Gauss theorems.

Group Theory: Groups, Subgroups, Abelian groups, Non-Abelian groups, Cyclic groups, Permutation groups, Normal subgroups, Lagrange’s Theorem for finite groups, Group homomorphisms and basic concepts of quotient groups.

Linear Algebra: Finite dimensional vector spaces, Linear independence of vectors, Basis, dimension, Linear transformations, Matrix representation, Range space, Null space, Rank-nullity theorem. Rank and inverse of a matrix, Determinant, Solutions of systems of linear equations, Consistency conditions, Eigen values and Eigen vectors for matrices, Cayley-Hamilton theorem.

Real Analysis: Interior points, Limit points, Open sets, Closed sets, Bounded sets, Connected sets, Compact sets, Completeness of R. Power series (of real variable), Taylor’s series, Radius and interval of convergence, Term-wise differentiation and integration of power series.

Numbers, Percentage, Profit, Loss & Discount, Ratio & Proportion, Simple & Compound Interest, Permutation& Combination & Probability, Time & Distance, Boats & streams, Races & Games, Time & Work, Pipes & Cistern, Calendar & Clocks, Area, Series completion & Coding – Decoding & Alphabet test, Direction sense test & Blood relations &arrangements, Syllogism, Number, Ranking & Time sequence test, Arithmetical reasoning, Inserting the missing character, Data sufficiency, Cubes and dice, Non-verbal reasoning.

Grammar: Parts of speech – Noun, Pronoun, Adjective, Adverb, Verb, Preposition, Conjunction Interjection; Tenses – Present, Past and Future Tense in Active and Passive Form; Modal Verbs – Can, Could, May, might, Should, Will, would.

Associative Language Skills: Vocabulary – Antonyms, Synonyms, one-word substitution, Word Analogies, Idioms and Phrases

Common Errors: Sentence Correction and Error Finding Exercises

Comprehension Passages: Closed and Open paragraphs, identifying key ideas or theme.

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