MCA Syllabus

**Syllabus of MCA Entrances**

**MATHEMATICS**

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1. __ALGEBRA__

Sets, Relations, Functions, Elementary Number Theory Including the relation ofcongruence Modulo, Simultaneous linear / quadratic equations, Indices,Logarithms, Arithmetic, Geometric and Harmonic progressions, Binomial theorem,Surds, Complex numbers, Demoivre’s theorem and its simple application.

2. __MATRICES AND DETERMINANTS__

Matrix operations, Definition and properties of determinats, Cofactors,Adjoint, Elementry Transformations, Rank and inverse of a Matrix, MatrixPolynomial, Characteristic Equations,Eigen Values, Latent Vectors, CaylayHamilton theorem, Linear system of Equations

3. __THEORY OF EQUATIONS__

Polynomials and their charcteristics, Roots of an equation, Relations betweenRoots and Coefficients,Transformation of Equations, Symmetric function etc.

4. __ABSTRACT ALGEBRA__

Groups, Cyclic groups, Subgroups, Normal Groups, Lagrange’stheorem, Homomorphism, Isomorphism, Ring, Field, Vector Spaces, LinearIndependence of Vectors, Basis, Dimension, Linear Transformation anddiagonalisation of Matrices etc

5. __VECTOR ALGEBRA__

Scalar and Vector quantities their representation, Addition andsubtraction of vectors, Scalar and vector product of two vectors, Scalar tripleproduct, Expansion formula of Vector triple product

6. __TRIGONOMETRY__

Simple identities, trignometric equations, Properties of triangles, Solution oftriangle, Height and distance, Inverse function

7. __CALCULAS AND REALANALYSIS__

Real number system, Concept of neighborhood and limit points,Continuity and limits, Indeterminate forms, properties of continuous functionsin closed interval, Differentiation, Successive Differentiation, Maxima Minima,Roll's theorem, Mean value theorems, Maclaurine's series and Taylor's series,Integration, definite integral, Evaluation of length, Area and volume ofcurves, Curvature, Asymptotes, Tracing of curves, Partial Differentiation,functions of two variables, definition of partial derivates, Totaldifferentiation, Sequence, Sequence of real numbers, Convergent Sequences,Cauchy Sequences, Monotonic Sequences, Infinite series of positive terms andtheir different test of convergence,Alternating infinite series and Leibnitz'stest of convergence, Absolute convergence, Conditional convergence, UniformConvergence, Multiple integration, Change of order and change of variables,Application to evaluation of Area, Surface and volume.

8. __DIFFERENTIAL EQUATIONS__

Differential equations of first order and their solutions,Linear differential equations with constant coefficients, Homogenous lineardifferential equations, Orthogonal Trajectories, Singular solutions.

9. __COORDINATE GEOMETRY__

** 2-d:** Pair of straight lines,Transformation of coordinate system, Circles, Parabola, Ellipse and Hyperbola,Pair of tangents from a point, Chord of contact, Equation of chord in terms ofmiddle point, Diameter of Conic, Conjugate diameter, Classification of curvesof second degree.

** 3-d:** Introduction to linesand planes, Spheres, Quadric Cones and Cylinders

10. __LINEAR PROGRAMMING__

Linear inequalities with two variables, Mathematical formulationof L.P.P, Basic concepts of graphical and Simplex method.

11. __NUMERICAL ANALYSIS__

Interpolation, Extrapolation, Quadrature formula, Simpson's1/3rd rule, Trapezoidal rule, Solution of non-linear equations using iterativemethods, Numerical differentiation.

12. __STATISTICS__

Classifications of Data and frequency distribution, Calculation of measures ofCentral tendency and measures of dispersion, Skewness and Kurtosis, Permutationand Combination, Probability, Random variables and distribution functions,Mathematical expectations and generating functions, Binomial, Poisson,Geometric, Exponential and Normal distributions, Curve fitting and principal ofleast square, Correlation and Regression,Index numbers and theirimportance,Simple Time Series analysis, Sampling and large sample tests,test ofsignificance based on t, Chi-square and F distributions.

**COMPUTER AWARENESS**

1. __COMPUTER FUNDAMENTALS__

Organization of a computer, Central Processing Unit (CPU),Structure of instructions in CPU, input / output devices, computer Memory,memory organization, back-up devices.

2. __DATA REPRESENTATION__

Representation of characters, integers, and fractions, binaryand Hexadecimal representations

3. __BINARY ARITHMETIC__

Addition, subtraction, division, multiplication, singlearithmetic and two complement arithmetic, floating point representation ofnumbers, normalized floating point representation, Boolean Algebra, truthtables, Venn diagrams

4. __COMPUTER ARCHITECTURE__

Block structure of computers, communication between processorand I / O devices, interrupts

5. __COMPUTER LANGUAGE__

Assembly language and high level language, Multi-programming andtime sharing operating systems, Computer Programming in C

6. __MATHEMATICAL LOGIC__

Venn Diagrams in logic, Logical operators, Negations, LogicalEquivalence and Tautology

7. __FLOW CHART ANDALGORITHMS__

8. __DATA STRUCTURE__

**ANALYTICAL ABILITY ANDLOGICAL REASONING**

1. Logical Reasoning,

2. Quantitative Reasoning

3. Visuo-Spatial Reasoning

4. Analytical Reasoning

**ENGLISH**

1. Reading Comprehension

2. Grammar

3. Vocabulary