For M.C.A. :MCA (3Year) : Any graduate with minimum 50% marks in graduation or equivalent having mathematics either in 10+2 or graduation level as one of the subject. Candidate should have been born on or after 01.07.1993

**MATHEMATICS :**

**Algebra of sets:** Set Operations , Union , Intersection, Difference , Symmetric Difference, Compliment , Venn Diagram , Cartesian Product of sets , Relation and Function , Inverse of a Function,Composite Function, Equivalence Relation , Kind of function.

**Number System:** Real number (algebraic and other prosperties), rational and irrational numbers, Complex number, Algebra of complex number ,conjugate and square root of aq complex number , cube roots of unity, Demoiver’s Theorem with simple applications. Permutation and combinations and their simple applications, mathematical induction, Binomial Theorem. Determinants up to third order, Minors and cofactors, Properties of determinants. Matrices up to third order, types of matrices. Algebra of matrices, Adjoint and inverse of a matrix . Application of determinants and matrices to the solution of linear equation(in three unknows)

**Probability and Statistics:** Average (Mean, Median, and Mode), Dispersion (Standard deviation and Variance), Definition of prabability, Mutually exclusive events, Independent events, Addition theorem.

**Coordinate Geometry:** Co-ordinate Geometry of Two Dimensions :Straight lines, Pair of staright lines, Circles, Equations of tangents and normal to a circle, Equations of parabola, Ellipse and hyperbola, Ellipse and hyperbola in simple forms and their tangents (Focus, directix, eccentricity and latus rectum in all cases) Co-ordinate Geometry of Three Dimensions :Distance and division formulae, Direction cosines and direction ratios, Projections, Angles between planes, Angle between a line and plane, Equations of a sphere general equation.

**Calculus:** Differential Calculas:Concept of limit, Continuity, Derivation of standard function, Successive defferentiation, Simple Cases, Leibnitz Theorem, Partial Differentiation, Derivatives as rate measure, Maxima and Minima, Indeterminate forms, Geometrical applications such as tangents and normals to the plane curves. Integeral Calculas: Standard method of integration (Substitution, by parts, by partial fractions, etc), Definite integrals and properties of definite integrals, Areas under plane curves, Differential equations only simple cases such as :

**Trigonometry:** Compound angles , Multiple and sub-multiple angles, solution of trigonometric equations, properties of triangles, Inverse Circular Function.

**Vector:** Fundamentals, Dot and cross product of two vectors, Scalar triple product, Simple applications (to geometry, work and moment).

**ANALYTICAL ABILITY AND LOGICAL REASONING:**

Question in this section will test logical reasoning and quantitative reasoning.

**COMPUTER AWARENESS :**

**Computer Basics: **Organization of a Computer, Central Processing Unit (CPU), Structure of instructions in CPU, input / output devices, computer memory, backup devices.

**Data Representation:** Representation of characters, integers and fractions, binary and hexadecimal representations , Binary Arithmetic : Addition , subtraction, multiplication, division, simple arithmetic and two’s complement arithmetic, floating point representation of numbers, Boolean algebra, truth tables, Venn diagrams.

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