Syllabus for KIITEE MCA Programme

MATHEMATICS

Unit :-1 Algebra of Sets : Set operations, Union, Intersection, Difference, SymmetricDifference, Complement, Venn Diagram, Cartesian products of sets, Relation and Function, Composite Function, Inverse of a Function, Equivalence Relation, Kinds of Function.

Unit :-2 Number Systems : Real numbers (algebraic and other properties), rational and irrational numbers, Complex numbers, Algebra of complex numbers, Conjugate and square root of a complex number, cube roots of unity, De-moivre’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)

Unit 3:-Trigonometry : Compound angles, Multiple and Sub-multiple angles, solution of trigonometric equations, Properties of triangles, Inverse circular function.

Unit 4:-Co-ordinate Geometry of Two Dimensions : Straight lines, pairs of straight lines, Circles, Equations of tangents and normals 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)

Unit 5:-Co-ordinate Geometry of Three Dimensions: Distance and division formulae, Direction cosines and direction ratios. Projections, Angles between two planes, Angle between a line and plane.Equations of a sphere-general equation.

Unit 6:-Vector Fundamentals, Dot and Cross product of two vectors, Scalar triple product, Simple Applications (to geometry, work and moment).

Unit 7:-Differential Calculus : Concept of limit, continuity, Derivation of standard functions, successive differentiation, simple cases, Leibnitz Theorem, Partial differentiation, Simple cases, derivatives as rate measure, Maxima and minima, indeterminate forms, Geometrical applications such as tangents and normals to plane curves.

Unit 8:-Integral Calculus:- Standard methods of integration ( substitution, by pars, by partial fractions etc.) Definite integrals and properties of Definite Integrals, Areas under plane curves, Differential Equations only simple cases such as

(i) dy/dx = f(x)

(ii) dy/dx=f(x) g (y)

(iii) d2y/dx2 = f(x) and application to motions in a straight line.

Unit 9:-Probability and Statistics :

Averages (Mean, Median and Mode), Dispersion (standard deviation and variance). Definition of probability, Mutually exclusive events, Independent events, Addition theorem.

COMPUTER AWARENESS

Computer Basics: Organization of a Computer, Central Processing Unit (CPU), Structure of instructions in CPU, input/output devices, computer memory, back-up 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 diagram.

ANALYTICAL ABILITY AND LOGICAL REASONING

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

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Veermata Jijabai Tech.Institute MCA Entrance Exam Syllabus

• Computer Concepts
  • Computer Basics: Organization of a computer, characteristics of a computer, Central Processing Unit (CPU), structure of instructions in CPU, input / output devices, computer memory, primary memory and secondary memory, memory organization, backup devices.
  • Data Representation: Representation of characters, integers and fractions, binary and hexadecimal representations.
  • Binary Arithmetic: Addition, subtraction, division, multiplication, signed arithmetic and two-complement arithmetic, floating point, representation of numbers, normalized floating point representations. Boolean algebra, truth tables and Venn diagrams.
  • Computer architecture: Block structure of computers, communication between processor and I/O devices, interrupts, multiprogramming, and virtual memory.
  • Computer language: Assembly language and characteristics of high-level language.
  • Multiprogramming and Timesharing operating systems
  • Computer Programming in C: Data types, expression, evaluation, precedence rules, type conversions, sequential structure, selective structure, repetitive structure, functions (including recursion), arrays, pointers, structures and unions, operations on bits, file processing, preprocessor.
• General Aptitude: The main objectives of this part is to assess the general aptitude of the candidate to pursue a technical profession
  • Logical Reasoning: quantitative reasoning, visuo-spatial reasoning, high school mathematics, vocabulary, English comprehension and verbal ability.
• Mathematics
  • Algebra: Fundamental operations in algebra, expansion, factorization, simultaneous linear / quadratic equations, indices, logarithms, permutations and combinations.
  • Geometry: Angles at a point and parallel lines, triangles, polygons of n sides, circles, geometric transformations – particularly similarity, rotation and reflection, areas.
  • Trigonometry: Trigonometrical ratios, two-dimensional problems on heights and distances.
  • Coordinate Geometry: Rectangular Cartesian coordinates, equations of a line, mid-point, intersections etc., equations of a circle, distance formulae, simple geometric transformations such as translation, rotation, scaling.
  • Mensuration: Areas, triangles and quadrilaterals, area and circumference of circles, volumes and surface areas of simple solids such as cubes, spheres, cylinders and cones.

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Vellore Institute of Technology MCA Entrance Exam Syllabus

English
Sentence Correction, Comprehension

Logical Reasoning

Mathematics
Algebra sets, relations and functions, Summation of series, Progressions (Arithmetic, Geometric and Harmonic), Partial fractions, complex numbers, logarithms.

Differential and Integral Calculus
Limit-Continuity-Differentiability, Successive differentiation, Leibniz theorem (definition and applications), Mean Value Theorems (Role’s and Lagrange’s definitions only), Maxima and Minima, Indefinite and definite integrals, Trapezoidal, Simpson’s rules of integration, Partial differentiation.

Statistics
Mean, median, mode, moments, mean deviation, standard deviation. Moments, correlation and regression.

Probability
Probability, conditional probability, Baye’s theorem, Binomial, Poisson, normal distributions.

Coordinate Geometry
Distance between two points, section formulae, collinear points, centroid. Translation and rotation of coordinates, plane, perpendicular and parallel conditions, Straight-line (slope, slope-intercept form , intercept form, normal form), parallel lines; perpendicular lines; intersection of two lines; Angle between two lines, line passing through intersection of two lines, foot of perpendicular, circle given center and radius, circle passing through extremities of a diameter, circle passing through three points, great circle.

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University of Hyderabad MCA Entrance Exam Syllabus

General Mental Ability :- consisting of items on reasoning, analysis, comprehension and synthesis.

Mathematical topics :- Sets, Relations, Integration, Differentiation, Analytical Geometry, Trigonometry, Matrices, Vectors, Determinants, Differential Equations, Elementary Probability and Statistics, Number Systems, Data Representation, Algorithms and Flowcharts.

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Delhi University MCA Entrance Exam Syllabus

The admission test will carry objective type questions. It will consist of:

1. i.            Quantitative and Mathematical Ability Test
2. ii.            Deductive and Logical Ability Test

The suggested outline of the syllabus for the admission test is as follows:

Quantitative and Mathematical Ability Test

Algebra: Sets, groups, fields, vector spaces; Complex numbers: Demoivre’s theorem and its simple applications; matrices, determinants; Relation between roots sand co-efficients of an equation; Scalar and vector products, triple products.

Calculus: Real number system; Continuity and limits; Differentiation; Integration; Definite integral; Evaluation of lengths and areas of curves; Curvature; Asymptotes; Tracing of curves; Partial differentiation; Differential equations of first order and their solutions; Linear differential equations with constant coefficients; Homogeneous Linear differential equations.

Geometry:
Two-dimensions: straight lines, circles, parabola, hyperbola and ellipse; Classification of curves of second degree.
Three-dimensions: Spheres, quadric cones and cylinders.

Real Analysis:
Sequences: Sequence of real numbers; Convergent sequences, Cauchy sequences; Monotonic sequences; Bounds; Infinite series and their different tests of convergence; Absolute convergence; Uniform convergence.
Properties of continuous functions; Roll’s theorem, Mean Value theorem; Taylor’s and Mclaurin’s series, Maxima and Minima; Indeterminate forms.

Statistics and Linear Programming: Frequency distributions and measures of dispersion, skewness and kurtosis; Permutations and combinations, Probability; Random variables and distribution functions; Mathematical expectation and generating functions; Binomial, Poisson, Normal distribution; Curve fitting and principle of least squares; Correlation and regression; Sampling and large sample test; Test of significance based on t, x² and F distributions.
Formulation of simple linear programming problems; basic concepts of graphical and simplex methods.

Deductive and Logical Ability Test

Interpretation of data, problem solving, flowcharts and algorithms;
Number system: binary, octal, hexadecimal; Truth values, logical operations, logic functions and their evaluation.

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University of Pune MCA Entrance Exam Syllabus

Mathematics

• Set theory: Set operations, relations, functions.
• Propositional logic: Formulation, deduction, evaluation, puzzles.
• Linear Algebra: Solution of a system of linear equations. Determinant and inverse of a matrix, basic properties of matrices.
• Co-ordinate Geometry and Conic Sections: Equations of lines and planes, vector products; definitions and properties of conic sections.
• Trigonometry: Identities, computation of heights and lengths.
• Differential Calculus: Total and partial differentiation, limit of a function.
• Integral Calculus: Definite and indefinite integrals, solution of differential equations, computation of areas and volumes.
• Series and sequences: sum, mean, convergence, limit.
• Real and complex numbers: surds, solution of equations on complex domain.
• Polynomials: solution of quadratic equations, properties of roots of polynomials with real coefficients, binomial expansion, Taylor series.
• Permutations and Combinations.
• Elementary Probability Theory: Computing probability from combinatorial reasoning, conditional probability.

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University of West Bengal MCA Entrance Exam Syllabus

JECA-2007: Question Paper will have two parts

Part – I: Objective type questions on Aptitude Test (100 marks)

Time: One hour

Syllabus of Aptitude test for JECA-2007

• (i) Reasoning , (ii) Problem Solving, (iii) Quantitative Comparison, (iv) Discrete Quantitative Analysis & (v) Data Interpretation.

Part-II: Mathematics (100 marks)

Short Question (not of multiple choice type) to be worked out in details.

Time: One and a half hour.

Syllabus of Mathematics for JECA –2007.

• Analytical Geometry: Cartesian and polar coordinate; Straight line; Circle; Ellipse; Parabola; Hyperbola; Translation & Rotation of axes.
• Algebra: Complex number, De Moiver’s theorem, Solution of linear equations, Determinants, Matrices, Summation of single series, Addition of vectors, Scalar and Vector products, Inequation, Sets and elements, Universal set, Empty set, Subsets, Venn diagram, Union and intersection of sets, Complements, Algebra of sets, Finite sets, Class of sets, Partitions, Cross product, Group, Ring and Field.
• Calculus: Limit, Continuity, Differentiation; Maxima & minima; Taylor & Maclaruin’s Series; Definite and indefinite integrals; First and second order differential equation; Functions of several variables; Partial differentiation.
• Probability & Statistics: Permutation, Combination; Probability; Probability distributions; Mean; Median; Mode; Standard Deviation; Correlation co-efficients.

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UP Technical University MCA Entrance Exam Syllabus

1. MATHEMATICS
   MODERN ALGEBRA: Idempotent law, identities, complementary laws, Demorgan’s theorem, mapping, inverse relation, equivalence relation, Piano’s Axiom, definition of rational numbers and integers through equivalence relation.
   ALGEBRA: Surds, solution of simultaneous and quadratic equations, arithmetic, geometric and harmonic progression, Binomial theorem for any index, logarithms, exponential and logarithmic series, determinants.
   PROBABILITY: Definition, dependent and independent events, numerical problems on addition and multiplication of probability, theorems of probability.
   TRIGONOMETRY: Simple identities, trigonometric equations, properties of triangles, use of mathematical tables, solution of triangles, height and distance, inverse functions, DeMoiver’s theorem.
   CO-ORDINATE GEOMETRY: Co-ordinate geometry of the straight lines, pair of straight lines, circle, parabola, ellipse and hyperbola and their properties.
   CALCULUS: Differentiation of function of functions, tangents and normal, simple examples of maxima of minima, limits of function, integration of function (by parts, by substitution and by partial fraction), definite integral (application to volumes and surfaces of frustums of sphere, cone and cylinder).
   VECTORS: Position vector, addition and subtraction of vectors, scalar and vector products and their applications.
   DYNAMICS: Velocity, composition of velocity, relative velocity, acceleration, composition of acceleration, motion under gravity, projectiles, laws of motions, principles of conservation of momentum and energy, direct impact of smooth bodies, pulleys.
   STATICS: Composition of co-planar, concurrent and parallel forces, moments and couples, resultant of set of coplanar forces and conditions of equilibrium, determination of Centroides in simple case, problems involving friction.
2. STATISTICS
   Theory of probability, Mean, Median, Mode, Dispersion and Standard Deviation.
3. LOGICAL ABILITY
   Questions to test analytical and reasoning capability of candidates.

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University of Jammu MCA Entrance Exam Syllabus

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IIC Delhi MCA Entrance Exam Syllabus

• The entrance examination will consist of a multiple-choice question paper of 3 hours duration having two parts.
  Part I: General English Comprehension; Analytical Ability and Reasoning.
  Part II: Mathematics, Physics, Electronics and Basic knowledge of Computers.
  Though there is no fixed syllabus for the entrance test, a broad outline of the syllabus is suggested below.
  • PART- I
    Marks : 30 (Vocabulary and Comprehension: 10; Analytical Ability and Reasoning: 20)
    This part is intended to test the candidate’s vocabulary and analytical skills at a level essential for accurate comprehension and presentation of material appropriate for this degree. The language background expected will be of the level of English at Senior Secondary Examination. The paper will include passages for comprehension, test of vocabulary (synonyms and antonyms), elementary grammar and syntax.
    The section on Analytical Ability and Reasoning will include standard questions on pattern recognition, logic, Venn diagrams etc. It is not intended to be subject-specific.
  • PART- II
    Marks : 120 (Mathematics: 40; Physics: 40; Electronics and Basic knowledge of Computer: 40)
    This part is intended to test knowledge of the subject.

    MATHEMATICS
    Scalar and vector fields, tangent and normal vectors, gradient, divergence, curl, vector identities, Gauss, Stokes’s and Green’s theorem. Convergent and divergent sequences and series, tests for convergence and divergence, absolute and conditional convergence. Limits, continuity and differentiability of functions. Solutions of first and second order linear homogeneous differential equations. Partial differential equations, separation of variable method. Vibrations of rectangular membranes. Systematic and random errors, Normal law of error. Least square fitting of data (linear case). Fourier series, Fourier transform, Sine and cosine transform, convolution theorem. Laplace transform: transforms of elementary functions and solution of simple differential equations. Matrix algebra. Singular and non-singular matrices. Inverse of a matrix. Eigenvalues and eigenvectors, Hermitian and skew-hermitian, symmetric and antisymmetric, orthogonal and unitary matrices. Similarity transformation, Cayley-Hamilton theorem. Definitions of random sample, parameter, and statistics. Concept of sampling distribution and standard error. Sampling distribution of mean and variance of a random sample from a normal population. Tests of significance. Complex variables: residues, poles, Cauchy’s theorem.

    PHYSICS
    Motion of a charged particle in electric and magnetic fields. Idea of conservation of momentum. Conservative and nonconservative forces. Motion involving both translation and rotation. Motion of a particle under a central force field. Inertial and noninertial frames, fictitious forces. Postulates of special relativity, Lorentz transformation, relativistic transformation of velocity, frequency, energy and momentum. Maxwell’s law of distribution of velocities, mean free path. Transport phenomena: viscosity, conduction and diffusion (simple ideas only). Brownian motion. Laws of thermodynamics: real gases. Properties of thermal radiation, Kirchoff’s law, Stefan-Boltzman law, and Wien’s displacement law. Plank’s law of black body radiation. Fermi-Dirac & Bose-Einstein distribution. Magnetic force between current elements, Ampere’s law. Torque on a current loop in a uniform magnetic field. Faraday’s law of induction, self and mutual induction, energy stored in electric and magnetic field, B-H curve, and energy loss in hysteresis. Maxwell’s equations, wave equation, plane waves in dielectric media. Polarization of e.m. waves; linear, circular and elliptical polarization. Light propagation in uniaxial crystals, double refraction. Modes in rectangular waveguides, energy flow and attenuation in waveguides (simple ideas only).
    Interference, division of amplitude and wavefront. Young’s double slit experiment, biprism, Newton’s rings, Fresnel diffraction due to slit. Fraunhoffer diffraction from single slit. Diffraction grating. Spatial and temporal coherence; elementary concept of laser. Photoelectric effect, Compton effect, wave particle duality, wave packet. Two-slit experiment with electrons. Wave amplitude and wave functions, uncertainty principle, Schrodinger’s equation, probabilistic interpretation. Stationary states, one- dimensional simple harmonic oscillator, infinite and finite potential well. Orbital angular momentum and azimuthal quantum numbers, and space quantization. Electron spin, Stern-Gerlach experiment. Magnetic dipole moment and energy in a magnetic field (classical view only). Zeeman effect, spin-orbit coupling, total angular momentum, vector model of atom: LS and JJ coupling. Law of radioactive decay, theory of successive radioactive transformations, nuclear fission and fusion. X-ray diffraction and Bragg’s Law. Specific heat of solids, Einstein and Debye theories.

    ELECTRONICS AND BASIC KNOWLEDGE OF COMPUTERS
    Network analysis: Kirchoff’s current & voltage law, Norton & Thevenin’s theorem, Mesh and node analysis. Basic features of semiconductor material, diode, transistor, FET, MOSFET and SCR and their applications (rectifier, waveshaping, amplifier & oscillators). Concept of feedback. OP-AMPS & their simple applications, integration, differentiation. Boolean algebra, n-array arithmetics (binary, octal, hexadecimal, 1′s complement 2′s complement). Logic families (RTL, DTL, DCTL, TTL), K-map. Combinational circuits (Adder, Subtractor, MUX, DEMUX), look- ahead carry concept, sequential circuits (flip-flops, registers, counters and memories). Basic idea of modulation & demodulation; AM, FM, PPM, PWM and PAM. Elementary ideas of satellite communication. Multimeters (analog & digital), Q-meter, frequency meter, strain gauge, thermocouple. Basic architecture of 8 bit microprocessors, and simple programmes based on arithmetic instructions. Computer basics, data representation, input/output units, compiler, memory, micro-processor, computer architecture. Fundamentals of high level languages. Disk Operating System (DOS). Computer generations and classifications.

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Thapar Institute of Engg. & Tech. MCA Entrance Exam Syllabus

Section-I
Mathematics

1. Geometry: Two-Dimentional; straight lines, circles and conic sections, Three-Dimensional; straight lines and spheres.

2. Algebra: Sets theory, Relations, Mappings and its applications, Permutations and Combinations, Bionomial Theorem, Complex numbers and their properties: Demoivre’s theorem and its applications.

3. Calculus: Limits, Continuity and Differentiability, Rolle’s and Mean value theorems, Differentiation, Partial Differentiation, Maxima and Minima of functions of one and two variable. Successive differentiation. Integration by using substitution, partial fraction and by parts, Definite integral and its properties, Applications of definite integral to evaluate length and are of simple plane curves.

4. Vector Analysis: Scalar and vector products including their applications.

5. Statistics, Probability and Linear Programming : Measures of Central tendency, Dispersion, Skewness and Kurtosis. Correlation and Regression. Basic concepts of probability, Conditional probability, Baye’s theorem, Discrete and continuous distributions (Binomial, Poisson, and normal distributions), Fundamentals of linear programming problems, Graphical solution, Simplex method and its variants.

6. Matrices: Types of matrices, rank of a matrix, solution of system of linear equations, Cayley Hamilton theorem, Inverse of a matrix, Determinant and its properties.

7. Ordinary Differential Equations: Differential equations of first order and their solutions, Linear differential equations of first and higher order with constant coefficients.

8. Numerical Analysis: Solution of non-linear equations using iterative methods, Interpolation (Newton’s, Lagrange’s and Forward formulae), Numerical Integration (Trapezoid and Simpson Rule).

Section-II

Computer Awareness

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

o Data Representation: Representation of characters, integers, and fractions, binary and hexadecimal representations, Binary Arithmetic: Addition, subtraction, division, multiplication, floating point representation of numbers, normalized floating point representation, Boolean algebra: truth tables, Venn diagrams.

o Computer Architecture: Block structure of computers, communications between processor and I/O devices, interrupts.

o Computer Language and Operating Systems: Flow charts and algorithms, Concepts of low level and high level languages, Computer programming in C (data types, loop and control statements, functions), Fundamentals of operating systems: multiprogramming, multitasking and time sharing systems.

Section-III

General Knowledge/Analytical Ability

The question in this section will cover logical reasoning, quantitative reasoning, visual-spatial reasoning and also this section shall carry questions to test the general awareness about business, finance, industry, transportation, scientific inventions, information technology, governance, healthcare and cultural dimensions etc.

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TANCET MCA Entrance Exam Syllabus

ELIGIBILITY

• A pass in any recognised Bachelor’s Degree of minimum 10+2+3 years duration in any discipline with core Mathematics at +2 school level. (Or) Mathematics / Statistics as one of the subjects at the degree level.

PATTERN

• The Question paper will have 100 objective type questions in 2 hours duration.

SYLLABUS

The Question Paper will be designed to test the capability of the candidates in the following areas:

• Quantitative Ability
• Analytical Reasoning
• Logical Reasoning
• Computer Awareness

There may also be a few questions on verbal activity, basic sciences etc. Candidates have to answer 100 objective type questions in 2 hours. Each question will be followed by four alternate answers.

Evaluation Scheme:
While evaluating the answers, one mark is awarded for each correct answer and 1/3 mark is deducted for each wrong answer. No deduction will be made for questions left unanswered. Multiple shading will be considered as wrong answer and 1/3 mark will be deducted.

TEST DATE & TIME : 26-5-2007 (Saturday) 02.30 p.m. to 4.30 p.m

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Damodar Thackersay University MCA Entrance Exam Syllabus

ELIGIBILITY

• Bachelors Degree with 55% marks and mathematics upto higher secondary or its equivalent.

PATTERN

• An individual should have a minimum 50% credit in the general aptitude and computer concepts of E-Level test. (The score of CST is valid for one year only).

SYLLABUS

The syllabus is same as that of CST.

• General Aptitude: Logical reasoning, quantitative reasoning, visuo-spatial reasoning, high school math’s, vocabulary, English comprehension & verbal ability.
• Mathematics: Set, relations & mapping, pure arithmetic, algebra, geometry, trigonometry, co-ordinate geometry, mensuration.
• Computer Concepts: Computer basics, data representation, binary arith- metic, computer languages (assembly languages & characteristics of high level languages etc.).

NUMBER OF SEATS: 25
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Symbiosis Centre for IT MCA Entrance Exam Syllabus

Logical Reasoning & Analytical Thinking, Mathematical Skills and English comprehension / General Knowledge.

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Symbiosis Institute of C.S & Research MCA Entrance Exam Syllabus

1. General English: Reading Comprehension, Verbal Reasoning, Verbal Ability

2. Quantitative, Data Interpretation & Data Sufficiency

3. General Awareness: General Knowledge, Current Affairs, Business Scenario

4. Analytical & Logical Reasoning.

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