




MEGALEAP 
Comprehensive MCA Entrance Coaching 


ARENA 

MEGALEAP  the time bound brilliant and exhaustive course proudly conducted by SANMACS INDIA, towards MCA Entrance Examination, is taught and guided by the resultoriented professionals who are undoubtedly great doyens in their fields having immaculate expertise and specialization in their respective areas. Needless to say, they have pioneered hundreds of students of SANMACS INDIA to join the Software/ I.T. industries of India and abroad perennially.


ENTRANCE INFORMA 

MCA is a time bound three year (sixsemester) course, approved by All India Council of Technical Education (AICTE) and conducted by almost all the Universities of India.
The selection of the students is based on a written test. The aspiring students with Bachelor's or equivalent degree thereof with minimum of 50% to 60% (subject to notification) are eligible. (This apart, candidates appearing for Bachelor's degree can also apply). Some Universities may also need mathematics at the graduation level. The entrance test mainly consists of Mathematics, and Logical and Analytical Reasoning. In some universities, the knowledge of Elementary English and Computer Awareness is also examined. Everywhere, there is a paucity of admissible seats, owing to highcaliber competitions. Hence, mainly those students who figure out in the topmost priorities are able to procure the assured seats.
Exactly with these intentions to tailor the students to capture the high profile MCA seats, SANMACS INDIA (a provenly pioneer institution which has annexed the umpteen proportions of seats at various premier MCA entrance tests, consistently with an accelerating success rate beyond 80% for all the several years since its inception with an incredible passion) has been conducting MEGALEAP  the time bound preparatory course for MCA ENTRANCE TEST for admission to the various premier institutions of India.


COURSE PROFILE 

Any Student desirous of doing MCA from a good University/Institute is eligible to apply for this course. Different Eligibility Criterions are to be met for different Megaleap Variants i.e., Regular , Jet, Combo, Swing etc.
The time duration for different courses are different. The Course Curriculum includes adequate number of regular classroom sessions along with periodic tests and follow up discussions. The institute maintains its distinctness from other similar coaching centers by engaging the students with sufficiently suitable assignment problems for home practice apart from the classroom lectures by professional experts in the respective fields. Barring this, the center arranges periodic tests as well as quick follow up discussions enabling the students with the wide opportunity to interact closely with the teachers of the faculty. It has a double advantage. On the one hand, it consolidates a student's competence to deal with tricklish and twisted questions and on the other hand boosts up his confidence satisfactorily. Further more, monthly tests are religiously conducted even after the regular course period in order to help the student remain always in touch with detailed and exhaustive testtopics. To sum up, the teaching members of the institute treat every entrance testaspiring examinee with great academic personal care.


COURSE CONTENTS 

The Institute abides mainly by the following syllabus: 

MATHEMATICS 

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


MATRICES AND DETERMINANTS
Matrix operations, Definition and properties of determinats, Cofactors, Adjoint, Elementry Transformations, Rank and inverse of a Matrix, Matrix Polynomial, Characteristic Equations,Eigen Values, Latent Vectors, Caylay Hamilton theorem, Linear system of Equations


THEORY OF EQUATIONS
Polynomials and their charcteristics, Roots of an equation, Relations between Roots and Coefficients,Transformation of Equations, Symmetric function etc.


ABSTRACT ALGEBRA
Groups, Cyclic groups, Subgroups, Normal Groups, Lagrange’s theorem, Homomorphism, Isomorphism, Ring, Field, Vector Spaces, Linear Independence of Vectors, Basis, Dimension, Linear Transformation and diagonalisation of Matrices etc 

VECTOR ALGEBRA
Scalar and Vector quantities their representation, Addition and subtraction of vectors, Scalar and vector product of two vectors, Scalar triple product, Expansion formula of Vector triple product 

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


CALCULAS AND REAL ANALYSIS
Real number system, Concept of neighborhood and limit points, Continuity and limits, Indeterminate forms, properties of continuous functions in 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 of curves, Curvature, Asymptotes, Tracing of curves, Partial Differentiation, functions of two variables, definition of partial derivates, Total differentiation, Sequence, Sequence of real numbers, Convergent Sequences, Cauchy Sequences, Monotonic Sequences, Infinite series of positive terms and their different test of convergence,Alternating infinite series and Leibnitz's test of convergence, Absolute convergence, Conditional convergence, Uniform Convergence, Multiple integration, Change of order and change of variables, Application to evaluation of Area, Surface and volume.


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


COORDINATE GEOMETRY 

2d:
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 of middle point, Diameter of Conic, Conjugate diameter, Classification of curves of second degree. 

3d: Introduction to lines and planes, Spheres, Quadric Cones and Cylinders. 

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

NUMERICAL ANALYSIS
Interpolation, Extrapolation, Quadrature formula, Simpson's 1/3rd rule, Trapezoidal rule, Solution of nonlinear equations using iterative methods, Numerical differentiation.


STATISTICS
Classifications of Data and frequency distribution, Calculation of measures of Central tendency and measures of dispersion, Skewness and Kurtosis, Permutation and Combination, Probability, Random variables and distribution functions, Mathematical expectations and generating functions, Binomial, Poisson, Geometric, Exponential and Normal distributions, Curve fitting and principal of least square, Correlation and Regression,Index numbers and their importance,Simple Time Series analysis, Sampling and large sample tests,test of significance based on t, Chisquare and F distributions 

COMPUTER AWARENESS 

COMPUTER BASICS
Organization of a computer, Central Processing Unit (CPU), Structure of instructions in CPU, input / output devices, computer Memory, memory organization, backup devices. 

DATA REPRESENTATION Representation of characters, integers, and fractions, binary and Hexadecimal representations 

BINARY ARITHMETIC Addition, subtraction, division, multiplication, single arithmetic and two complement arithmetic, floating point representation of numbers, normalized floating point representation, Boolean Algebra, truth tables, Venn diagrams 

COMPUTER ARCHITECTURE Block structure of computers, communication between processor and I / O devices, interrupts 

COMPUTER LANGUAGE Assembly language and high level language, Multiprogramming and time sharing operating systems, Computer Programming in C 

MATHEMATICAL LOGIC Venn Diagrams in logic, Logical operators, Negations, Logical Equivalence and Tautology 

FLOW CHART AND ALGORITHMS 

BASICS OF DATA STRUCTURE 

ANALYTICAL ABILITY AND LOGICAL REASONING
This part of the syllabi deals with enhancing candidates logical reasoning, quantitative reasoning and visuospatial Reasoning besides grooming the students to deal with practical logical situations in the best possible manner. 

ELEMENTARY ENGLISH AWARENESS
Basic English Awareness of the students would be enriched to cater to the needs of a MCA Entrance Examination The institute heartily welcomes the feedback from its passedout students pursuing MCA course form different Universities as well as its enrolled students also with many other multifarious topics to supplement its syllabus with broader unforeseen up to date topics. The institute vows to remain abreast of every additional information in the study curriculum and pledges to transport them inside the cerebral cavity of the students. 

Note :
The aforesaid studycontent is open to any modification and/ or alteration depending upon the amenable factors and conditions.
The institute heartily welcomes the feedback from its passedout students pursuing MCA course from different Universities as well as its enrolled students also with many other multifarious topics to supplement its syllabus with broader unforeseen up to date topics. The institute vows to remain abreast of every additional information in the study curriculum and pledges to transport them inside the cerebral cavity of the students. 














