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GOA CET Maths Syllabus
Engineering Entrance , Goa CET (Engg)
Mathematics Subject Syllabus GOA Common Entrance Test:
UNIT -I : RELATIONS AND FUNCTIONS
1. Relations and Functions :
Types of relations : reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function.
Binary operations.
2. Inverse Trigonometric Functions.
Definition range, domain, principal value branches, Graphs of Triangle & inverse trigonometric functions. Elementary properties of inverse trigonometric
functions. Periodicity of function and fundamental period.
UNIT - II : ALGEBRA
1. Matrices :
Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix. Symmetric and skew symmetric matrices. Addition, multiplication and
scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication Non-commutatively of multiplication of matrices &
existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations.
PROSPECTUS FOR PROFESSIONAL DEGREE COURSES 2008-09 DIRECTORATE OF TECHNICAL EDUCATION, ALTO-PORVORIM, GOA, 403521
Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
2. Determinants :
Determinant of a square matrix (up to 3 x 3 matrices) properties of determinations, minors, cofactors and applications of determinants in finding the
area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by
examples, solving system of linear equations in two or three variables ( having unique solution ) using inverse of a matrix.
UNIT - III CALCULUS
1. Limits , Continuity and Differentiability :
Revision of algebraic limits, exponential limits, logarithmic limits, limits of trigonometric and inverse trigonometric functions. Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivatives of ax , ex , log x , apx+q, eax+b , log ( ax + b ) using first principle. Derivative of functions expressed in parametric forms. Second order derivatives Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretations.
2. Applications of Derivatives :
Applications of derivatives rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima and minima (First derivative test motivated geometrically and Second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
3. Integrals
MISSED CHECK FROM PDF
Applications of the Integrals :
Applications in finding the area under simple curves, especially lines, area of circles/parabolas/ellipses (in standard form only), are between the two above
said curves (the region should be clearly identifiable).
5. Differential Equations :
Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by methods of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type.
UNIT - IV : VECTORS AND THREE-DIMENSIONAL
GEOMETRY
1. Vectors :
Vectors and scalars, magnitude and direction of a vector. Direction cosines /rations of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position product of vectors, projection of a vector on a line. Vector (cross) product of vectors, scalar triple product , volume of a parallelepiped, vector triple product and its properties.
2. Three - dimensional Geometry :
Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane, Distance of a point from a plane.
UNITS - V : PROBABILTY
1. Probability :
Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye's theorem Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trial and Binominal distribution.
APPENDIX
1. Proofs in Mathematics :
Through a variety of examples related to mathematics & already familiar to the leaner, bring out different kinds of proofs direct, contra positive, by contradictions, by counter example.
2. Mathematical Modelling :
Modelling real-life problems where many constraints may really needs to be ingoted (continuing form Class XI) However now the models concerned would use techniques/results of matrices, calculus and linear programming.
PROSPECTUS FOR PROFESSIONAL DEGREE COURSES 2008-09 DIRECTORATE OF TECHNICAL EDUCATION, ALTO-PORVORIM, GOA, 403521
Prescribed textbooks (Published by Goa Board of Secondary and Higher Secondary Education, Porvorim)
1. Mathematics Part-I Textbook for Class XIIth
2. Mathematics Part-II Textbook for Class XIIth
Prepare Goa Cet physics exam syllabus as designed by Goa common entrance test board, for perfect preparation.
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