GCET Maths Syllabus 2017 | GCET 2017 Maths Syllabus
For the mathematics site course the maths subjects comes in the GCET 2017 test. The maths is also one of the essential subject in GCET 2017 test and there are only 6 units comes into GCET 2017 test. Here we give detail about
GCET mathematics syllabus please read it very carefully.
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 inverse trigonometric functions. Elementary properties of
inverse trigonometric functions.
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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-commutativity of multiplication of
matrices and 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. 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 × 3 matrices), properties of
determinants, 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.
GCET Maths Syllabus 2017 UNIT III: CALCULUS
1. Continuity and Differentiability Continuity and differentiability, derivative of
composite functions, chain rule, derivatives of inverse trigonometric functions,
derivative of implicit function. Concepts of exponential, logarithmic functions.
Derivatives of x e
log and x
e . Logarithmic differentiation. 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 and 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 Integration as inverse process of differentiation. Integration of a variety of
functions by substitution, by partial fractions and by parts, only simple integrals of
the type –
∫ ±
2 2
x a
dx
, ∫
±
2 2
x a
dx
, ∫
−
2 2
a x
dx
,∫ ax + bx + c
dx
2
, ∫
ax + bx + c
dx
2
dx
ax bx c
px q
∫ + +
+
2
( )
, dx
ax bx c
px q
∫
+ +
+
2
( )
, a x dx ∫
±
2 2
, x a dx ∫
−
2 2
ax bx c dx ∫
+ +
2
, px q ax bx c dx ∫
+ + +
2
( )
to be evaluated.
Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without
proof). Basic properties of definite integrals and evaluation of definite integrals.
4. Applications of the Integrals Applications in finding the area under simple curves,
especially lines, arcs of circles/parabolas/ellipses (in standard form only), area
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 method of separation
of variables, homogeneous differential equations of first order and first degree.
Solutions of linear differential equation of the type –
Py Q
dx
dy
+ = where P and Q are functions of x or constant
Px Q
dy
dx
+ = where P and Q are functions of y or constant
GCET Maths Syllabus 2017 UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY
1. Vectors Vectors and scalars, magnitude and direction of a vector. Direction
cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and coplanar
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 vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection
of a vector on a line. Vector (cross) product of vectors, scalar triple product.
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.
GCET Maths Syllabus 2017 UNIT V: LINEAR PROGRAMMING
Introduction, related terminology such as constraints, objective function,
optimization, different types of linear programming (L.P.) problems, mathematical
formulation of L.P. problems, graphical method of solution for problems in two
variables, feasible and infeasible regions, feasible and infeasible solutions, optimal
feasible solutions (up to three non-trivial constraints).
GCET Maths Syllabus 2017 UNIT VI: 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) trials
and Binomial distribution.
www.dtegoa.gov.in
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