JKBOPEE CET Maths syllabus 2017| JKBOPEE Maths syllabus 2017 | Jammu & Kashmir CET Maths syllabus 2017In the JKOPEE CET 2017 there are 3 compulsory papers i.e. Physics, chemistry and Maths for PCM students who want to take degree in engineering stream. Here we serve JKBOPEE CET mathematics syllabus for JKBOPEE CET 2017 exam for engineering stream students.
UNIT 1: SETS, RELATIONS AND FUNCTIONS (Marks: 06)
Sets and their representation, finite and infinite sets, empty set subsets, subset of real numbers especially intervals, power set , universal set. Venn diagram, union and intersection of sets. Difference of sets, Compliment of a set. Ordered pairs, Cartesian product of sets, number of elements in the Cartesian product of two finite sets. Relations, Domain, co- domain and range of relation, types of relations, reflexive, symmetric, transitive and equivalence relations. Functions as special kind of relations from one set to another, domain, co-domain and range of a function. One to one, onto functions. Real valued functions of the real variable; constant, identity, polynomial, rational, modulus, signum and the greatest integer functions with their graphs. Sum, difference, product and quotients of functions. Composit ion of functions, inverse of a function, binary operations.
Linear inequation: Algebraic solution of linear inequalities in one variable and two variables.
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UNIT 3: SEQUENCE AND SERIES, PERMUTATION AND COMBINATION & BINOMIAL THEOREM (Marks: 06)
Sequence and series: Arithmetic progression (A.P), arithmetic mean (A.M), nth term, sum to n-terms of an A.P, Geometric
progression (G.P) , Geometric Mean (G.M), nth term, sum to n-terms and sum to infinity of a G.P. Relation between A.M and
G.M. Sum to n terms of 𝑛 , 𝑛
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Permutation and combination: Fundamental principle of counting, factorial n, permutations P(n,r) and combinations C(n,r),
Binomial Theorem:. Binomial theorem for positive integral power. general and middle terms in the Binomial expansion.
Pascal‘s triangle and simple applications.
UNIT 4: TRIGONOMETRIC AND INVERSE TRIGONOMETRY FUNCTIONS (Marks: 06)
Positive and negative angles, measuring angles in radians and in degrees, Conversion from one measure to another. Definition
of trigonometric functions with the help of unit circle. Periodicity of Trigonometric functions. Basic Trigonometric identities
x=1 for all Sign of x etc. Trigonometric functions and their graphs. Expressions for
) cot( ), tan( ), cos( ), sin( y x y x y x y x
, sum and product formulae.
Identities related to Sin2x, Cos2x, tan2x, Sin3x, Cos3x, and tan3x. General and principal solutions of trigonometric equations
of the type Sin x= Sin a, Cos x= Cos a , Tan x= Tan a.
Inverse trigonometric functions, range, domain, principal value branches. Graphs of inverse trigonometric functions,
elementary properties of inverse trigonometric functions
UNIT 5: MATRICES AND DETERMINANTS (Marks: 04)
Matrices, concepts, notation, order, equality, types of matrices, Zero matrix, transpose of matri x, Symmetric and skew
symmetric matrices. Addition, multiplication, scaler multiplication of matrices, simple properties of addition, multiplicatio n
and scaler multiplication of matrices. Non-commutativity of multiplication of matrices and existence of non-zero matrices
whose product is the zero matrix (order 2x2). Concept of elementary row and column operation, Invertible matrices and
uniqueness of inverse, if it exists. (Matrices with real entries).
Determinants of square matrix (upto 3x3 matrices) properties of determinants, minors, cofactors and applications of
determinants in finding 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 o f linear equations in two or three variables using inverse
of a matrix.
UNIT 6: LIMIT, CONTINUITY AND DIFFERENTIATION (Marks: 08)
Concept of limit of a function. Theorems on Limits, Evaluation of limits using standard results
Continuity of a function at a point. Continuity of Sum, product and quotient of functions. Derivative: definition of a
derivative of a function, geometrical interpretation of the derivative.
Derivative of sum, difference, product and quotient of two or more functions.
Derivative of algebraic and composite functions.
Derivative of trigonometric and inverse trigonometric functions.
Chain rule, derivative of implicit functions.
Derivative of logarithmic and exponential functions.
Derivative of functions expressed in parametric forms.
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Second order derivatives.
Rolle‘s and Lagrange‘s Mean Value Theorem and their geometrical interpretation and their simple applications.
Application of Derivative: rate of change, increasing and decreasing functions, tangents and normals, approximation, maxima
and minima (first derivative and second derivative test). Simple problems.
UNIT 7: INTEGRATION AND DIFFERENTIAL EQUATIONS (Marks: 07)
Integration as inverse process of differentiation. Integration of variety of functions by Substitution, by parts, by partial
fractions. Simple integrals of the type:
Definite integrals as a Limit of a sum. Fundamental Theorem of calculus. Basic properties of definite integrals Evaluation of
Application of integrals: Application in finding the area under simple curves, especially lines. Areas of cir cles, parabolas and
ellipses (in standard form) Area under the curve y= Sinx, y= Cosx, area between the above two curves.
Differential Equations: Definition, order and degree of a differential equation. General and particular solutions of a
differential equation. Formation of a differential equation whose general solution is given. Solution of differentiation equation
by method of separation of variables. Solution of Homogeneous differential equation of first order and first degree. Solution of
linear differential equation of the type:
+ 𝑝𝑦 = 𝑞, where p and q are functions of x alone and
+ 𝑝𝑥 = 𝑞, where p and q are functions of y alone.
UNIT 8: STRAIGHT LINES AND CONIC SECTIONS (Marks: 05)
Distance between two points, section, slope of a line, angle between two lines, various forms of equations of lines, point -slope
form, intercept form, two point form, and normal form. General equation of a line, distance of a point from a line. Conic
Section: Sections of a cone, circles, parabola, ellipse, hyperbola, a point, a straight line and a pair of intersecting lines as a
degenerated case of conic section. Standard equation of a circle, parabola, ellipse, and hyperbola and their simple propertie s.
UNIT 9: STATISTICS AND PROBABILITY (Marks: 06)
STATISTICS Measure of dispersion, mean, deviation, variance and standard deviation of ungrouped/ grouped data. Analysis
of frequency distribution with equal means but different variances.
PROBABILITY : Random Experiment: outcome, sample spaces.
Events: Mutually exclusive and exhaustive events. Axiomatic (set theoretic) probability, probability of an event, probability of
―Not‖ and ―Or‖ events. Multiplication theorem on probability, conditional probability, independent e vents, total probability,
Baye‘s theorem, random variable and its probability, distribution, mean and variance of a random variable. Repeated
independent (Bernouli) trials and Binomial distribution.
UNIT 10: VECTORS AND THREE DIMENSIONAL GEOMETRY (Marks: 06)
Vectors and scalars, magnitude and direction of a vector Direction Cosines and ratios of a vector. Types of vector, equal, zero,
unit, parallel and collinear vectors. Position vector of a point , negative of a vector, components of a vector, addition of
vectors, Scalar multiplication, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of
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vectors, projection of a vector on a line. Vector (cross) product of vectors, Scalar triple product. Coordinate axes and
Coordinate planes in three dimensions of a point, distance between two points and sectional formula.
STRAIGHT LINES AND SPACE Direction cosines and direction ratios of a line joining two points. Cartesian and vector
equation of a line ( in various forms), coplanar and skew-lines, shortest distance between two lines.
PLANES Cartesian and vector equation of a plane( in various forms). Distance of a point from a plane.
i. Two lines
ii. Two planes.
iii. A line and a plane