JKBOPEE CET Maths syllabus JKCET JKBOPEE Maths syllabus 2017 | Jammu & Kashmir CET Maths syllabus 2017 www.jakbopee.net - Educational Portal

# JKBOPEE CET Maths syllabus JKCET JKBOPEE Maths syllabus 2017 | Jammu & Kashmir CET Maths syllabus 2017 www.jakbopee.net

## JKBOPEE CET Maths syllabus 2017| JKBOPEE Maths syllabus 2017 | Jammu & Kashmir CET Maths syllabus 2017

In 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.
--> UNIT 2: COMPLEX NUMBER; LINEAR INEQUATION; LINEAR PROGRAMMING    (Marks: 06)Complex number: Conjugate of a complex number, modulus and amplitude (argument) of a complex number, Argand‘s plane and  polar  representation  of  complex  numbers, algebraic  properties  of  complex  numbers.  Fundamental  theorem  of  algebra, solution of Quadratic equation in the complex number system. Square root of a complex number.
Linear inequation: Algebraic solution of linear inequalities in one variable and  two variables.

## JKBOPEE CET Maths syllabus 2017

Linear programming: Introduction , definition of related terminology such as constraint s, objective function, optimization, different type of linear programming problem (L.P), mathematical formulation of L.P problem, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions , optimal feasible solutions.
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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.JKBOPEE CET Maths syllabus 2017
Permutation and combination: Fundamental principle of counting, factorial n,  permutations P(n,r) and combinations C(n,r),
simple applications.
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
sin
2
x+cos
2
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.
  Logarithmic differentiation.
  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
definite integrals.
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:
𝑑𝑦
𝑑𝑥
+  𝑝𝑦 = 𝑞, where p and q are functions of x alone and
𝑑𝑥
𝑑𝑦
+  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.
Angle between:
i. Two lines
ii. Two planes.
iii. A line and a plane

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