# JKCET 2022 Mathematics Syllabus (Released) – Get Mathematics Syllabus PDF Here

The **Jammu and Kashmir Board of Professional Entrance Examination (JKBPEE) **has organized the Jammu and Kashmir Common Entrance Test **(JKCET 2022).**

which is the state level entrance test and it is offering various professional courses to the candidates through this entrance examination known as **JKCET 2022.
**

JKCET is conducted for taking admission into the Various **Engineering Professional courses.** JKCET will help the candidates to get admission into the **B.Tech** and **B.E** courses across the Jammu and Kashmir Union Territory.

## JKCET Mathematics Syllabus

**JKCET Mathematics Syllabus 2022** has been released officially by the **JKCET 2022** authority online. Students can download the **JKCET 2022 syllabus** into PDF format.

**Unit 1-**

**Sets, Relations, And Functions (Marks -06)**

Sets and their representation, finite and infinite sets, empty set subsets, a subset of real numbers especially intervals, power set, universal set. Venn diagram, union, and the intersection of sets.

The difference of sets, Complement of a set.Ordered pairs, Cartesian product of sets, number of elements in the Cartesian product of two finite sets.

Relations, Domain, codomain, and range of a relation, types of relations, reflexive, symmetric, transitive, and equivalence relations. Functions as a 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. Composition of functions, the inverse of a function, binary operations.

**Unit 2: **

**Complex Number; Linear In equation; 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.

The fundamental theorem of algebra, solution of Quadratic equation in the complex number system.The square root of a complex number.

**Linear Inequation:**

The Algebraic solution of linear inequalities in one variable and two variables. Linear programming: Introduction, the definition of related terminology such as constraints, the objective function, optimization, a different type of linear programming problem (L.P), the 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 ****Theorems (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 2and n 3. 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 the unit circle. Periodicity of Trigonometric functions.

Basic Trigonometric identities sin2 x+cos2 x=1 for all Sign of x etc.

Trigonometric functions and their graphs. Expressions for sin(x y),cos(x y),tan(x y),cot(x y), 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 a matrix, Symmetric, and skew-symmetric matrices. Addition, multiplication, scalar multiplication of matrices, simple properties of addition, multiplication, and scalar multiplication of matrices. Non-commutativity of multiplication of matrices and existence of non zero matrices whose product is the zero matrices **(order 2×2).**

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 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 a number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables using the inverse of a matrix. differentiation. Integration of a variety of functions by

**Unit 6: **

## Limit, Continuity, And Differentiation (Marks: 08)

Concept of the 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.

- A derivative of the sum, difference, product, and quotient of two or more functions.
- A derivative of algebraic and composite functions.A derivative of trigonometric and inverse trigonometric functions.
- Chain rule, derivative of implicit functions.
- The derivative of logarithmic and exponential functions.Logarithmic differentiation.
- The derivative of functions expressed in parametric forms. 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 the inverse process of diSubstitution, by parts, by partial fractions. 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 circles, parabolas, and ellipses **(in standard form)** Area under the curve y= Sinx, y= Cox, 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. The solution of differential equations by the method of separation of variables.

The solution of Homogeneous differential equation of first order and first degree. The solution of the linear differential equation of the type.

**Unit 8: **

**Straight Lines and Conic Sections (Marks: 05)**

Distance between two points, section, the slope of a line, the 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 the conic section. Standard equation of a circle, parabola, ellipse, and hyperbola and their simple properties.

**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 events, total probability, Baye’s theorem, random variable and its probability, distribution, mean and variance of a random variable. Repeated independent **(Bernoulli)** 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.

The position vector of appointing, negative of a vector, components of a vector, the addition of vectors, Scalar multiplication, 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. Coordinate axes and coordinate planes in three dimensions of a point, the 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, the shortest distance between two lines.

**Planes:** Cartesian and vector equation of a plane **(in various forms)**. The 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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