# CHSE Odisha Class 12 Math Book Solutions | Elements of Mathematics Class 12 CHSE Odisha Solutions Pdf Download

## CHSE Odisha 12th Class Math Book Solutions | Elements of Mathematics Class 12 Solutions CHSE Odisha Pdf Download

Elements of Mathematics CHSE Solutions Class 12 Chapter 1 Relation and Function

CHSE Math Solution Class 12 Pdf Chapter 2 Inverse Trigonometric Functions

Elements of Mathematics Class 12 Volume 2 Chapter 3 Linear Programming

Elements of Mathematics Class 12 Book Solutions Chapter 4 Matrices

Elements of Mathematics Class 12 CHSE Odisha Pdf Download Chapter 6 Probability

Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 7 Continuity and Differentiability

Plus 2 2nd Year Science Math Book Pdf Chapter 8 Application of Derivatives

Elements of Mathematics Class 12 Solutions CHSE Odisha Pdf Download Chapter 9 Integration

Class 12 Elements of Mathematics Book Pdf Chapter 10 Area Under Plane Curves

CHSE Odisha Class 12 Math Book Pdf Chapter 11 Differential Equations

Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 13 Three Dimensional Geometry

### CHSE Odisha Class 12 Maths Syllabus (+2 2nd year)

Mathematics (+2 2nd year)
Course Structure

 Unit Topic Marks No. of Periods I Relations and Functions & Linear Programming 20 45 II Algebra and Probability 20 45 III Differential Calculus 20 45 IV Integral Calculus 20 45 V Vector 3-D Geometry 20 45 Total 100 220

General Instructions:

1. All questions are compulsory in Group A, which are very short answer-type questions. All questions in the group are to be answered in one word, one sentence, or as per the exact requirement of the question. (1 × 10 = 10 Marks)
2. Group B contains 5(five) questions and each question has 5 bits, out of which only 3 bits are to be answered (Each bit carries 4 Marks) (4 × 15 = 60 Marks)
3. Group-C contains 5(five) questions and each question contains 2/3 bits, out of which only 1(one) bit is to be answered. Each bit caries 6(six) Mark (6 × 5 = 30 Marks)

Unit I Relations and Functions

Chapter 1 Relations and Functions
Types of relations, reflexive, symmetric, transitive, and equivalence relations. One-to-one and onto functions, composite functions, the inverse of a function. Binary operations.

Chapter 2 Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

Chapter 3 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 (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit II Algebra

Chapter 4 Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices; Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication, and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (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).

Chapter 5 Determinants
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle, and Adjoint and inverse of a square matrix. Consistency, inconsistency, and a number of solutions of a system of linear equations by examples, solving a system of linear equations in two or three variables (having unique solution) using the inverse of a matrix.

Chapter 6 Probability
Conditional probability, multiplication theorem on probability. Independent events, total probability, Baye’s theorem, Random variable, and its probability distribution, mean and variance of a random variable. Independent (Bernoulli) trials and Binomial distribution.

Unit III Differential Calculus

Chapter 7 Continuity and Differentiability
Continuity and differentiability, a derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.
Derivatives of logarithmic and exponential functions. 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 interpretation.

Chapter 8 Applications of Derivatives
Applications of derivatives: rate of change of bodies, increasing and decreasing functions, tangents, and normals, use of derivatives in approximation, maxima, and minima (first derivative test motivates 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).

Unit IV Integral Calculus

Chapter 9 Integration
Integration as the inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions, and by parts, Evaluation of simple integrals of the following types and problems based on them.
$$\int \frac{d x}{x^2 \pm a^2}, \int \frac{d x}{x^2 \pm a^2}, \int \frac{d x}{a^2-x^2}, \int \frac{d x}{a x^2+b x+c}$$
$$\int \frac{d x}{a x^2+b x+c}, \int \frac{p x+q}{a x^2+b x+c} d x$$
$$\int \frac{p x+q}{a x^2+b x+c} d x, \int \sqrt{a^2 \pm x^2} d x$$
$$\int \sqrt{x^2-a^2} d x$$
$$\int \sqrt{a x^2+b x+c} d x, \int(p x+q) \sqrt{a x^2+b x+c} d x$$
Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

Chapter 10 Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/parabolas/ ellipses (in standard form only). The area between any of the two above-said curves (the region should be clearly identifiable).

Chapter 11 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 the method of separation of variables, solutions of homogeneous differential equations of the first order and first degree. Solutions of linear differential equation of the type:
$$\frac{dy}{dx}$$ + py = q, wherep and q are functions of x or constants.
$$\frac{dx}{dy}$$ + px = q, where p and q are functions of y or constants.

Unit V Vectors and Three-Dimensional Geometry

Chapter 12 Vectors
Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, the addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties, and application of scalar (dot) product of vectors, vector (cross) product of vectors, a scalar triple product of vectors, and Coplanarity of three vectors.

Chapter 13 Three-dimensional Geometry
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

Books Recommended:
Bureau’s Higher Secondary (+2) Elements of Mathematics, Part-II, Published by Odisha State Bureau of Text Book Preparation and Production, Bhubaneswar.