## 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**

- Chapter 1 Relation and Function Ex 1(a)
- Chapter 1 Relation and Function Ex 1(b)
- Chapter 1 Relation and Function Ex 1(c)

**CHSE Math Solution Class 12 Pdf Chapter 2 Inverse Trigonometric Functions**

**Elements of Mathematics Class 12 Volume 2 Chapter 3 Linear Programming**

- Chapter 3 Linear Programming Ex 3(a)
- Chapter 3 Linear Programming Ex 3(b)
- Chapter 3 Linear Programming Additional Exercise

**Elements of Mathematics Class 12 Book Solutions Chapter 4 Matrices**

**CHSE Odisha Class 12 Math Book Pdf Download Chapter 5 Determinants**

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

- Chapter 6 Probability Ex 6(a)
- Chapter 6 Probability Ex 6(b)
- Chapter 6 Probability Ex 6(c)
- Chapter 6 Probability Ex 6(d)
- Chapter 6 Probability Additional Exercise

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

- Chapter 7 Continuity and Differentiability Ex 7(a)
- Chapter 7 Continuity and Differentiability Ex 7(b)
- Chapter 7 Continuity and Differentiability Ex 7(c)
- Chapter 7 Continuity and Differentiability Ex 7(d)
- Chapter 7 Continuity and Differentiability Ex 7(e)
- Chapter 7 Continuity and Differentiability Ex 7(f)
- Chapter 7 Continuity and Differentiability Ex 7(g)
- Chapter 7 Continuity and Differentiability Ex 7(h)
- Chapter 7 Continuity and Differentiability Ex 7(i)
- Chapter 7 Continuity and Differentiability Ex 7(j)
- Chapter 7 Continuity and Differentiability Ex 7(k)
- Chapter 7 Continuity and Differentiability Ex 7(l)
- Chapter 7 Continuity and Differentiability Ex 7(m)

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

- Chapter 8 Application of Derivatives Ex 8(a)
- Chapter 8 Application of Derivatives Ex 8(b)
- Chapter 8 Application of Derivatives Ex 8(c)
- Chapter 8 Application of Derivatives Ex 8(d)
- Chapter 8 Application of Derivatives Ex 8(e)
- Chapter 8 Application of Derivatives Ex 8(f)
- Chapter 8 Application of Derivatives Additional Exercise

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

- Chapter 9 Integration Ex 9(a)
- Chapter 9 Integration Ex 9(b)
- Chapter 9 Integration Ex 9(c)
- Chapter 9 Integration Ex 9(d)
- Chapter 9 Integration Ex 9(e)
- Chapter 9 Integration Ex 9(f)
- Chapter 9 Integration Ex 9(g)
- Chapter 9 Integration Ex 9(h)
- Chapter 9 Integration Ex 9(i)
- Chapter 9 Integration Ex 9(j)
- Chapter 9 Integration Ex 9(k)
- Chapter 9 Integration Ex 9(l)
- Chapter 9 Integration Additional Exercise

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

**CHSE Odisha Class 12 Math Book Pdf Chapter 11 Differential Equations**

- Chapter 11 Differential Equations Ex 11(a)
- Chapter 11 Differential Equations Ex 11(b)
- Chapter 11 Differential Equations Ex 11(c)
- Chapter 11 Differential Equations Additional Exercise

**Elements of Mathematics Class 12 Odisha Pdf Download Chapter 12 Vectors**

- Chapter 12 Vectors Ex 12(a)
- Chapter 12 Vectors Ex 12(b)
- Chapter 12 Vectors Ex 12(c)
- Chapter 12 Vectors Ex 12(d)
- Chapter 12 Vectors Additional Exercise

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

- Chapter 13 Three Dimensional Geometry Ex 13(a)
- Chapter 13 Three Dimensional Geometry Ex 13(b)
- Chapter 13 Three Dimensional Geometry Ex 13(c)
- Chapter 13 Three Dimensional Geometry Additional Exercise

### 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:

- 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)
- 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)
- 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.