CHSE Odisha +2 2nd Year Math Book Solutions | Elements of Mathematics Vol 2 | Elements of Mathematics Vol 1
Chapter-1 Relation and Function
Chapter-2 Inverse Trigonometric Functions
- Inverse Trigonometric Functions Ex 2
Chapter-3 Linear Programming
- Linear Programming Ex 3(a)
- Linear Programming Ex 3(b)
Chapter-4 Matrices
- Matrices Ex 4(a)
- Matrices Ex 4(b)
Chapter-5 Determinants
- Determinants Ex 5(a)
- Determinants Ex 5(b)
Chapter-6 Probability
- Probability Ex 6(a)
- Probability Ex 6(b)
- Probability Ex 6(c)
- Probability Ex 6(d)
Chapter-7 Continuity and Differentiability
- Continuity and Differentiability Ex 7(a)
- Continuity and Differentiability Ex 7(b)
- Continuity and Differentiability Ex 7(c)
- Continuity and Differentiability Ex 7(d)
- Continuity and Differentiability Ex 7(e)
- Continuity and Differentiability Ex 7(f)
- Continuity and Differentiability Ex 7(g)
- Continuity and Differentiability Ex 7(h)
- Continuity and Differentiability Ex 7(i)
- Continuity and Differentiability Ex 7(j)
- Continuity and Differentiability Ex 7(k)
- Continuity and Differentiability Ex 7(l)
- Continuity and Differentiability Ex 7(m)
Chapter-8 Application of Derivatives
- Application of Derivatives Ex 8(a)
- Application of Derivatives Ex 8(b)
- Application of Derivatives Ex 8(c)
- Application of Derivatives Ex 8(d)
- Application of Derivatives Ex 8(e)
- Application of Derivatives Ex 8(f)
- Application of Derivatives Additional Exercise
Chapter-9 Integration
- Integration Ex 9(a)
- Integration Ex 9(b)
- Integration Ex 9(c)
- Integration Ex 9(d)
- Integration Ex 9(e)
- Integration Ex 9(f)
- Integration Ex 9(g)
- Integration Ex 9(h)
- Integration Ex 9(i)
- Integration Ex 9(j)
- Integration Ex 9(k)
- Integration Ex 9(l)
Chapter-10 Area Under Plane Curves
- Area Under Plane Curves Ex 10
Chapter-11 Differential Equations
- Differential Equations Ex 11(a)
- Differential Equations Ex 11(b)
- Differential Equations Ex 11(c)
Chapter-12 Vectors
- Vectors Ex 12(a)
- Vectors Ex 12(b)
- Vectors Ex 12(c)
- Vectors Ex 12(d)
Chapter-13 Three Dimensional Geometry
- Three Dimensional Geometry Ex 13(a)
- Three Dimensional Geometry Ex 13(b)
- Three Dimensional Geometry Ex 13(c)
CHSE Odisha Plus 2 Mathematics Syllabus (Class 12)
| 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.
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:
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.