Together with mathematics class 9 pdf

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Mathematics 12 by R D Sharma is a very good book for the concepts and practice material including a lots of solved questions with proper explanation. If you have done a chapter, the Together With Maths is very good to get proper practice. Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function.

Definition, range, domain, principal value branch. Elementary properties of inverse trigonometric functions. 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.

Adjoint and inverse of a square matrix. Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Derivatives of logarithmic and exponential functions. Integration as inverse process of differentiation.

Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the types given in the syllabus and problems based on them. Basic properties of definite integrals and evaluation of definite integrals. 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 method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type given in the syllabus. Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Direction cosines and direction ratios of a line joining two points.