Logarithmic differentiation, derivative of, functions expressed in parametric forms. Concept of exponential and, logarithmic functions., Derivatives of logarithmic and exponential functions. Continuity and Differentiability, (20 Periods), Continuity and differentiability, derivative of composite functions, chain rule, derivatives of, inverse trigonometric functions, derivative of implicit functions. Consistency, inconsistency and number of solutions of system of linear, equations by examples, solving system of linear equations in two or three variables (having, unique solution) using inverse of a matrix.,, UNIT-III: CALCULUS, 1. Determinants, (25 Periods), Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle.
Invertible matrices and proof of the uniqueness of, inverse, if it exists (Here all matrices will have real entries).Ģ. Concept, of elementary row and column operations. Non-commutativity of multiplication of matrices and existence of nonzero matrices whose product is the zero matrix (restrict to square matrices of order 2). Simple properties of addition, multiplication, and scalar multiplication. Operation on matrices: Addition and, multiplication and multiplication with a scalar. Matrices, , (25 Periods),, Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of, a matrix, symmetric and skew symmetric matrices. Graphs of inverse trigonometric functions., Elementary properties of inverse trigonometric functions.,, UNIT-II: ALGEBRA, 1. Inverse Trigonometric Functions,, (15 Periods),, Definition, range, domain, principal value branch. One to one and onto, functions, composite functions, inverse of a function., 2. Relations and Functions,, (15 Periods),, Types of relations: reflexive, symmetric, transitive and equivalence relations. SYLLABUS, Central Board of Secondary Education, New Delhi, MATHEMATICS Class–XII, (2021-22), Time: 3 hours, S.