RD Sharma Class 12 Solutions for Maths 2023 For Term 1 & Term 2: Students can readily download RD Sharma Solutions for Class 12 Maths PDF to begin proper study for their upcoming board exams or competitive exams. These solutions will shift every student's attitude toward Mathematics and will undoubtedly help them realize how enjoyable and simple the subject is, as Mathematics is a difficult subject for Class 12 students. Download the RD Sharma Class 12 Maths Solutions now and go over all of the questions.
Students also have access to extra online study materials and resources, such as notes, books, question papers, exemplar problems, worksheets, and so on, which are available at Kopykitab.
These RD Sharma Solutions Class 12 can be used by students to gain knowledge.
Relations and their properties, types of relations, the inverse of a relation, equivalence relation, some important conclusions on relations, reflexive relation, symmetric relation, and transitive relations are all covered in Chapter 1 of the RD Sharma textbook.
The second chapter, Functions of RD Sharma Class 12 Maths, covers a variety of topics, like the definition of functions, the graph of a function, function as a correspondence, function as a set of ordered pairs, vertical line test, modulus function, greatest integer function, constant function, identity function, properties of greatest integer function, smallest integer functions and its properties, fractional part function, signum function, exponential function, logarithmic function, reciprocal and square root function, square function, square root function, cube function, reciprocal squared function, operations on real function, kinds of functions such as one-one, many-one and onto function, bijection, the composition of functions and its properties and composition of real functions.
Meanwhile, students will learn how to relate the graphs of a function to its inverse in this chapter.
In Chapter 3 of RD Sharma's Maths Exam textbook, we will focus on a binary operation, the number of binary operations, types of binary operations such as commutativity, associativity and distributivity, an identity element, inverse of an element, composition table, addition modulo ‘n’, and multiplication modulo ‘n’.
The concept of the inverse of a function is covered in Chapter 4 of RD Sharma Solutions Maths. Students will get to learn about the definition and concept of inverse trigonometric functions, the inverse of the cosine function, the inverse of the sine function, the inverse of the tangent function, the inverse of the cosecant function, the inverse of the secant function, inverse of the cotangent function, and properties of inverse trigonometric functions.
The definitions of Matrices begin Chapter 5 of the RD Sharma textbook. Students will learn about types of matrices, equality of matrices, the addition of matrices, properties of matrix addition, multiplication of a matrix by a scalar, properties of scalar multiplication, subtraction of matrices, multiplication of matrices, properties of matrix multiplication, positive integral powers of a square matrix, transpose of a matrix, properties of transpose, symmetric and skew-symmetric matrices via examples. Students can find exercises that adequately explain these concepts and provide solutions here.
The sixth chapter of RD Sharma's textbook contains a definition of determinants, determinant of a square matrix of order 1, 2, and 3, determinant of a square matrix of order 3 by using the Sarrus diagram, singular matrix, minors, and cofactors, properties of determinants, evaluation of determinants, applications of determinants to coordinate geometry and applications of determinants in solving a system of linear equations and condition for consistency.
Students can find exercises that appropriately explain the 12th-Grade Board Exam Ch 6 concepts here.
The concept of the adjoint of a square matrix, the inverse of a matrix, some important results on invertible matrices, elementary transformations of elementary operations of a matrix via examples, and verbal problems related to it are all covered in Chapter 7. We have included exercises with solutions based on the chapter's topics.
We continue our discussions on equations starting with definition, consistent system, homogeneous and non-homogeneous systems, matrix method for the solution of a non-homogeneous system, and final solution of a homogeneous system of linear equations. in Chapter 8 of the RD Sharma textbook.
Students focus on the following topics in this chapter: the definition of continuity, continuity at a point, algebra of continuous function, continuity on an interval, continuity on an open interval, continuity on a closed interval, continuous function, everywhere continuous function, and properties of continuous functions.
The answers to the exercises in this chapter can be found here.
Differentiability is the focus of this chapter. We will apply the basic facts and formulae we learned in Class 11 in this chapter, along with the topics like differentiability at a point, differentiability in a set, and some useful results on differentiability.
The solutions to the exercises from this chapter, which have adequately explained the topic, have been put here.
Topics relating to differentiation, differentiation of inverse trigonometric functions from first principles, differentiation of a function, differentiation of inverse trigonometric function by chain rule, differentiation by using trigonometric substitutions, differentiation of implicit functions, logarithmic differentiation, differentiation of infinite series, differentiation of parametric functions and differentiation of a function with respect to another function via illustrations are covered in Chapter 11 of RD Sharma's Class 12 Maths.
Higher-order derivatives are introduced to students in this chapter. This chapter covers the following topics: proving relations involving various order derivatives of cartesian functions, proving relations involving various order derivatives of parametric functions, and proving relations involving various order derivatives via illustrations.
The derivative as a rate measurer is introduced to students in this chapter. This chapter's concepts include: how to find the rate measurer of derivative and related rates in which the rate of change of one of the quantities involved is required, corresponding to the given rate of change of another quantity. This chapter provides extra word problems to assist students in effectively learning sentence formation.
Differentials and errors are covered in Chapter 14 of RD Sharma's Class 12 Maths. The following are some of the topics that are discussed: the definition of differentials, absolute error, relative error, percentage error, the geometrical meaning of differentials with algorithms, and finding the approximate value using differentials.
Theorems related to mean values will be discussed in this chapter. It also covers Rolle’s theorem, geometrical interpretation of Rolle’s theorem, algebraic interpretation of Rolle’s theorem, the applicability of Rolle’s theorem, Lagrange’s mean value theorem, geometrical interpretation of Lagrange’s mean value theorem, verification of Lagrange’s mean value theorem, applications of Lagrange’s mean value theorem and proving inequalities by using Lagrange’s mean value theorem.
This chapter deals with the slope of a line, slopes of tangent and normal, finding slopes of tangent and normal at a given point, finding the point on a given curve at which tangent is parallel or perpendicular to a given line, and normal with an algorithm, finding the equation of tangent and normal to a curve at a point, finding tangent and normal parallel or perpendicular to a given line, finding tangent or normal passing through a given point, angle of intersection of two curves and orthogonal curves.
Below are links to the solutions for each of the exercises in this chapter.
The topic of increasing and decreasing functions, solution of rational algebraic inequations with algorithms, strictly increasing functions, strictly decreasing functions, monotonic functions, monotonic increasing, and monotonic decreasing functions, necessary and sufficient conditions for monotonicity, finding the intervals in which a function is increasing or decreasing and proving the monotonicity of a function on a given interval is covered in Chapter 17 of RD Sharma's textbook.
Maxima and Minima, Chapter 18 in RD Sharma's textbook, deal with the maximum and minimum values of a function in its domain, the definition of maximum, local maxima, and local minima, the definition and meaning of local maximum, the first derivative test for local maxima and minima along with algorithm, higher-order derivative test, point of inflection, properties of maxima and minima, maximum and minimum values in the closed interval and applied problems on maxima and minima. Students can find exercises that adequately explain these ideas and provide solutions here.
Students focus on the following topics in this chapter: indefinite integral, primitive and antiderivative, fundamental integration formulae, some standard results on integration, integration of trigonometric functions, integration of exponential functions, geometrical interpretation of indefinite integral, comparison between differentiation and integration, methods of integration, integration by substitution, integration by parts, integration of rational algebraic functions by using partial fractions and integration of some special irrational algebraic functions. These concepts are well-explained with examples. The answers to the exercises in this chapter can be found here.
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