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RD Sharma is one of the noteworthy books when it comes to the preparation of Mathematics. RD Sharma Class 12 Textbooks<\/strong> is based on the latest syllabus prescribed by the CBSE. Students can download RD Sharma Solutions for Class 12 from this page.<\/p>\n\n\n\n

R.D. Sharma (Ravi Dutt Sharma) is a popular name when we talk about mathematics. R.D. Sharma\u2019s textbooks for mathematics today are a popular choice among students and others who prepare for competitive exams. The solutions provided here also talk about various mathematics techniques, tips and tricks for quick and easy calculations and you can conquer maths easily.<\/p>\n\n\n\n

You can also Download\u00a0Class 12 Maths NCERT Solutions<\/a>\u00a0to help you to revise the complete Syllabus and score more marks in your examinations.<\/p>\n\n\n\n

RD Sharma Solutions Class 12 are a set of solutions to the questions and exercises in the textbook “RD Sharma Mathematics” commonly used in schools in India for Class 12. The solutions provide step-by-step explanations of how to solve the questions, making it easier for students to understand the concepts and techniques involved.<\/p>\n\n\n\n

RD Sharma Solutions Class 12<\/h2>\n\n\n\n

RD Sharma Solutions Class 12 cover a wide range of topics, including algebra, geometry, trigonometry, and calculus, and are designed to help students build a strong foundation in math and prepare for higher studies and career opportunities in science, engineering, and other fields.<\/p>\n\n\n\n

These solutions are properly explained with correct methods and explanations that will aid the students while solving the questions.<\/p>\n\n\n\n

Here we are covering complete chapters of RD Sharma Class 12 Solutions to help the students for their studies exam preparation.<\/p>\n\n\n\n

Check the list of the chapters given below that are covered in Class 12 RD Sharma<\/p>\n\n\n\n

RD Sharma Solutions for Class 12 Chapter Wise<\/th><\/tr><\/thead>
Chapter 1\u2013Relation<\/a>
<\/strong>The chapter Relations in this textbook contains two exercises that are based on the relations and their properties, types of relations, inverse of a relation, equivalence relation, some useful results on relations, reflexive relation, symmetric relation, and transitive relation.<\/td><\/tr>
Chapter 2\u2013Functions<\/a>
<\/strong>The chapter functions in this book give an account of various topics such as the definition of functions, function as a correspondence, function as a set of ordered pairs, the graph of a function, vertical line test, constant function, identity function, modulus function, the greatest integer function, properties of the greatest integer function covered in its two exercises, exercise 2.1 and 2.1.
While the topics like the smallest integer functions and their 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 are covered in Exercise 2.3.<\/td><\/tr>
Chapter 3\u2013Binary Operations<\/a>
<\/strong>The chapter binary operation consists of a total of five exercises that are based on 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 \u2018n\u2019, and multiplication modulo \u2018n\u2019.<\/td><\/tr>
Chapter 4\u2013Inverse Trigonometric Functions<\/a>
<\/strong>There is only one exercise in this chapter that is based on the definition and meaning of inverse trigonometric functions, the inverse of the sine function, inverse of the cosine function, inverse of the tangent function, inverse of secant function, inverse of cosecant function, inverse of cotangent function, and properties of inverse trigonometric functions.<\/td><\/tr>
Chapter 5\u2013Algebra of Matrices<\/a>
<\/strong>The chapter Algebra of Matrices in this book contains a total of five exercises. Exercises 5.1 and 5.2 are based on the 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. Moreover, the exercises 5.3 to 5.5 are based on the topics 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.<\/td><\/tr>
Chapter 6\u2013Determinants<\/a>
<\/strong>This chapter in this book provides 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 Sarrus diagram, singular matrix covered in first three exercises 6.1 to 6.3. However, exercises 6.4 and 6.5 are based on the topics 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 conditions for consistency. <\/td><\/tr>
Chapter 7\u2013Adjoint and Inverse of a Matrix<\/a>
<\/strong>Adjoint and Inverse of a Matrix, we shall see the definition of the adjoint of a square matrix, the inverse of a matrix, some useful results on invertible matrices, elementary transformations of elementary operations of a matrix via examples, and verbal problems related to it. <\/td><\/tr>
Chapter 8\u2013Solution of Simultaneous Linear Equations<\/a>
<\/strong>The chapter Solutions of Simultaneous Linear Equations in this book based on the topics 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. The mentioned topics are covered in a total of two exercises only.<\/td><\/tr>
Chapter 9\u2013Continuity<\/a>
<\/strong>The chapter continuity is covered in two exercises only that concentrate on 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.<\/td><\/tr>
Chapter 10\u2013Differentiability<\/a>
<\/strong>The chapter differentiability is based on the advanced concepts of the previous class i.e. differentiability at a point, differentiability in a set, and some useful results on differentiability. The concepts are explained in two exercises thoroughly.<\/td><\/tr>
Chapter 11\u2013Differentiation<\/a>
<\/strong>The Differentiation in this book constitutes topics related 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.<\/td><\/tr>
Chapter 12\u2013Higher Order Derivatives<\/a>
<\/strong>The concepts covered in this chapter are 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 covered in only one exercise.<\/td><\/tr>
Chapter 13\u2013Derivatives as a Rate Measurer<\/a>
<\/strong>This chapter introduced the derivative as a rate measurer. The concepts in this chapter cover how to find 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 covered in its two exercises. <\/td><\/tr>
Chapter 14\u2013Differentials, Errors and Approximations<\/a>
<\/strong>This chapter deals with the topic of differentials and errors. The topics that are discussed include the definition of differentials, absolute error, relative error, percentage error, the geometrical meaning of differentials with algorithms, and finding the approximate value using differentials.<\/td><\/tr>
Chapter 15\u2013Mean Value Theorems<\/a>
<\/strong>This chapter is all about the theorems related to mean values. It also deals with Rolle\u2019s theorem, geometrical interpretation of Rolle\u2019s theorem, algebraic interpretation of Rolle\u2019s theorem, the applicability of Rolle\u2019s theorem, Lagrange\u2019s mean value theorem, geometrical interpretation of Lagrange\u2019s mean value theorem, verification of Lagrange\u2019s mean value theorem, applications of Lagrange\u2019s mean value theorem and proving inequalities by using Lagrange\u2019s mean value theorem covered in its two exercises.<\/td><\/tr>
Chapter 16\u2013Tangents and Normals<\/a>
<\/strong>The chapter basically 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, which is covered in its first exercise only. Moreover, the topics like the equations of tangent, 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 are covered in its last two exercises 16.2 and 16.3.<\/td><\/tr>
Chapter 17\u2013Increasing and Decreasing Functions<\/a>
<\/strong>The present chapter deals with the concepts of increasing and decreasing functions, solution of rational algebraic inequations with algorithms, strictly increasing functions, strictly decreasing functions which are covered in its first exercise that is exercise 17.1. However, the 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 are covered in its Exercise 17.2.<\/td><\/tr>
Chapter 18\u2013Maxima and Minima<\/a>
<\/strong>The chapter Maxima and Minima deal with the maximum and minimum values of a function in its domain, the definition of maximum, local maxima, and local minima, definition, and meaning of local maximum covered in the first two exercises while, the first derivative test for local maxima and minima along with algorithm, higher-order derivative test, point of inflection, point of inflection, properties of maxima and minima, maximum and minimum values in the closed interval and applied problems on maxima and minima are covered in exercises 18.3, 18.4 and 18.5. <\/td><\/tr>
Chapter 19\u2013Indefinite Integrals<\/a>
<\/strong>The chapter indefinite integrals explain the concepts of the primitive and anti derivative, 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 explained very well through examples in total of thirty-two exercises.<\/td><\/tr>
Chapter 20: Definite Integrals
<\/strong>This chapter comes in the continuation of the above-mentioned chapter. This chapter helps to learn about the definite integral of a function that remains associated with the antiderivative and indefinite integral explained in its first three exercises, Exercises 20.1, 20.2, and 20.3. However, the other topics like the definite integrals as a limit of a sum, properties of definite integrals, fundamental theorem of calculus, etc are covered in exercises 20.4 and 20.5.<\/td><\/tr>
Chapter 21: Areas of Bounded Regions
<\/strong>There are four exercises in this chapter that helps to learn about how to draw the rough sketches of several types of curves that mainly enclose one region.<\/td><\/tr>
Chapter 22: Differential Equations
<\/strong>The present chapter consists of a total of eleven exercises that cover different topics like how to solve the differential equations, what properties can be used to solve differential equations, etc.<\/td><\/tr>
Chapter 23 Algebra of Vectors
<\/strong>The chapter Algebra of vectors refers to the action of performing algebraic operations on different types of vectors. In total nine exercises the concepts of the vectors in 2D, as well as 3D space, are also explained.<\/td><\/tr>
Chapter 24: Scalar Or Dot Product
<\/strong>This chapter consists of two exercises that help to understand how to find scalar products of vectors along with the important properties of scalar or dot products.<\/td><\/tr>
Chapter 25: Vector or Cross Product
<\/strong>This chapter in the present book covers the topics like equality of vectors, vector products, properties of vector products, vector products of unit vectors, vector products of perpendicular vectors, area of a triangle, and parallelogram in just one exercise only.<\/td><\/tr>
Chapter 26: Scalar Triple Product
<\/strong>This chapter is also a part of vector algebra which helps to learn how to find the scalar triple product of vectors and properties of the scalar triple product explained in one exercise only.<\/td><\/tr>
Chapter 27: Direction Cosines and Direction Ratios<\/strong>
This chapter is an elaborated version of trigonometry. This chapter helps to learn about direction ratios that provide an easy way to specify the direction of a line in any 3D space. Here is only one exercise that includes the problems based on the mentioned topics.<\/td><\/tr>
Chapter 28 Straight line in space<\/strong>
The chapter straight line in space discusses a line that extends on both sides still infinitely without any use of curves. This chapter in total contains five exercises only that help to understand each and every concept of a straight line.<\/td><\/tr>
Chapter 29: The plane<\/strong>
A plane refers to a flat 2D surface that contains infinite dimensions but has zero thickness. The present chapter has fifteen exercises that basically help to understand the concepts such as finding slope, x-intercept, and y-intercept.  <\/td><\/tr>
Chapter 30: Linear programming<\/strong>
This chapter gives the knowledge about some methods that help in the formation of linear equations. Here are five exercises in which the problems like finding the maximum and minimum value of an equation within a given set of conditions can be asked.<\/td><\/tr>
Chapter 31: Probability<\/strong>
The probability in this class is a bit advanced than the probability learned in previous classes. There are seven exercises that help to study different methods to find the probability of different organized events. <\/td><\/tr>
Chapter 32: Mean and variance of a random variable<\/strong>
This chapter is an extension of the probability chapter. There are two exercises in this chapter that covers different topics like Bayes theorem, how to find the mean of random variables, and how to find the variance of random variables. <\/td><\/tr>
Chapter 33: Binomial Distribution<\/strong>
This chapter is an extension of statistics and probability. There are only two exercises in this chapter that includes problems based on the binomial distribution and how to calculate Bernoulli trials.<\/td><\/tr><\/tbody><\/table>
RD Sharma Solutions for Class 12 Chapter Wise<\/figcaption><\/figure>\n\n\n\n

RD Sharma Solutions Class 12 are available online, in the form of PDFs or online interactive tools, and can be accessed by students for free or at a nominal cost. They are an important resource for students preparing for exams, as they provide detailed explanations and examples that can help students learn and practice different math concepts.<\/p>\n\n\n\n

Overall, RD Sharma Solutions Class 12 are a valuable resource for students and teachers looking to improve their understanding and skills in mathematics.<\/p>\n\n\n\n

Benefits of Using RD Sharma Solutions<\/strong><\/h2>\n\n\n\n