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# RD Sharma Maths Solutions for Class 6 to 12

Here is a complete list of RD Sharma Solutions for Class 6 to 12. These solutions will help students to score good in exams like JEE Mains and Advanced as well as in their board exams

## RD Sharma Solutions for Class 6

The RD Sharma Solutions for Class 6 th are designed to provide best practice problems and inculcate problem-solving skills. The journey begins with Chapter 1, knowing our numbers. It includes writing numerals in varied numerical forms, word format, expanded notation, place value, face value, etc. It introduces students to the Indian and International system of numeration. Chapter 2 is playing with numbers, and it includes factors, multiples, divisibility test, odd and even numbers. Prime factorisation, HCF, LCM, and statement problems are also included in the concepts of prime, co-prime and composite numbers. Chapter 3 is whole numbers, and it briefs students about successors, predecessor, number line and various analytical problems. Chapter 4 is operations on whole numbers, and it is designed to provide overall practice to the students on pattern and word problems. Different properties like associative property, distributive property are also explained in this chapter.

Chapter 5 is about negative numbers and integers, and it includes the introduction of integers, how to represent them on a number line, their arrangement in ascending and descending order. Students get to practice questions on arithmetic problems related to integers. Chapter 6 is Fractions, where students learn how to divide a figure into shaded and unshaded regions based on fractions. Representation of fractions on the number line, conversion of fractions, simplification, ascending and descending arrangements are included. Later, students learn how to solve word problems related to fractions and perform arithmetic calculations with them. Chapter 7 is decimals, and it includes addition, subtraction, multiplication and division of decimals. It also covers decimals on the number line, converting fractions to decimals or vice-versa and related word problems. Chapter 8 is an introduction to algebra, and it is a part of mathematics in which the concept of variables and constants are introduced.

This chapter deals with numbers, variable entities and signs which have their specific operations. Students are introduced to 'x' related problems and their procedures to get the answer. Chapter 9 is ratio, proportion and unitary method. Here, students learn how to express certain fractions and word problems in ratios and represent various units in simplest forms and related problems. Chapter 10 is basic geometrical concepts. It helps students understand the formation of lines, angles and shapes. It gives a basic idea about parallel and intersecting lines, collinear points, curved and closed figures. Chapter 11 gives information on various angles like an acute, obtuse, straight, complete, right angle, etc. Chapter 12 is based on triangles. It is a plane figure formed by three non- parallel line segments. This chapter deals with calculating the angles of a triangle under varied conditions and certain terms like median, bisector, altitude, types of triangles, etc. Chapter 13 is quadrilaterals. Here students learn about quadrilaterals, formulas and techniques to find sides and angles of different quadrilaterals and related word problems. Chapter 14 is circles, and students get acquainted with terms like chord, diameter, arc and segment of a circle.

Students learn various tricks to find these entities of the circle when a few others are given. In chapter 15, pair of lines and transversal, students learn how to draw parallel lines and calculate the distance between them. It also includes concepts like transversals, angles made by transversals and the relation between angles. Chapter 16 is the three-dimensional understanding of shapes that we see every day around us. Students get a brief idea about faces, edges and vertices of various shapes like cube, cuboids, cylinder, sphere, pyramid, etc. Chapter 17 is symmetry.

Here students learn how different objects in nature possess symmetry and how to classify them on this basis. Chapter 18 is basic geometrical tools which explain the use of tools like ruler, dividers, compass, and protractor to the students, which are used to construct various geometrical shapes. Chapter 19 is geometrical constructions. Here, students learn how to draw a line, line segment, perpendiculars and angles using geometrical tools. Chapter 20 is mensuration, and it includes problems based on perimeter and area covered by various shapes. The last three chapters belong to the concept of Data Handling, where students will make the presentation of data and draw pictographs and bar graphs.

The chapters contained in the RD Sharma Solutions for class 6 are:

## RD Sharma Solutions for Class 7

Chapter 1 is integers, where students will learn how to perform arithmetic operations using the concept of BODMAS in integers. Chapter 2 is fractions. Various formulae are introduced to solve problems involving fractions. The difficulty level of word problems has also increased by moulding the language to enhance students' logical thinking. Chapter 3 is decimals, and it discusses addition, subtraction, multiplication and division of decimals, and related problems are solved. Chapter 4 is rational numbers, where students learn how to represent rational numbers with required numerators and denominators. The concept of equivalent pairs and the number line is also studied. Chapter 5 is operations on rational numbers, and it includes learning statement problems and complex equations. Chapter 6 is exponents.

The chapter provides knowledge about using the laws of exponents to solve a statement question or a problem. Students get exposure to solving questions based on prime factorisation, laws of exponents and expanded exponential form. Chapter 7 is algebraic expressions, and here students learn about factors and coefficients, like and unlike terms, operations of positive/negative terms and how to solve various algebraic expressions. Types of brackets and the use of two variables or group symbols are also introduced in this chapter. Chapter 8 is linear equations in one variable. A linear equation can be regarded as an equation that has one as its highest power. Students learn how to analyse a statement problem to frame a linear equation and solve it to obtain the final answer. Different methods like the trial and error method and systematic assuming methods are also learnt to solve the equations thus formed. Chapter 9 is ratio and proportion, and it teaches students to convert ratios in simplest forms and define the term proportionality, ratio and equivalent ratio. Students learn how to compare two different entities to get the value of the third one. Chapter 10 is the unitary method which teaches the students how to find the value of many articles by first knowing the value of a single article.

Chapter 11 in the class 7 th RD Sharma is a percentage, where students learn the conversion of fractions, ratios and decimals to percentage or vice versa and find a percentage of a given number. Chapter 12 is profit and loss. Students learn to solve problems involving co-relation of cost price, selling price, profit, loss and adjacent percentages. Chapter 13 is simple interest where students are introduced to principal, interest rate, amount, time, etc. This chapter holds great importance in solving several finance-related problems at home or the workplace. Chapter 14 is lines and angles. The exterior, interior, alternate, corresponding and corresponding angles are explained in this chapter. Problems involve questions in which angles are calculated by correlating various concepts. Chapter 15 is the properties of triangles. It contains various types of triangles, and their angle sum property and elements are studied here.

Furthermore, students get acquainted with the Pythagoras theorem, triplets, its converse and related problems. Chapter 16 is congruence which introduces various conditions of congruency of various shapes are studied in this chapter. Chapter 17 is construction, and as the name suggests, the construction of various types of shapes, especially the triangles, is learnt here. Chapter 18 is symmetry. The chapter introduces different types of lines of symmetry in different types of shapes. Chapter 19 is visualising solids, and it involves analysing various figures and Euler's formula. Chapter 20 and 21 is mensuration, where students learn how to calculate the perimeter and area of rectilinear figures. The last four chapters include data handling; here, the young minds get to know how to collect and organise data, central values, construction of bar graphs and probability. The Aakash RD Sharma Solutions help these 7 th graders a lot with building their concepts. The solutions play a vital role in guiding the students and supporting them when they are stuck on a problem.

The chapter in the RD Sharma Solutions for class 7 includes the following:

## RD Sharma Solutions For Class 8

Chapter 1 is rational numbers, where students learn how to use various properties to solve different operations of rational numbers. Chapter 2 powers teaches students to express numbers in the form of powers, or vice versa is studied here. Chapter 3 is squares and square roots where subtopics include making prime factors, identifying perfect squares, and Pythagorean triples. Chapter 4 is cubes and cube roots. Here, students learn how to calculate cubes and cube roots using the column method and cube root tables. Chapter 5 plays with numbers and helps the students to solve the problems in which digits of a number are interchanged to get the original number. Various divisibility tests are also studied in this chapter. Chapter 6 is algebraic expressions and identities, and this chapter explains how to solve problems involving logical operations of monomials and binomials. Chapter 7 is factorisation, and it includes the factorisation of monomials, binomials, and polynomials. Chapter 8 is the division of algebraic expressions, and it includes learning how a monomial divides another monomial and polynomial via the long division method. Chapter 9 is a linear equation in one variable, and it deals with solving questions involving making equations in one variable, having variables on one side and numerals on the other. Cross-multiplication and transposition methods are employed for solving the equations.

Chapter 10 is direct and inverse variations. Students learn about two different types of variations, i.e. direct and inverse. Chapter 11 is time and work, and it teaches about the general rules and problems related to time and works under various circumstances. Chapter 12 is a percentage, and it focuses on conversion and percent related word problems are reviewed here. Chapter 13 is based on profit, loss, discount and value-added TAX (VAT), and terms like marked price (MP), discount%, gain%, etc., are studied, and problem questions are analysed. These chapters are very important for students as they involve problems that they face in real life too. Chapter 14 is compound interest, and various formulas are included in this chapter which helps students find out compound interest when calculated annually, half-yearly and quarterly. Population growth and depreciation related problems are also studied here. Chapter 15, 16 and 17 revolves around understanding the shapes of polygons and quadrilaterals. Topics such as angle sum property of triangles and quadrilaterals, interior and exterior angle sum property and types of quadrilaterals are included. Chapter 18 is practical geometry, where students learn the construction of quadrilaterals under certain given conditions. Chapter 19 is visualising shapes, three-dimensional representation of shapes like a prism, pyramids, polyhedral, etc. and their visualisation is studied. Chapter 20, 21 and 22 includes mensuration in three parts. In the first part, we study the area of a trapezium and a polygon. In the second part, volumes and surface areas of cube and cuboids are studied. In contrast, the third part includes the surface area and volume of a right circular solid or hollow cylinder.

Chapters 23, 24, 25 and 26 covers data handling in three portions. The first part includes classification and tabulation of data and its conversion from raw data to grouped data. The second portion is the graphical representation of data in the form of a bar graph, histogram, pie- chart, etc. and the last topic is probability. Finally, the last chapter is an introduction to graphs. Here students learn how to draw different types of graphs in a Cartesian plane via plotting various points.

The chapters of class 8th curriculum which are included in the RD Sharma Solutions provided by the Aakash Institute are:

## RD Sharma Solutions For Class 9

Chapter 1 of RD Sharma Solutions Math for class 9 th is numbers. It includes topics such as types of numbers, i.e. rational and irrational, their representation on the number line, perfect squares and laws of exponents. Students learn how to present rational numbers as decimals. Chapter 2 is exponents of real numbers. Here various laws of integral exponents and rational exponents of a real number are studied. The students practise assumption and simplification based problems. Chapter 3 is rationalisation, and it contains problems based on identities and the rationalisation of the denominator. Chapter 4 is algebraic identities, where students study various identities and their use in solving various binomial and trinomial based questions. Chapter 5 is a factorisation of algebraic expressions, and factorisation represents a larger number as a product of small numbers. Students will learn how to perform factorisation using the formulae for the cube of a binomial and factorisation of algebraic expressions.

Chapter 6 is a factorisation of polynomials. The concept of zeros of a polynomial, remainder theorem and the factor theorem is studied here. Solving questions based on the factorisation of polynomials using factor theorem helps the students grasp the chapter better. Chapter 7 introduces Euclid's geometry, and this chapter explains the concepts like theorems and axioms, incidence properties, parallel and intersecting lines, line segment, length axioms and plane. Chapter 8 is lines and angles. The chapter contains information about types of angles and their co-relation. The types of questions involving a determination of angle under various conditions are also studied here. Chapter 9 is a triangle and its angles. The questions included in this chapter are based on the concepts like angle sum property of triangle, angle sum property of exterior and interior angles, etc. Chapter 10 is congruent triangles, and it explains that congruence in geometry is the property of two different objects with the same shape and size. Congruence criteria of triangles and inequality relations are studied in this chapter.

Chapter 11 coordinates geometry explains Cartesian coordinates, plotting of points, various formulas and tricks are studied over here. Chapter 12 is Heron's Formula; this new concept and its applications are taught to the students. Chapter 13 is a linear equation in two variables, and this chapter deals with questions in which solutions are calculated via graphical representation of linear equations. Practising the word problems will make the concept crystal clear. Chapter 14 is quadrilaterals; their properties and important facts are studied in this chapter. The surface area, perimeter, median of a triangle and various properties are studied in this chapter. Chapter 15 is areas of a parallelogram, and as the name indicates, this chapter includes questions in which sides, angles and other entities of a closed figure are calculated using different rules, theorems and properties.

Chapter 16 is circles, and it deals mainly with the topics like a chord, segment, arcs, etc. Problems are based on cyclic quadrilaterals, congruence of circles and various combined properties of quadrilaterals. Chapter 17 is construction. Here, students learn the construction of line segment, angle, bisector, circle, perpendicular, triangle, etc., using various geometry tools. Chapter 18 is the surface area and volume of cuboids and a cube. The chapter contains practise problems for the students to get the essence of the concepts taught. Chapter 19 is the surface area and volume of a right circular cylinder, and questions based on daily life cylindrical objects such as a container or a plastic tin are present in this chapter. Chapter 20 is the surface area of the right circular cone. The formulas to find the same are introduced in the chapter.

Chapter 21 is the surface area and volume of a sphere. The concept, formulae of surface area and volume of a solid or hollow sphere is studied in this chapter and applied in the question given. Chapter 22 and 23 is a tabular and graphical representation of statistical data. Chapter 24 measures central tendency, and it involves basic concepts like the arithmetic mean of grouped data, median, and how to measure the central tendency of data. The last chapter is probability, and it is one of the most interesting chapters of this book.

The chapters included in the RD Sharma Solutions for class 9 are listed below:

## RD Sharma Solutions For Class 10

Chapter 1 of RD Sharma Class 10th is Real Numbers. This chapter begins with the introduction of Euclid's division algorithm and the fundamental theorem of arithmetic. Students will learn how to find LCM and HCF using Euclid's division lemma. The chapter also revisits rational and irrational numbers. How to prove these numbers as irrational and their decimal expansions is also studied here. Chapter 2 is polynomials, and linear polynomials, the geometric meaning of the zeros of a polynomial, the relationship between zeros and coefficients of a polynomial are topics covered in this chapter. Students also learn the division algorithm for polynomials and their verification. Chapter 3 is pair of linear equations in two variables; it involves concepts like graphical and algebraic methods of solution of a pair of linear equation. Students learn how to apply substitution, elimination and cross-multiplication methods for solving upstream and downstream problems. Chapter 4 is triangles, and this chapter deals with similar figures, the similarity of triangles and criteria of similarity of triangles. Questions are based on finding the area of similar triangles, Pythagoras theorem and congruence of triangles.

Chapter 5 is trigonometric ratios, and 6 is trigonometric identities. In these chapters, students will learn about various trigonometric functions, formulas and questions based on them. Chapter 7 is statistics, and it revolves around mean mode and median. The mean of a grouped data is the average of all observations, the observation having maximum frequency is called mode, and the median is a measure of central tendency, which gives the value of the middle-most observation in the data. Chapter 8 is quadratic equations. Here, students learn how to check if an equation is quadratic or not and find the solution of a quadratic equation by factorisation. Chapter 9 is arithmetic progression, and it is a series of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term. Students will get well-acquainted with terms like infinite arithmetic progressions, n th term of an AP and the sum of first n terms of an AP. Different types of practice problems are included in the chapter. Chapter 10 covers the basics of a circle like a tangent, the length of a tangent, the angle subtended by them and related questions.

Chapter 11 is construction, and here, students learn step-wise division of a line segment and construction of tangents to a circle. Chapter 12 is some applications of trigonometry. The concept of height and distance, angle of depression, angle of elevation, line of sight and questions based on them are included in this chapter. Chapter 13 is a probability that includes a lot of theoretical approaches. Here, the students learn to find the probability of a sure event, impossible event, elementary event, complimentary event, etc. Chapter 14 is coordinate geometry, and terms like abscissa and ordinate are introduced in this chapter. Further topics to be included are distance formula, section formula, and problems based on them.

Chapter 15 is related to circles. This chapter begins with an overview of the perimeter and area of a circle. Then, students learn to calculate the sector and segment of a circle and areas of the combination of plane figures. Chapter 16 is surface area and volumes, and the chapter introduces solids like cube, cuboids, cone, cylinder and sphere. The basic aim of the chapter is to teach students to calculate the surface area and volume of a combination of solids and the conversion problems of solids from one shape to another. The frustum of a cone and questions based on them is a new topic for the students. The RD Sharma solutions provide much-required help to the students for their board exams.

The RD Sharma solutions for class 10 contain the topics which help the students to prepare efficiently for their school and board exams, and the chapters contained in the solutions include:

## RD Sharma Solutions For Class 11

The first chapter of RD Sharma Solutions of Class 11th is Sets. The concept of set serves as a fundamental part of present-day mathematics. This chapter deals with sets and their representations, types of sets, i.e. empty sets, finite and infinite sets, subsets and power sets. Students get to know about the Venn diagram, properties of the operation of union and intersection, complement of a set, its properties and practical problems on union and intersection of two sets. Chapter 2 is relations, and in this chapter the product of sets and relations is explained. Chapter 3 is functions that explain that a special type of relation is called function. Algebra of real functions, different functions and their graphs is also studied in this chapter. Chapter 4 is a measurement of angles. The students learn the most common measurement units, i.e. degree measure and radian measure. Relation between radian and real numbers and the relation between degree and radian are other relevant topics. Chapter 5 is trigonometric functions, and topics like fundamental trigonometric identities, signs of trigonometric ratios or identities and trigonometric ratios of allied angles are studied. Chapter 6 helps students learn how to draw graphs of trigonometric functions and their algorithms. Chapter 7 is trigonometric ratios of compound angles, and this chapter includes finding trigonometric ratios of sum and difference of two angles and maximum and minimum values of trigonometric expressions. Chapter 8 is transformation formulae which deal with the formulae to transform the product into sum or difference and formulae to transform the sum or difference into the product.

Chapter 9 is trigonometric ratios of multiple and sub-multiple angles. The students learn how to express trigonometric ratios of angle 2A in terms of that angle A, A in terms of A/2, angle A/2 in terms of Cos A, 3A in terms of angle A, etc. and practice problems based on them. Chapter 10 is sine and cosine formulae and their applications. This chapter involves the law of sines or sine rule, applications of sine formula in problems on heights and distances and problems based on them. Other important concepts are the law of cosines, projection formulae and the law of tangents.

Chapter 11 is trigonometric equations, and it explains the general solutions of trigonometric equations. Chapter 12 is mathematical induction which uses the principles of mathematical induction and problems based on the concept. Chapter 13 is complex numbers, and students understand the need for complex numbers, integral power of iota and equality, addition, subtraction, multiplication and division of complex numbers in this chapter. Conjugates, modulus, reciprocals, square roots and representation of complex numbers are some other topics included in the chapter. Chapter 14 is quadratic equations, and it includes quadratic equations with real and complex coefficients and related practice problems. Chapter 15 is linear equations, and topics like solutions of an inequation, solving linear equations in one variable, and applying linear inequations in one variable are studied here. Chapter 16 is permutation, and this chapter includes fundamental principles of counting, permutations under different conditions, permutation of objects not all distinct and problems based on them.

Chapter 17 is a combination. The chapter begins by clearing the basic difference between a permutation and combination, properties and practical problems. Chapter 18 is binomial theorem, and it contains subtopics like positive integral index, general and middle terms in binomial expansion, and related problems. Chapter 19 is arithmetic progression, and it includes representation of a sequence, selection of terms in an AP and their properties. The 20 th chapter is geometric progression. The problems of this chapter are based on the sum of the terms of a GP and the selection of terms in GP.

Chapter 21 is some special series, including sum to 'n' terms of some special series, methods of difference and summation of special series. Chapter 22 is a brief review of the Cartesian system of rectangular coordinates, which covers topics like the Cartesian coordinate system, area of the triangle, section formulae, centroid, in-centres and ex- centres of a triangle. Chapter 23 is the straight lines, and it includes the introduction of straight lines, the slope of a line, the angle between two lines, intercepts, lines parallel and perpendicular to a given line, etc. Chapter 24 is Circles, and it covers standard equations of a circle. Chapter 25 is Parabola.

Conic sections, their analytical definitions and general equations are the chapter's highlights. The next chapter, ellipse, includes the ellipse equation in standard form, ordinate, double ordinate and latus-rectum. Chapter 27 is a hyperbola, and it gives a summary of the hyperbola equation in standard form. Chapter 28 introduces three-dimensional coordinate geometry; this chapter covers concepts like coordinates of a point in space, distance formulae and section formulae. Chapter 29 teaches students about limits, the informal approach to limits, the algebra of limits and methods of evaluation of algebraic limits at infinity are the highlighted topics of this chapter. Chapter 30 is derivatives, and it includes physical integration of derivatives at a point, derivatives of a function, product rule for differentiation, etc.

Chapter 31 is mathematical reasoning. It introduces students to statements, the negation of statements, basic connectives, and basic connectives quantifiers and validity of a statement. Chapter 32 is statistics, and it briefs about measures of dispersion, variance and standard deviation. The last one is chapter 33, Probability. It deals with random experiments, events, types of events and axiomatic approach to probability.

The chapters included in the Class 11th RD Sharma Solutions are mentioned below:

## RD Sharma Solutions For Class 12

The first chapter is relations, and it covers topics like recapitulation, types of relationships and problems based on them. Chapter 2 is function. It shows functions as a set of ordered pairs, correspondence and machine. Furthermore, it includes modulus function, the graph of a function, logarithmic function, reciprocal function, and bijection. Thus, students get a brief knowledge about properties of functions, compositions of real functions, inverse function, the relation between the graph of a function and its inverse, etc. Chapter 3 is binary operations, and this chapter deals with several binary operations, their types, identity element, composition table and their use in solving problems. Chapter 4 is inverse trigonometric functions. As the name indicates, this chapter includes inverses of various trigonometric functions and their properties. Chapter 5 includes the definition of the matrix, types of matrix, equality of matrix, their fundamental operations and properties. Chapter 6 is determinants, and it covers concepts like a determinant of a square matrix of various orders, singular matrix, properties and evaluation of determinants, applications of determinants in coordinate geometry, and solving a system of linear equations. Chapter 7 is adjoint and inverse of a matrix.

The chapter explains some useful results on invertible matrices, the elementary transformation of the matrix, and various methods of finding the inverse of a matrix. Chapter 8 is the solution of the simultaneous linear equation. This chapter includes a consistent system, a solution of the homogeneous system of a linear equation and a matrix method for an unknown homogenous system. Chapter 9 is continuity, and it deals with the intuitive notion of continuity at a point, algebra of continuous function, continuity of an interval and properties of continuous function. Chapter 10 is differentiability, and this chapter involves various theorems, differentiability in a set and meaning of differentiability at a point.

Chapter 11 is differentiation; concepts like recapitulation, differentiation of inverse trigonometric functions from first principles, differentiation by using trigonometric substitutions, differentiation of implicit functions and logarithmic functions are covered in this chapter. Differentiation of parametric function and differentiation of function concerning another function is also covered here. Chapter 12 is higher-order derivatives, and it includes definitions and notations on proving various relations. Chapter 13 is derivative as a rate measurer, and it contains related rates and rate measurement by using derivatives. Chapter 14 is differentials, errors, and approximations; it introduces terms like absolute error, relative error, and problems. Chapter 15 is mean value theorems. The chapter begins with Rolle's Theorem, its algebraic interpretation and its applications. Next comes Lagrange's mean value theorem, its geometrical interpretation verification and application. Chapter 16 is tangents and normals, and it includes the slope of a line, the slope of tangent and normal and equations related to them. Chapter 17 is increasing and decreasing functions, and topics like algebraic inequations, definitions of strictly increasing function, etc., are highlighted in this chapter. Chapter 18 is maxima and minima, and it includes concepts like maximum and minimum functions in its domain, derivative tests for local maxima and minima and applied problems. Chapter 19 is indefinite integrals. This chapter deals with fundamental integration formulas, geometrical interpretation of indefinite integral, integration methods, and evaluation of integral forms. Chapter 20 is definite integrals, and it deals with the fundamental theorem of fundamental calculus, evaluating definite integrals and their properties.

Chapter 21 is the area of bounded regions, and it includes definite integrals, areas using vertical and horizontal stripes, etc. Chapter 22 is differential equations. In this chapter, students will learn the degree of the differential equation, the formation and solution of the differential equation, geometrical interpretation and problems based on them. Chapter 23 is the algebra of vectors, and it explains the types of vectors and their representation. Chapter 24 is a scalar or dot product. It explains the properties of the scalar product and some geometrical problems. Chapter 25 is vector and cross-product, and it includes properties of vector product Lagrange's identity rule and problems based on them. Chapter 26 is a scalar triple product. The chapter includes a graphical interpretation of scalar product and related problems. Chapter 27 is directions cosines and direction ratios. In this chapter, students will face distance formula and section formula questions. Chapter 28 is a straight line in space, and the main topics of this chapter are vectors and Cartesian equations of this line intersection of two lines. Chapter 29 is plain, and it revolves around an intercept formed by a plane. Chapter 30 is linear programming. The chapter deals with the iso-cost method and different types of linear programming problems.

Chapter 31 is probability, and students get to learn about multiplication and conditional theorems of probability. Chapter 32 is the mean and variance of a random variable, and it revolves around discrete random variables, their mean and probability distribution. The last chapter is binomial distribution, and it covers topics like Bernoulli Theorem, Binomial distribution, mean and variance of binomial distribution and questions based on them. The RD Sharma solutions by the Aakash Institute provides the necessary boost to help the students understand these important topics.

The chapters in class 12 RD Sharma included in the solutions are:

Ques 1. How are RD Sharma solutions helpful?
Students need to understand the topics by reading and then solving the problems. Usually, the students try to solve exercise questions and get stuck on questions and in these situations, the RD Sharma solutions help them get out of doubt. Moreover, these solutions provide a comprehensive step-by-step explanation of the topics.

Ques 2. Is it necessary for students to study RD Sharma in junior classes like 6 th and 7 th ?
Yes, as it is said that practice makes a man perfect and maths is a subject that requires fundamentals which makes the earlier classes very important. Hence, it is good for 6 th and 7 th class students to solve RD Sharma questions. The Aakash RD Sharma Solutions help the students a lot in building these concepts.

Ques 3. Where can someone find RD Sharma Solutions?
RD Sharma solutions contain an explanation of all the questions. The RD Sharma solutions are prepared by the faculty members of the Aakash Institute. The solutions PDF can be obtained free of cost from the official Aakash website.

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