# RD Sharma Class 11 Solutions for Maths

RD Sharma Solutions for class 11 covers different types of questions with varying difficulty levels. Practicing these questions with solutions may ensure that students can do a good practice of all types of questions that can be framed in the examination. This ensures that they excel in their final examination for the subject of mathematics. In case of any doubts, students can easily refer to the chapter-wise solutions provided below, to ease their studying without any interruption in between. By referring to these solutions, students can get to know various ways of solving questions.

### Chapter 1: Sets

The chapter Sets in this book covers all the basics and advanced concepts related to sets like the definition of Sets, Operations on sets, types of sets, the laws of the algebra of sets, roaster form or tabular form, set-builder form, subsets, results on the number of elements in sets, universal set, power set, and Venn diagrams. This book contains a total of eight exercises that helps to understand the mentioned topics.

- Exercise 1.1
- Exercise 1.2
- Exercise 1.3
- Exercise 1.4 Set 1, Set 2
- Exercise 1.5
- Exercise 1.6 Set 1, Set 2
- Exercise 1.7
- Exercise 1.8 Set 1, Set 2

### Chapter 2: Relations

A relation is basically about two sets between two sets. This chapter consists of three exercises which cover mainly algebra of real functions, a Cartesian product of sets, Equality of ordered pairs as the primary components of relation. Exercises 2.1 and 2.2 are mainly about the introduction of relations and the Cartesian product of sets and the domain and range of the relation R, visual representation of relations. Moreover, Exercise 2.3 is based on the types of relations and co-domain, domain, and range of a relation.

- Exercise 2.1
- Exercise 2.2
- Exercise 2.3 Set 1, Set 2

### Chapter 3: Functions

The function is related to a set of inputs is from a set of possible outputs where each input belongs to exactly one output. There is a total of four exercises in this chapter. Exercises 3.1 and 3.2 are about the determination of range, domain, values of functions at different intervals, etc. However, in exercises 3.3 and 3.4, the range and domain of the real-valued functions and the values of the functions with graphical and other methods are needed to find.

- Exercise 3.1 Set 1, Set 2
- Exercise 3.2
- Exercise 3.3
- Exercise 3.4

### Chapter 4: Measurement of Angles

In this chapter the questions are related to determine the degree, radians, express the angles, length of an arc, determine the angle, find the number of sides of a polygon. There is only one exercise, exercise 4.1 which is based on the mentioned topics.

### Chapter 5: **Trigonometric Functions**

This chapter consists of only three exercises, Exercise 5.1 contains questions in which the values of Trigonometric identities are needed to prove. Further in exercises 5.2 and 5.3, the problems from Trigonometric functions and Trigonometric ratios are included in this chapter.

- Exercise 5.1 Set 1, Set 2
- Exercise 5.2
- Exercise 5.3

### Chapter 6: Graphs of Trigonometric Functions

The present chapter includes the graphs of the six trigonometric functions and their solutions when the maximum and the minimum turning points are given. This is discussed in three exercises covering all the topics related to this chapter.

### Chapter 7: Trigonometric Ratios of Compound Angles

This chapter has two exercises based on the concept of compound angle, multiple angles, inverse function, and their properties, the transformational formula, and some short and simple techniques to identify the expression of angles.

- Exercise 7.1 Set 1, Set 2
- Exercise 7.2

### Chapter 8: Transformation Formulae

The chapter Transformation formulae is completely based on the transformation formulae and their application. This chapter contains mainly two exercises that contain questions from basic to advanced level.

- Exercise 8.1
- Exercise 8.2 Set 1, Set 2

### Chapter 9: Trigonometric Ratios of Multiple and Sub Multiple Angles

As the name of the chapter suggests Trigonometric ratios of multiple and sub-multiple angles, comprise mainly the formulae which when applied make the calculation and its procedure easier and shorter. There are various formulae, whose applications are discussed in the three exercises of this chapter.

- Exercise 9.1 Set 1, Set 2, Set 3
- Exercise 9.2
- Exercise 9.3

### Chapter 10: Sine and Cosine Formulae and their Applications

This chapter provides the knowledge of Sin and Cosine rule by applying them in different ways to determine the sides and angles of the triangle. There are only total two exercises that help to understand the mentioned topics.

### Chapter 11: Trigonometric Equations

The problems of this chapter are based on the methods to determine the solution of the trigonometric equations. There is only one exercise that discusses the methods like the R method, the quadratic equations’ method, the formula of double and triple angle, or the sum to product formula.

### Chapter 12: Mathematical Induction

The chapter Mathematical induction in this book has two exercises only. The questions in these exercises are based on solving mathematical statements with the proper applicability of principle and hypothesis.

- Exercise 12.1
- Exercise 12.2 Set 1, Set 2, Set 3

### Chapter 13: Complex Numbers

The present chapter consists of only four exercises, in which Exercises 13.1 and 13.2 are based on the basic concepts of the complex number. Further, exercises 13.3 and 13.4 are based on the representation of a complex number and complex equations.

- Exercise 13.1
- Exercise 13.2 Set 1, Set 2
- Exercise 13.3
- Exercise 13.4

### Chapter 14: Quadratic Equations

The chapter Quadratic equations have two exercises out of which Exercise 14.1 is based on basic quadratic equations which are to be solved by the factorization method.

- Exercise 14.1 Set 1, Set 2
- Exercise 14.2

### Chapter 15: Linear Inequations

This chapter has six exercises based on solving basic inequalities of x in relation to R, the system of equations representation of the solutions on graphs, and problems related to the occurrence of no solution in inequality.

- Exercise 15.1 Set 1, Set 2
- Exercise 15.2 Set 1, Set 2
- Exercise 15.3
- Exercise 15.4
- Exercise 15.5
- Exercise 15.6

### Chapter 16: **Permutations**

The chapter permutations include topics factorial, fundamental principles of counting, permutations, permutations under certain conditions, and permutations of objects not all distinct. There are total five exercises that are based on these topics.

- Exercise 16.1
- Exercise 16.2 Set 1, Set 2, Set 3
- Exercise 16.3 Set 1, Set 2
- Exercise 16.4
- Exercise 16.5 Set 1, Set 2

### Chapter 17: **Combinations**

This chapter is based on the simple applications of the basic formula of combination. There are three exercises in this chapter based on the topic like the determination of a number of ways for a particular selection of objects, application of permutation, and combinations in practical problems.

### Chapter 18: Binomial Theorem

This chapter with two exercises focuses on the application of binomial theorem for the expansion of various small functions of one or two degrees.

- Exercise 18.1
- Exercise 18.2 Set 1, Set 2, Set 3

### Chapter 19: Arithmetic Progressions

The chapter Arithmetic progressions consist of seven exercises in total. The problems in these exercises are based on the basic concept of arithmetic progressions, sequence, general terms of an arithmetic progression, selections of terms in an arithmetic progression, sums to ‘n’ numbers of arithmetic progressions, properties of arithmetic progressions, insertions of arithmetic means and applications of arithmetic progressions.

- Exercise 19.1
- Exercise 19.2 Set 1, Set 2
- Exercise 19.3
- Exercise 19.4 Set 1, Set 2, Set 3
- Exercise 19.5
- Exercise 19.6
- Exercise 19.7 Set 1, Set 2

### Chapter 20: **Geometric Progressions**

This chapter comprises the problems related to the general term of GP, which required the selection of terms of GP, the common ratio, determination of missing terms, and application of the sum of infinite geometric progression formulas in six exercises.

- Exercise 20.1 Set 1, Set 2
- Exercise 20.2
- Exercise 20.3 Set 1, Set 2
- Exercise 20.4
- Exercise 20.5 Set 1, Set 2
- Exercise 20.6

### Chapter 21: Some Special Series

The two exercises of the present chapter discuss the sum of the special series, the determination of the successive difference in the series, and the application of these special series.

### Chapter 22: Brief Review of Cartesian System of Rectangular Coordinates

The chapter Brief review of the Cartesian system of rectangular coordinates includes three main exercises that discuss the basic concepts of the Cartesian system, equation of the locus at given points, axis, distances from the axis, and all its possible combinations and their applications.

### Chapter 23: The Straight Lines

The chapter straight lines in this book widely covered all the topics related to the straight lines in its total nineteen exercises. Exercises 23.1 to 23.7 mainly focus on the formation of the equation of the line while changing the other values in each question from slope, points, and intercepts. The problems in Exercises 23.8 to 23.10 are based on the determination of the distance between lines and axes, a point and a line, and between parallel lines. However, the rest exercises covered in the chapter are based on the same topics discussed previously, but the level of the problems is a bit advanced.

- Exercise 23.1 Set 1, Set 2
- Exercise 23.2
- Exercise 23.3
- Exercise 23.4
- Exercise 23.5
- Exercise 23.6 Set 1, Set 2
- Exercise 23.7
- Exercise 23.8
- Exercise 23.9
- Exercise 23.10 Set 1, Set 2
- Exercise 23.11
- Exercise 23.12 Set 1, Set 2, Set 3
- Exercise 23.13
- Exercise 23.14
- Exercise 23.15
- Exercise 23.16
- Exercise 23.17
- Exercise 23.18
- Exercise 23.19

### Chapter 24: The Circle

The chapter Circles in this book contains only three exercises. Each exercise is designed in such a way that it covers problems from basic to an advanced level covering all the topics. The problems are based on determining the circle’s equation when the Centre and radius of the circle are provided, determination of the general equations of a circle, the diameter, chord of a circle, area of a circle.

- Exercise 24.1 Set 1, Set 2
- Exercise 24.2
- Exercise 24.3

### Chapter 25: Parabola

This chapter consists of only one exercise that covers the topic like the definition of parabola, parametric coordinates, tangents and normal, and terms related to parabola; vertex, focus, equation of directrix, equation of axis, and tangent to the vertex.

### Chapter 26: Ellipse

The chapter ellipse covers all the topics like the equation of an ellipse, related parameters, foci, directrix, eccentricity, and latus rectum of the ellipse in only one exercise.

### Chapter 27: Hyperbola

This chapter is composed of only one exercise that covers the basic concepts of Hyperbola, determination of the equation of a hyperbola in the case when eccentricity, foci, and the equation of directrix are provided.

### Chapter 28: Introduction to 3D Coordinate Geometry

The introduction to 3D coordinate geometry included the problems from the length of the edges, octant, images of a point in the 3D system, distances between two-point, and collinearity of points, mainly in three exercises.

- Exercise 28.1
- Exercise 28.2 Set 1, Set 2
- Exercise 28.3

### Chapter 29: Limits

This chapter is based on the topics like the evaluation of algebraic limits, trigonometric limits, exponential and logarithmic limits. These topics are discussed in total of eleven exercises which contain numerous numbers of problem-based it.

- Exercise 29.1
- Exercise 29.2
- Exercise 29.3
- Exercise 29.4 Set 1, Set 2
- Exercise 29.5 Set 1, Set 2
- Exercise 29.6 Set 1, Set 2
- Exercise 29.7 Set 1, Set 2
- Exercise 29.8 Set 1, Set 2
- Exercise 29.9
- Exercise 29.10 Set 1, Set 2
- Exercise 29.11

### Chapter 30: **Derivatives**

This chapter in the present chapter helps to find the derivative with all the possible variations in the derivatives. There are five exercises present in this chapter, Exercise 30.1 helps to build up the basic knowledge to evaluate the derivative of simple fractions, exercises 30.2 and 30.3 focus on the evaluation of derivatives of the first and second degrees and some complicated higher degrees fractions. Later exercises 30.4 and 30.5 work out on the problem related to the trigonometric and logarithmic functions.

- Exercise 30.1
- Exercise 30.2 Set 1, Set 2
- Exercise 30.3
- Exercise 30.4 Set 1, Set 2, Set 3
- Exercise 30.5 Set 1, Set 2

### Chapter 31: Mathematical Reasoning

This chapter helps students to learn about the concepts like statements, the negation of a statement, compound statements, basic connectives, quantifiers, implications, and validity of statements. There is a total of six exercises that overall cover the mentioned topics in brief.

### Chapter 32: Statistics

This chapter helps to understand the methods of determination of a representative value of the given data. Further, the topics like measures of dispersion, range, mean deviation, limitations of mean deviation, variance, and standard deviation, and analysis of frequency distribution are discussed in the seven exercises present in this chapter.

### Chapter 33: **Probability**

The topics like random experiments, elementary events called outcomes and sample space, special events like exclusive or exhaustive, etc. There are total four exercises in this chapter with various problems related to the above-mentioned topics.

- Exercise 33.1 Set 1, Set 2
- Exercise 33.2
- Exercise 33.3 Set 1, Set 2, Set 3
- Exercise 33.4 Set 1, Set 2