The transition from high school to pre-university (11th grade) is not easy because students are about to get exposed to so much more pressure than they ever used to be. 11th grade is one of the most crucial stages in anyone's life because it contains all the basic topics and concepts related to college studies. So, at Aakash, we advise the students to concentrate on their 11th Grade subjects to obtain a basic idea of their specialization.
Mathematics is a fundamental and analytical subject that acts as a base to many other domains such as Accounts, Science and Engineering etc. So, we provide students with the best possible way to study and enhance their knowledge to be helpful for their examinations and their career.
At Aakash, RD Sharma Solutions for Class 11 Maths PDF are provided to the students to educate them on relevant subjects and help them score good marks in their examinations. The experienced subject matter experts at our Aakash Institute prepare the solutions for all the problems step-wise. They also evaluate the contents before publishing them to ensure the provided topics are relevant to the subject and are error-free. This will help the students acquire knowledge without difficulties.
One of the easiest ways to ensure that the preparations for their exams are going well is to make sure they cover all the basic concepts that lead to advanced-level problem-solving abilities. One incredible thing about using our solutions is that students need not worry about difficulty level because, at Aakash, we provide the best possible answers in a very easy-to-understand manner. It also saves students' time as they don't need to check elsewhere. Furthermore, students can download the free materials available on our website in PDF format. This can be done effortlessly by just clicking on the download button. All the materials are available and can be accessed on all types of devices such as smartphones, PCs, laptops and tablets.
This is the very first chapter in RD Sharma Solutions for Class 11th Maths. It deals with sets. Sets are defined as a collection of well-defined elements which does not change from person to person. A set can be represented by a capital letter. The number of objects in the finite set is termed to be the cardinal number of a set. In this chapter, students learn about the usage of sets and the different types of sets based on their elements. This chapter holds value as the topics discussed in it will be applied in the following chapters.
'Relation' in mathematics is termed as the relationship between two or more sets of values. For example, if we consider both x and y as two sets of ordered pairs, and set x has relation with set y, then the values present in the set x are considered the domain while y is called range. After understanding these concepts, students are exposed to exercise problems to excel in this topic. These help us crack problems related to the relation between the given set of elements and their usage.
Chapter 3 deals with the function as a correspondence between two sets related to the other. Moreover, a function is best described as a relation. It is between a set of inputs that have definite outputs such that each input is related to exactly one output. The students are engaged with numerical problems in order to solidify their knowledge of this concept. So, this is a summary of what this chapter is going to talk about.
In the previous years, students have studied some of the basics of trigonometry, a branch in mathematics that deals with the angles and sides of a triangle. In RD Sharma Solutions for Class 11 Maths Chapter 4- Measurement of Angles, students can learn the relation between degrees, radians and real numbers. These are some of the key concepts that are covered in this chapter. Along with this, solution problems are also taught to the students using detailed explanations of each solution.
This chapter talks exclusively about the definitions of trigonometric ratios to any given angle that is then termed as a trigonometric function. Trigonometric functions are described as circular functions that can be easily defined in terms of the functions of an angle of any triangle. Following are the basic trigonometric functions; sine, cosine, tangent, cotangent, secant and cosecant.
The trigonometric functions are classified as periodic functions. In this chapter, the students study the graphs of these trigonometric functions subjected to their periods. Since these functions are periodic, there is a clear repetition seen in the values obtained by these functions. To provide more knowledge on this topic, students are exposed to some of the basic exercise problems and can also solve them on their own with the help of the support provided by our experts.
'Trigonometric functions' include trigonometric ratios and compound and multiple angles used to get consistent results. In RD Sharma Solutions for Class 11 Maths Chapter 7, students learn some of the formulae that express trigonometric functions' values while performing addition or subtraction of two real numbers. Additionally, students also get to study compound angles. A compound angle is termed the sum of two or more angles.
In this chapter, students are provided with the opportunity to study about two sets of transformation formulae. Formulae transform the product into a sum or difference, and Formulae transform the sum or difference into a product. These are the fundamental concepts mentioned in this chapter, so one should have a thorough acquaintance with these formulae. The RD Sharma Solutions for Class 11 Maths Chapter 8 consists of two unique exercises.
Chapter 9-Trigonometric ratios of Multiple and Sub-Multiple Angles deal with the formula that expresses trigonometric functions at two, three or multiple times of the value A or half, one-third (sub-multiple) of the value of the angle A. After acquiring knowledge, RD Sharma Solutions for Class 11 Maths Chapter 9 help to solve exercise problems for students to practice and prepare for their exams.
The RD Sharma Solutions for Class 11 Maths Chapter 10 helps students achieve good grades in their exams by providing quality content on relevant topics such as trigonometric relations with the elements of a triangle. Apart from this, other important concepts such as the laws of sines, cosines, projection formulae, Napier's analogy and the area of a triangle are discussed in this chapter.
This chapter is based on the intricacies of trigonometric equations. Trigonometric equations are the equations that are formed by using trigonometric values of various unknown angles. They can be expressed as the ratios of sin, cot, cos, tan, sec, cosec. All possible values that possess the ability to satisfy the given trigonometric equations are considered the given trigonometric equation solutions.
The RD Sharma Solutions for Class 11 Maths Chapter 12 deals with the topic called mathematical induction. It is a mathematical technique that is mainly used in proving a statement, a theorem or a formula and is true for every natural number. This method involves two basic steps, namely, the Base step and the Inductive step. The Base step is mainly used for proving whether the statement is true for the initial value. The inductive step proves that if the statement is true for the nth iteration, it is also true for the (n + 1)th iteration.
Chapter 13-Complex Numbers deals with the concept that complex numbers are nothing but the simple combination of real numbers and imaginary numbers. Other important topics in the chapter include the introduction of 'iota', the operations based on it, imaginary quantities, cube root of unity, division, multiplication and modulus of complex numbers. After understanding the basics, students solve the exercise problems, which will help them in their exams.
In the previous chapters, students have learnt about quadratic equations with real roots and real coefficients. Meanwhile, with the help of Chapter 14-Quadratic Equations, students get to learn some other important concepts such as quadratic equations with real coefficients and complex roots. With the help of materials provided by our experts, students can get a clear idea of how to solve the problems based on the concepts discussed in this chapter.
The main concepts covered in Chapter 15-Linear Inequations are the linear inequations in one and two variables. Linear inequalities are equations where two expressions or values are compared using inequality signs such as <, >, ≤, ≥. The knowledge acquired from this chapter will help the students to solve problems in many different domains, namely Mathematics, Science, Engineering and Linear Programming.
Permutations are nothing but the process of ordering a list of objects. For instance, arranging 10 people in a line is considered equivalent to finding permutations of 10 objects. In RD Sharma Solutions for Class 11 Maths Chapter 16, the term and notation of factorial are introduced. The fundamental concepts explained in this chapter include factorial, fundamental principles of counting, permutations, permutations of objects, permutations under certain conditions etc.
The main concepts discussed in RD Sharma Solutions for Class 11 Maths Chapter 17 are Combinations, Properties of Combinations, practical problems of combinations, and mixed problems on both combinations and permutations. Combinations can be described as the different selections made by considering either some or all of the number of objects irrespective of their arrangements. Therefore, the concepts in this chapter need to be understood thoroughly as they find applications in the chapters that follow.
Chapter 18-Binomial Theorem introduces a new concept related to the chapters that dealt with permutation and combination. The binomial theorem can be defined as the method of expanding an expression that has been raised to any finite power. Binomial expressions can sometimes be very lengthy and tedious to calculate. So, using the binomial theorem makes it easier to calculate a binomial expression raised to a very large power. Thus, it is considered a powerful expansion tool that applies concepts like algebra, probability, etc. In this chapter, students learn concepts like the Binomial theorem and some of its important conclusions and general and middle terms in a binomial expansion.
Arithmetic progression is considered a sequence in which the difference between the term and the previous term is constant. For instance, the series of natural numbers: 10, 20, 30, 40, 50,… is termed as an AP, which has a common difference between two successive terms equal to 10. The chapter deals with concepts such as the general form of an arithmetic series, the nth term of an arithmetic series and the sum of n terms. In addition, there are questions based on the difference of the sum of two different arithmetic series. Apart from just grasping the concepts, students also get to solve the practice problems and exercise problems to further enhance their knowledge.
Before diving deep into this topic, students are taught what exactly a geometric progression is. The Geometric progression is defined as follows: it is a sequence of terms where each succeeding term is being generated by multiplying the preceding terms with a constant value. GP denotes the sequence, and the multiplying term is known as the common ratio. In RD Sharma Solutions for Class 11 Maths Chapter 20, students also get exposed to exercise questions based on the general form of a geometric progression, common ratio, nth term of the GP, the sum of n terms of a GP. The exercises and the solutions provided get the students to solve the problems on their own after mastering this basic concept.
In RD Sharma Solutions for Class 11 Maths Chapter 21, various special series are covered, including the series formed by the sum of previously taught sequences. Moreover, topics such as calculating the sum of these series and the method of difference are covered. Along with the concepts, exercise and practise problems are also provided.
The RD Sharma Solutions for Class 11 Maths Chapter 22 consists of topics such as the Cartesian coordinate system, the distance between any two points, the section formula, the area of a triangle, the locus, and the origin's shifting. Students get a whole new idea of how these concepts work and use these concepts to understand the concepts taught in higher classes, not only in mathematics but also in other subjects.
A straight is defined as a curve where it forms the shortest distance between any two given points on a cartesian plane. Every straight line satisfies an equation that is comparable to the general equation of the straight line given by y=mx+c In RD Sharma Solutions for Class 11 Maths Chapter 23, students get to study the concept of straight lines with the help of numerous examples that help the students to understand the topics easily and thoroughly. The chapter contains the general form of the straight line, intercept form, and two-point form. The chapter also teaches the students about the locus of a straight line and the family of straight lines. Moreover, the solutions provided are explained in detail and in an easily understandable manner.
This is the chapter where students get an opportunity to learn the concepts related to circles and also the equation of any circle whose centre and radius are already given. The chapter also has subtopics such as the general form of the circle, the locus of a circle, tangents to a circle and a few other topics. The chapter has various shortcut methods provided to solve various types of problems quickly.
A parabola is a U-shaped curve where any point is at an equal distance from a fixed point known as the focus and from a fixed straight line known as the directrix. The RD Sharma Solutions for Class 11 Maths Chapter 25 explains the parabola topics and discusses finding the general equation of a conic section where its directrix, eccentricity, and focus are given. Some basic problems are also discussed in this chapter.
An Ellipse is nothing but the locus of all those points in a plane such that the sum of their distances from the two fixed points in the plane is constant. This chapter deals with the concept of an ellipse and determines the equation of an ellipse in the standard and other forms.
A Hyperbola can be defined as an open curve with two branches, the intersection of a plane with both the halves of a double cone. We have seen a hyperbola in the previous grades, but in Chapter 27-Hyperbola, students learn about it in detail by determining its equation in a standard form.
The key topics covered in the RD Sharma Solutions for Class 11 Maths Chapter 28-Introduction to 3D Coordinate Geometry are the coordinates of a point, the distance formula and the section formula. These concepts involve problems that will help the students grasp the concepts better by applying them to solve these numerical problems.
In this chapter, the concepts of limits and their derivations are explained briefly. Other concepts, namely evaluating algebraic limits, trigonometric limits, exponential limits and logarithmic limits, are also discussed in this chapter.
Chapter 30-Derivatives provides a basic knowledge of derivation at a point. Other important topics such as the derivative of a function, differentiation from the first principles and the fundamental rules for differentiation are also taught to the students.
In this chapter, students study the concepts of statements, the negotiation of a statement, compound statements, quantifiers, basic connectives, statements' validity, and their implications. The solutions provided for all these concepts are designed so that everyone can understand them without much difficulty.
Students have already learnt the methods of representing the provided data both graphically and in tabular form. Furthermore, in RD Sharma Solutions for Class 11 Maths Chapter 32-Statistics, they are about to get exposed to the following topics; Range, Mean deviation, Measures of dispersion, Limitations of mean deviation, variance and standard deviation, and analysis of frequency distribution. These concepts that deal with a set of arranged data are of great importance as they find numerous applications in day-to-day life.
Students have learnt all the classical and statistical approaches of probability in their previous grades. Additionally, in this chapter, they get to study topics such as sample spaces, random experiments, events, algebra and types of events. All these concepts are structured based on CBSE norms.
Ques 1. Is solving RD Sharma with the help of solutions enough for the preparation of the board exam?
Ans. RD Sharma Solutions for Class 11 Maths is considered one of the best books for school examinations. The questions provided in the book are enough to understand the topics that provide the base for the topics in class 12th. Thus, the book for 11th, along with the solutions, provide the complete package for your exam preparation for class 11th and 12th. So, it is advised to download the freely available PDF and use it as much as possible.
Ques 2. Why is the Aakash RD Sharma Solutions for Class 11th Maths the best resource for scoring more in exams?
Ans. There are many exam resources available online as well in the market, but preparing with the help of the detailed solutions provided by the Aakash Institute, the RD Sharma Solutions textbook will help you to the fullest to score better marks in your exam because these are easy to understand, constantly updated and the solutions are prepared using the shortest methods.