RD Sharma Solutions for Class 12 Maths - Free PDF Download
In 12th Grade is a pivotal year in any student's life, with board exams that can set the tone for a person’s career. Mathematics is challenging to many students, and the pressure doesn't make it easier. Thankfully, a combination of the tried and tested R D Sharma class 12 solutions and our personalised approach to education are here to help. RD Sharma books have been recommended for years as a source of information to perfect your mathematical skills. They have proven to be indispensable for mastering the syllabus and creating the confidence that is needed to face this important year.
What's even better is that we make the RD Sharma class 12 mathematics solutions freely available in PDF format, allowing you to access the study material any time and anywhere. This is helpful not only because it helps with revisions but also because you can look over all the topics quickly. All this is only the first step of how we can help any you succeed in your mathematics board exam.
RD Sharma Textbook Solutions for Class 12 Maths
Crafted by teachers whose expertise is only matched by their passion, the RD Sharma class 12 solutions will ensure a deeper understanding of the difficult topics you will be studying in the 12th grade. Combine this with our interactive platform, and one-on-one attention and you are sure to understand every chapter down the very last problem. This is absolutely crucial in the 12th standard as these exams will set the course for your entire life, and as such, every solution counts.
Our teachers have spared no effort in creating the best learning experience possible by employing the latest technologies in conjunction with the tried and tested expertise of RD Sharma. They are highly trained, deeply passionate about education, and truly believe in the power of merging technology and textbooks. The CBSE class 12 RD Sharma solutions in free PDF format will give you the confidence to do well in your board exams as well as in the competitive exams.
Below mentioned chapter wise details of Class 12 RD Sharma Solutions:
Chapter 1 Relations
The first chapter of class 12th is about Relations, what are these relations about? As you have already got the gist of it in class XI, the connections cover the main topics, notion, domain and codomain. This chapter has theorems and problems which will clarify your concept about the same. You need to get bright ideas about four concepts important in this chapter, reflexive relations, symmetric relations, transitive relations and antisymmetric relations.
Chapter 2 Functions
As we talk about relations, the next chapter covers the sets. The same A to B sets which you have been learning since your 11th standard. The types of functions you will be learning about is Reciprocal function, square functions, Square root functions, Cube functions, Cube root functions.
This is our duty to make these functions simplified for you which will make your 12th boards an interesting one, rather than the one which gives you stress.
Chapter 3 Binary Operations
What are binary operations? The binary process, when multiplied on a nonempty set A, is a function from A × A to A. Addition, subtraction, multiplication is the kind of binary services on Z. Addition becomes a binary operation on Q as Division is NOT a binary operation on Z. This is how the basic of this chapter sums up. With this understanding, you can easily score well, with the right practice.
Chapter 4: Inverse of Trigonometric functions
Inverse Trigonometric Functions can also be anti-trigonometric functions, arcus functions or cyclometric functions. They have their applications in a practical manner in physics, geometry, navigation and engineering. Inverse Trigonometric Functions are used to get an angle from any of the angle’s trigonometric function. They are expressed as the inverse of cosecant, tangent, cosine, sine, secant and cotangent. These rules of trigonometric will help you in physics also which will cover the major part of it.
Chapter 5 Algebra of Matrices
The algebra of matrix consists of rows and columns with rules and concepts which will make you confused in the start but later you are going to love it. This chapter becomes straightforward ones you grasp the idea of it. And that is how we will be helping you in understanding the concept so that you can score good marks and with the continuous working of the sums you will get the idea with ease.
Chapter 6 Determinants
After knowing matrix and understanding the concept, the following chapter determinants is based on the same rules. This chapter takes the form ahead in a different format, and it becomes the elaborated version of the above. Determinants can easily be defined as the quantity or number which we can get by the addition of products of the elements given in a square matrix according. The determinant of a model “A” is either denoted by set A or |A|. This becomes the symbol of the determinant.
Chapter 7 Adjoint and the inverse of a Matrix
This becomes the third part of Matrix with an elaborated version again. In this chapter, it is about the adjoint concept of matrix. Adjoint of a model can be got by taking the transpose of the cofactor matrix of a square form and which is called the adjoint matrix. The properties of matrix become like Product of a square matrix X with its adjoints produces a diagonal pattern. You will learn about more features throughout the chapter.
Chapter 8 Solution of Simultaneous Equations
You have learnt about equations since your 7th standard so now it has become handy for you, here you get to learn more about linear equations. As we have done with one variable, there are also linear equations with two variables. This equation is essential to understand, and with various rules, this equation will make you think that it is complicated, but with our solutions, we want to make it easier for you.
Chapter 9 Continuity
Continuity is the concept which defines the equations and with some rules followed. For the function which is set in an interval, the continuity of the service can be stated if and only if the service is defined at all the points within the range, or else it becomes discontinuous in the given problem. Continuity is a straightforward concept and but with rules, you need to memorise it. Daily practice will help you to score well.
Chapter 10 Differentiability
Differentiability also comes in the same lines as continuity. The concepts of differentiability are in this chapter you are going to study about the following ideas: Differentiability at a point: Graphical, algebraic(function is differentiable), algebraic(function isn’t differentiable). With two types of differentiability, graphical and algebraic the chapter sums up in a simplified manner. Differentiability carries a lot of weight in the board exams, these concepts are simple so do not worry.
Chapter 11 Differentiation
This chapter is the start and essential of the central section which has derivatives and integrations which covers a maximum of your weight in 12th. After the function it is differentiable at every point of its domain, then each point in its field can also be associated with the derivative of the service at that point. Such a correspondence between two points in the domain and the set of values of derivatives at those points can define a new function which is known as the derivative or differentiation of the given task.
Chapter 12 Higher Order Derivative.
In this book of solutions which have made it simple for you the most challenging chapter of Derivative. Higher Order Derivatives will make you prove positive relations involving various order derivatives, for determining relationships involving different order derivative of parametric and cartesian functions straightforwardly. Derivatives and integration cover the essential part of the chapter in 12th standard, it is used even in physics, if you are thinking of pursuing any engineering. Derivatives are important.
Chapter 13 Derivative as a Rate measurer
This chapter is about Rate measurer, the derivative of a variable essentially is a way to account for the rate of change of a function which is by that of the variable. A fundamental tool of calculus, derivatives has applications in many situations when applied in the right manner and understanding. This chapter is more about using derivatives to practical applications, like if the radius of a cube is increasing variable, calculating the volume of the hub and more.
Chapter 14 Differentials Error and Approximation
It is in depth about the functions and explorations regarding the derivatives in a simplified manner. The formulas give very importantly for the boards. Based on this we have to understand derivatives. As your basics would have been cleared till now, derivatives are essential. This is the third part, and with the help of this your concepts would be sorted, once you are keen on basics, these chapters become simple and scoring you.
Chapter 15 Mean Value Theorems
As we start our journey towards the geometry part of the mathematics syllabus, it is time to understand the theorems and learn them. Understanding the concept, in theory, becomes very important as they are vital to make your answers useful in your examinations. That is why we have tried to make your theorem in a manner that you can grasp it quickly. Rolle’s theory will be introduced in this which is very important for your exams.
Chapter 16 Tangents and Normal
The chapter on tangents and reasonable is considered to be the relevant chapter, and thus, the students are required to practice a lot of questions to be able to understand the concepts as this is something which comes more natural with exercising. A tangent can be defined as a straight line touching a curve at a very particular point. A straight line that is perpendicular to the tangent that is the line whose gradient is -1/m (m= slope of the tangent) is called as a normal.
Chapter 17 Increasing and Decreasing Functions
Increasing and decreasing functions is again a chapter which is based on previous concepts. This makes it simple for you to understand the given problems. Differentiation will be used to find whether a function is increasing or decreasing with various rules applied. The issues need to be solved step by step in a simple manner and mathematics is something which improves with daily practice, so keep going it is a long but fruitful journey.
Chapter 18 Maxima and Minima
In this Chapter of Maxima and minimal it is based on, most common concepts in differential calculus part of mathematics. It is derived from the Latin word meaning the maximum and minimum value of a function respectively. They are fundamental concepts which are applicable both in Mathematics and Science. Whenever we need to find the maximum and minimum benefits of some service, firstly we need to distinguish between the concepts given.
Chapter 19 Indefinite Integrals
After derivation, integrals are another topic which has more weight. In this chapter, we will find a variety of questions based on different types of integration names. Integration by Substitution, by parts, partial functions. Integration by substitution covers a significant portion of it, and it has few rules and steps to memorise. Integration by parts and partial services will be easier if you understand prior concepts, this will help you to do good in your test.
Chapter 20 Definite Integrals
In this chapter which is a continuation of the above learns about the definite chapter integrals. The definite integral of a function which is closely related to the antiderivative and indefinite integral of a service. Also, in the chapter of definite integrals, we will cover the topic like Definite integrals as a limit of a sum, Fundamental Theorem of Calculus. Basic properties of definite integrals and evaluation of definite integrals.
Chapter 21 Area Bounded Regions
The chapters of Area Bounded Regions, the areas finding of adjacent regions is to identify the part whose territory is to be evaluated. To make this simpler, we first draw the rough sketches of the different curves which enclose the region. To attract the rough plans of the curves, students are advised to go through the chapter and understand the basics. The concepts are fundamental to understand and memorise it.
Chapter 22 Differential Equations
After learning about linear equations, it is time to understand differential equations. An equation containing a dependent variable, an independent variable and differential coefficients of the dependent variable concerning the independent variable is known as a differential Equation. We have tried to make the equations simpler and to the point. These solutions which are provided are designed in a way where you grasp the concept quickly, making mathematics effortless and worth.
Chapter 23 Algebra of Vectors
In this lesson, you will learn about so many concepts in a row. The action of performing algebraic operations on vectors are mostly Euclidean vectors and is called as vector algebra. Activities are on vectors in two-dimensional, and three-dimensional space is studied in courses on Mathematical Physics in an elaborate manner. The various algebraic services that are performed on vectors are like transposition, equality, addition & subtraction, multiplication & division by a scalar quantity, span, inner product & length, unit Vectors & normalisation, Orthonormality, orthogonal projection, orthogonal bases and Subspaces
Chapter 24 Scalar or Dot product
After learning of the chapter regarding vector which comprises of direction and magnitude. Two vectors can be multiplied by using Scalar or dot product. The dot product can be defined as an algebraic operation which gives a number as a product by also taking two equal-length sequences of numbers. A dot product can be represented using a central dot. Though the concepts in this chapter our tricky but we have tried to simplify for you.
Chapter 25 Vector or Cross Product
This is the next part in vector series, which shows the cross product in the vector part. These concepts become a tedious little one after the other, but as the chapters are in pieces, this will become easy for you. This part is the next level in the series of products, and you will be able to understand the concept with easy when these solutions are provided, it is worth it.
Chapter 26 Scalar Triple Product
After getting your concepts clear regarding vector and cross and also the part of Scalar Triple product this becomes very easy for you. Your primary focus should be getting your basic concepts evident in the earlier chapters to grasp this. Once you are clear with the ideas, then the next thing you need to concentrate on practising daily. This will help you a lot in the long run for mathematics both academically and practically.
Chapter 27 Direction Cosines and Direction Ratios
Trigonometry is an essential part we have discussed in chapter number 4 about the usage of it. This is a more elaborated version. Direction ratios provide a convenient way of specifying the direction of a line in three-dimensional space. Direction cosines are the cosines of the angles between a line and the coordinate axes. Trigonometry, as discussed earlier, is going to be very useful in your professional courses mainly marine engineering where it is used a lot.
Chapter 28 Straight line in Space
The straight line in space is about a line extending on both sides till infinity without any curves is called a straight line. It is an object in geometry which can characterise by zero and the width of the object which extends in opposite directions without any ends. A straight line is always the first topic to start within the geometry. It becomes the basis of geometrical constructions and knowing the basics of it helps a lot.
Chapter 29 The Plane
After learning about the line, a plane is a flat, 2-dimensional surface having infinite dimension, but having zero thickness. Such that if any two points there are in it, the line segment joining them lies entirely on the surface. A plane in 3-dimensional space. There is another crucial part of geometry. Line and plane define the basis of geometry, knowing it makes construction easier. When you move ahead for the profession course, it will help you a lot.
Chapter 30 Linear Programming
Linear programming is the process in which it takes various in linear inequalities is relating to a situation and finding the value obtainable under conditions. The topics in direct programming areas cover things like mathematical formulation of L.P, introduction, related terminology such as objective function, constraints. Different types of linear programming (L.P.) problems, problems, graphical method of solution for problems in two variables, feasible and infeasible solutions, optimal workable solutions (up to three non-trivial constraints, infeasible and viable regions.
Chapter 31 Probability
Probability is the word which talks about the possibility of certain things. These probabilities are found to be helpful in practical applications. As you have done chance in the earlier standard you know the rules and the concepts now. So, this is just going to be a cakewalk for you. Probability is simple, and it has laws which are based on the idea of possibilities, in these solutions we have simplified for you all the more.
Chapter 32 Mean and variance of Random Variable
In this chapter about variables, it is corresponding to every outcome of any random experiment, and a real number has associated this correspondence between the elements of the sample space associated to a random trial and the set of real numbers is defined as a random variable. This chapter covers a proper weight for 12th boards, the syllabus is made in a manner to simplify rules for you, and we have made everything schematic so that you can understand so many regulations and concept and memorise quickly.
Chapter 33 Binomial Distribution
In the last chapter of Binomial Distribution, A binomial Distribution can also be defined as when a random variable X that counts the number of successes, k, in the trials is said to have a binomial distribution with parameters. These parameters with the concept are simpler to understand. Your 12th standard syllabus ends with the more straightforward chapter, and you will enjoy it in the middle of those big numbers, this is a single chapter with simple concepts.
This syllabus is vast in number, but we are there for you. It is going to be a good year.
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