NCERT solutions for class 11 maths- Are you aiming to get good marks in class 11 maths and looking for the NCERT solutions to enhance your preparation? Then you are in the right place. NCERT Class 11 maths syllabus starts from chapter sets and ends with chapter probability. Solutions of NCERT class 11 maths are specially designed to help you in preparing for your examination. CBSE NCERT solutions for class 11 maths contains the step by step solutions to all the 16 chapters. You are well aware of the fact that mathematics is a subject that needs practice. So solving as many problems as possible is important to score more in mathematics. NCERT Class 11 maths is important for board exams as well as for the JEE main. To build a base for NCERT class 12 maths, each chapter is important and can be related to daily life applications. Each chapter of NCERT class 11 maths is divided into some main subtopics. In each chapter, there will be examples followed by exercises. At the end of the chapter, there are miscellaneous questions followed by miscellaneous exercises. NCERT solutions are an important tool when you are doing self-study for the exams along with while doing homework.
The concepts in this particular chapter will be used in solving problems of other chapters also. So there is no scope of skipping any chapter. NCERT solutions for class 11 can also be used while preparing for entrance exams like NDA. These Solutions are very elegantly answered using which one can create a strong base for board examinations as well as competitive exams.
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NCERT solutions for class 11 maths chapter 1 Sets: The theory of sets is introduced by a German mathematician Georg Cantor. A well-defined collection of objects is called sets. In your daily life, you use the concept of sets in different situations mainly to arrange things in order. For example, in the kitchen, we arrange masalas in one set, plates as another set, teacup as a different set, etc. This chapter will test your logical strength along with mathematical skills. The concept of sets is an important part of modern mathematics. Study of sequence, geometry, and probability, etc. use the knowledge of sets.
Solutions of NCERT class 11 maths chapter 2 Relations and Functions: This chapter is an introduction to the concept of relation and functions. In class 11 maths, you are going to learn half of the relations and functions. In our life, there are well-defined relations like mother and father, brother and sister, etc. In a similar way, you can form relations in mathematics. A relation from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. Functions are very important in the case of data analysis. Most of the higher-level examination tests your knowledge over the chapter relations and functions. The chapter is very important for schools as well as exams like JEE and CAT.
CBSE NCERT solutions for class 11 maths chapter 3. Trigonometric Functions: Trignometry is the chapter that evolves around a right-angle triangle. The chapter was in class 10th where you have gone through the properties and usage of the properties. You have also done its application in daily life through chapter heights and distances. Here in class 11 maths, you will study a bit higher level of trigonometry. The study of various trigonometric functions and properties are introduced in class 11 maths. The identities studied will be used mainly in calculus and also in Physics.
NCERT solutions for class 11 maths chapter 4 Principle of Mathematical Induction: This is a small but important chapter. The chapter Principle of Mathematical Induction contains one exercise with 24 questions in it. Induction is generalized by observing the patterns. The steps involved in solving the problems are the same. If you go through NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction then it will help you in fetching good marks in the examinations.
Solutions of NCERT class 11 maths chapter 5 Complex Numbers and Quadratic Equations: In previous classes, we have learned the concepts of linear equations with one variable, linear equations with two variables and quadratic equations. We have studied that has no real roots or it has imaginary roots. This chapter is introduced to extend the concept of the real number system. This is one of the important chapters of mathematics which has a lot of applications in Mathematics and other subjects like Physics. The concept of Complex Numbers is used in vector algebra Mathematics and for solving problems related to alternating circuits in Physics.
CBSE NCERT solutions for class 11 maths chapter 6 Linear Inequalities: We have studied how to solve linear equations in our high school classes. For example, if three pen and two scales cost 40 rupees and if 5 pen and six scales cost 80 rupees, to find the cost of pen and scale we use linear equations. Now consider the situation that you have given 120 rupees and you are asked to buy the maximum number of books that cost 33 rupees. This type of problem is formulated using linear inequality. That is if you can bye x number of books then 33x = 120. This is how linear inequality problems are formulated.
NCERT solutions for class 11 maths chapter 7 Permutations and Combinations: Before starting the concepts of Permutations and Combinations, it is mandatory to be familiar with the concepts of the fundamental principle of counting. So the chapter starts with the fundamental principle of counting. The combination means selection of the things and permutation means selection + arrangement. This is a chapter based on all new concepts. It is not linked with any of the chapters studied in the previous classes. Apart from class 11 maths, the chapter is also important for JEE Main, CAT and many other competitive examinations.
Solutions of NCERT class 11 maths chapter 8 Binomial Theorem: We have studied the expansions like (a+b)^{2} and (a+b)^{3} in previous classes. The binomial theorem is part of algebra which describes the algebraic expansion of powers and binomials. In this particular chapter Binomial Theorem, we will study how to expand (a+b)^{n} in an easy way. We will study the binomial theorem for positive integral indices only and It can be used only with positive integral values of n.
CBSE NCERT solutions for class 11 maths chapter 9 Sequences and Series: In class 10 maths, you have studied a chapter arithematic progression. The chapter 9 sequence and series of class 11 maths is the extended version of the class 10 chapter. In class 10 maths, we have studied only arithematic progression but in class 11 you will study arithematic progression, geometric progression, and harmonic progression. The chapter is a part of arithematic and the question on the chapter will be on finding nth term, sum, and combination of two series.
NCERT solutions for class 11 maths chapter 10. Straight Lines: In previous classes, we have gone through the two-dimensional coordinate geometry. In class 11 we will learn three-dimensional coordinate geometry. This is a very important chapter of co-ordinate geometry. We will use the concepts of this chapter in the coming chapters of coordinate geometry as well as physics. Mainly the concepts of slope and tangents will be used further in Maths, Physics, and Chemistry too.
Solutions of NCERT class 11 maths chapter 11 Conic Sections: The chapter is the extension of the equation of lines class 10 maths. In this particular chapter, we will study the concept of the equation of circles and its applications, the equation of ellipse and hyperbolas and its applications. Terms parabola and hyperbola has been introduced by a mathematician Apollonius. The curves introduced in the chapter are known as conic sections or conics. The concept studied in this chapter will be used in the NCERT class 12 chapter applications of integrals.
CBSE NCERT solutions for class 11 maths chapter 12 Introduction to Three Dimensional Geometry: In previous classes you have learned, to locate the position of a point in a plane, we need two intersecting lines in the plane. Both the lines are called coordinate axes and the two numbers are called coordinates of that point. In the previous classes, we have studied about points lying on a plane. Here in this chapter, we will learn about the points on a multidimensional figure. The NCERT Solutions for Class 11 Maths Chapter 12 is very important in the analysis of motion in space. In this chapter, we will study how to represent a point in space, the distance between two points in three dimensions and section formulae.
NCERT solutions for class 11 maths chapter 13. Limits and Derivatives: The chapter limits and derivatives in an introduction to the introductory chapter of calculus and the concept studied here will be further used in class 12 mathematics also. Calculus is the branch of mathematics in which we learn to deal with the study of change in the function's value as the points in the domain change. Through this chapter, you will learn the idea of derivative, then the definition of a limit and some algebra of limits. The chapter creates as strong foundations for calculus and plays a vital role in higher mathematics.
Solutions of NCERT class 11 maths chapter 14 Mathematical Reasoning: The chapter is structured in a manner that if you go through it in the given manner then this will definitely work well for you all in terms of an increase in logical ability. Logical ability is an important thing that one should have. Logic is important to make a decision or conclude some using some data points. In this chapter, we will discuss some fundamentals of deductive reasoning. In deductive reasoning we will be given some set of facts and using this fact we will deduct another fact.
CBSE NCERT solutions for class 11 maths chapter 15. Statistics: In previous classes, we have studied statistics. Here it is introduced with a bit higher level of concepts. Statistics on its own is an individual subject apart from mathematics. This is one of the most important chapters of NCERT Solutions for Class 11 Maths. We keep statistics on many things in our daily life. The concept that we will study in this chapter is widely used in data analysis. The statistics obtained using data will be helpful for prediction. This chapter is very important in daily life and for the exam also.
NCERT solutions for class 11 maths chapter 16. Probability: Before coming to the concept of probability, you must go through the concepts related to chapter permutation and combination. We are already aware of the basic concepts related to probability. In class 11 maths, the probability is of a bit higher level as compared to previous classes. It is a very important chapter for the board examination and many other competitive exams. The concept of random variable and probability will be used for prediction and estimation. We will find the probability on the basis of observations and collected data. The concept of sets, functions, statistics, and probability are used in the modern theory of machine learning and artificial intelligence.
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You will be much comfortable while doing homework using NCERT solutions for class 11 maths.
You can take out some observations, concepts, and formulae to solve some specific kinds of problems.
A collection of short notes can be made using these solutions which can be used in the exam time.
You will learn some mathematical reasoning based topics like- permutation and combination, probability, set theory, etc.
4. Evaluate the following limits
1.(iv) Write the negation of the following statement:
(iv) s: There exists a number such that .
1.(i) A box contains red marbles, blue marbles and green marbles. marbles are drawn from the box, what is the probability that (i) all will be blue?