NCERT Solutions for Class 11 Maths consist of solved answers for all the chapters, exercise-wise. This is a great material for students who are preparing for Class 11 exams.The solutions provided here are with respect to NCERT syllabus and curriculum. These materials are prepared by our expertise keeping on mind students understanding level.
NCERT textbooks are prescribed by CBSE board. So all the students who are studying under this board have the best solution materials here. Class 11 is also an important class for students, as the level of education increases here. In this standard, students have opted for Maths subject as their main subject, like Biology and Commerce. Students have to more focussed about their studies as this is the start of their future learning and career. Therefore, using these materials students can really score good marks in their final exams.
Class 11 Maths NCERT Solutions
NCERT solutions for 11th standard Maths subject covers the chapters which are present in the textbook, exercise-wise. The chapters covered here are Sets, Trigonometric functions, sequences and series, Three dimensional geometry, Relations and functions, statistics, binomial theorem, probability, etc. The solutions for these chapters are available in PDF format, which students can download easily and learn them as per their convenience.
NCERT Solutions for Class 11 Maths
- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutation and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight Lines Exercise 10.1
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability
Class 11 Maths NCERT Solutions PDF Download:
All the solutions for all the chapters for class 11 Maths subject have been arranged in a proper manner. Students can easily find answers for any question here which is mentioned in the book. These solutions are in accordance with 2019-2020 syllabus. So students need not worry about the given content for the solutions. They have well prepared and structured solutions available here, by us.
NCERT Solutions for Class 11 Maths Chapters
Solving the questions present in the textbooks is not an easy task. It requires mathematical and logical skills to solve those problems with a lot of efforts. Class 11th Maths is a next level Maths, where students will learn a large variety of topics, which they are going to face in higher studies as well, such as in Class 12th.
As we all know, 12th is the most important class for all the students, as after this they move to their college level. But you can get admission in a good recognized institute or university, only when you have score the minimum qualifying marks. And it is only then, you will be able to get good jobs or get placed directly from campus recruitment, conducted by colleges. Therefore, it very necessary for you to build a strong base in class 11 maths subject and understand the concepts deeply.
To make it easier for them to learn, we are providing here solutions for all the students of 11th standard, such that, they can clarify their doubts for all types of questions. Below are the introductions for each chapter and links for all the exercises, read them thoroughly.
Class 11 Maths Chapter 1 Sets
The concept of set serves as a fundamental part of the present day mathematics. Today this concept is being used in almost every branch of mathematics. Sets are used to define the concepts of relations and functions. The study of geometry, sequences, probability, etc. requires the knowledge of sets. Solve the problems for each exercise by clicking on below links;
Class 11 Maths Chapter 2 Relation and Functions
In this Chapter, we will learn how to link pairs of objects from two sets and then introduce relations between the two objects in the pair. Finally, we will learn about special relations which will qualify to be functions. The concept of function is very important in mathematics since it captures the idea of a mathematically precise correspondence between one quantity with the other.
Class 11 Maths Chapter 3 Trigonometric Functions
The word ‘trigonometry’ is derived from the Greek words ‘trigon’ and ‘metron’ and it means ‘measuring the sides of a triangle’. Trigonometry is used in many areas such as the science of seismology, designing electric circuits, describing the state of an atom, predicting the heights of tides in the ocean, analysing a musical tone and in many other areas.
Class 11 Maths Chapter 4 Principle of Mathematical Induction
Deduction in a nutshell is given a statement to be proven, often called a conjecture or a theorem in mathematics, valid deductive steps are derived and a proof may or may not be established, i.e., deduction is the application of a general case to a particular case. In contrast to deduction, inductive reasoning depends on working with each case, and developing a conjecture by observing incidences till we have observed each and every case. It is frequently used in mathematics and is a key aspect of scientific reasoning, where collecting and analysing data is the norm. Thus, in simple language, we can say the word induction means the generalisation from particular cases or facts.
In algebra or in other discipline of mathematics, there are certain results or statements that are formulated in terms of n, where n is a positive integer. To prove such statements the well-suited principle that is used–based on the specific technique, is known as the principle of mathematical induction.
Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations
In earlier classes, we have studied linear equations in one and two variables and quadratic equations in one variable. We have seen that the equation x 2 + 1 = 0 has no real solution as x 2 + 1 = 0 gives x 2 = – 1 and square of every real number is non-negative. So, we need to extend the real number system to a larger system so that we can find the solution of the equation x 2 = – 1. In fact, the main objective is to solve the equation ax2 + bx + c = 0, where D = b 2 – 4ac < 0, which is not possible in the system of real numbers.
Class 11 Maths Chapter 6 Linear Inequalities
In earlier classes, we have studied equations in one variable and two variables and also solved some statement problems by translating them in the form of equations. Now a natural question arises: ‘Is it always possible to translate a statement problem in the form of an equation? For example, the height of all the students in your class is less than 160 cm. Your classroom can occupy atmost 60 tables or chairs or both. Here we get certain statements involving a sign ‘<’ (less than), ‘>’ (greater than), ‘≤’ (less than or equal) and ≥ (greater than or equal) which are known as inequalities.
In this Chapter, we will study linear inequalities in one and two variables. The study of inequalities is very useful in solving problems in the field of science, mathematics, statistics, economics, psychology, etc.
Class 11 Maths Chapter 7 Permutations and Combination
In this Chapter, we shall learn some basic counting techniques which will enable us to answer this question without actually listing 3-digit arrangements. In fact, these techniques will be useful in determining the number of different ways of arranging and selecting objects without actually listing them. As a first step, we shall examine a principle which is most fundamental to the learning of these techniques.
Class 11 Maths Chapter 8 Binomial Theorem
In earlier classes, we have learnt how to find the squares and cubes of binomials like a + b and a – b. Using them, we could evaluate the numerical values of numbers like (98) 2 = (100 – 2) 2 , (999) 2 = (1000 – 1) 2 , etc. However, for higher powers like (98) 7 , (101) 10 , etc., the calculations become difficult by using repeated multiplication. This difficulty was overcome by a theorem known as binomial theorem. It gives an easier way to expand (a + b) n , where n is an integer or a rational number. In this Chapter, we study binomial theorem for positive integral indices only.
Class 11 Maths Chapter 9 Sequences and Series
Sequences, following specific patterns are called progressions. In previous class, we have studied about arithmetic progression (A.P). In this Chapter, besides discussing more about A.P.; arithmetic mean, geometric mean, relationship between A.M. and G.M., special series in forms of sum to n terms of consecutive natural numbers, sum to n terms of squares of natural numbers and sum to n terms of cubes of natural numbers will also be studied.
Class 11 Maths Chapter 10 Straight Lines
In the this Chapter, we shall continue the study of coordinate geometry to study properties of the simplest geometric figure – straight line. Despite its simplicity, the line is a vital concept of geometry and enters into our daily experiences in numerous interesting and useful ways. Main focus is on representing the line algebraically, for which slope is most essential.
Class 11 Maths Chapter 11 Conic Sections
In the preceding Chapter 10, we have studied various forms of the equations of a line. In this Chapter, we shall study about some other curves, viz., circles, ellipses, parabolas and hyperbolas. The names parabola and hyperbola are given by Apollonius. These curves are in fact, known as conic sections or more commonly conics because they can be obtained as intersections of a plane with a double napped right circular cone. These curves have a very wide range of applications in fields such as planetary motion, design of telescopes and antennas, reflectors in flashlights and automobile headlights, etc. Now, in the subsequent sections we will see how the intersection of a plane with a double napped right circular cone results in different types of curves.
Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry
To locate the position of a point in a plane, we need two intersecting mutually perpendicular lines in the plane. These lines are called the coordinate axes and the two numbers are called the coordinates of the point with respect to the axes. But in case, of 3D figures or sections, we need not only two but three points representing the perpendicular distances of the point from three mutually perpendicular planes. The three numbers representing the three distances are called the coordinates of the point with reference to the three coordinate planes. So, a point in space has three coordinates. In this Chapter, we shall study the basic concepts of geometry in three dimensional space.
Class 11 Maths Chapter 13 Limits and Derivatives
This chapter is an introduction to Calculus. Calculus is that branch of mathematics which mainly deals with the study of change in the value of a function as the points in the domain change. First, we give an intuitive idea of derivative (without actually defining it). Then we give a naive definition of limit and study some algebra of limits. Then we come back to a definition of derivative and study some algebra of derivatives. We also obtain derivatives of certain standard functions.
Class 11 Maths Chapter 14 Mathematical Reasoning
In this Chapter, we shall discuss about some basic ideas of Mathematical Reasoning. All of us know that human beings evolved from the lower species over many millennia. The main asset that made humans “superior” to other species was the ability to reason. How well this ability can be used depends on each person’s power of reasoning. How to develop this power? Here, we shall discuss the process of reasoning especially in the context of mathematics.
In mathematical language, there are two kinds of reasoning – inductive and deductive. We have already discussed the inductive reasoning in the context of mathematical induction. In this Chapter, we shall discuss some fundamentals of deductive reasoning.
Class 11 Maths Chapter 15 Statistics
We know that statistics deals with data collected for specific purposes. We can make decisions about the data by analysing and interpreting it. In earlier classes, we have studied methods of representing data graphically and in tabular form. This representation reveals certain salient features or characteristics of the data. We have also studied the methods of finding a representative value for the given data. This value is called the measure of central tendency. Recall mean (arithmetic mean), median and mode are three measures of central tendency. A measure of central tendency gives us a rough idea where data points are centred. But, in order to make better interpretation from the data, we should also have an idea how the data are scattered or how much they are bunched around a measure of central tendency.
Class 11 Maths Chapter 16 Probability
In earlier classes, we studied about the concept of probability as a measure of uncertainty of various phenomenon. We have obtained the probability of getting an even number in throwing a die as 3/6 i.e., ½ . Here the total possible outcomes are 1,2,3,4,5 and 6 (six in number). The outcomes in favour of the event of ‘getting an even number’ are 2,4,6 (i.e., three in number). In general, to obtain the probability of an event, we find the ratio of the number of outcomes favourable to the event, to the total number of equally likely outcomes. This theory of probability is known as classical theory of probability.
In this Chapter, we will study about this approach called axiomatic approach of probability. To understand this approach we must know about few basic terms viz. random experiment, sample space, events, etc.
We have tried to give the best solutions for all the chapters of NCERT textbooks Maths for class 11. If students finds here any difficulty, please drop a comment, we will try to resolve them as soon as possible.