CBSE NCERT Solutions For Class 11 Maths: All the students who are gearing up for the 11th Class exam as well as preparing for the Class 12 board exam should definitely refer to this article on CBSE NCERT Solutions for Class 11 Maths. This article is a relief for all those students who find mathematics tough and unmanageable. Scoring a good score in the mathematics exam is essential as it will further aid in choosing the streams accordingly. Students who want to score well in Class 11 Maths should definitely go through the below article on CBSE NCERT Solutions for Class 11 Maths. In this article, we bring you the complete NCERT Solutions for Class 11 Maths along with a detailed subject description.
CBSE NCERT Solutions For Class 11 Maths
Glance further to get the NCERT Solutions for CBSE Class 11 Maths. The solutions below are in the chapter-wise PDF form for each section and have been prepared by the best faculties at Embibe.
CBSE NCERT Solutions For Class 11 Maths
The CBSE NCERT Solutions for 11th Class Maths are provided below:
- 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: Permutations and Combinations
- Chapter 8: Binomial Theorem
- Chapter 9: Sequences and Series
- Chapter 10: Straight Lines
- 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
NCERT Solutions For Class 11 Maths Chapter Descriptions
CBSE NCERT Solutions for Class 11 Maths Chapter 1: Sets
A collection of objects which is well defined is considered a set. Set is defined by an existing rule, with which it is possible to conclude whether an object is a part of a set and whether a collection constitutes a set. Problems and solutions in this set tell us as to how to ascertain whether a collection is set, different types of sets, algebra of sets and power sets, how sets are represented using symbols, and Venn diagrams.
CBSE NCERT Solutions for Class 11 Maths Chapter 2: Relations and Functions
Much of mathematics is about finding a pattern – a recognisable link between quantities that change. In your daily life, you come across many patterns that characterise relations such as brother and sister, father and son, teacher and student. In mathematics also, you come across many relations such as number m is less than number n, line l is parallel to line m, set A is a subset of set B.
In all these, you notice that a relation involves pairs of objects in a certain order. In this chapter, you will learn how to link pairs of objects from two sets and then introduce relations between the two objects in the pair. Finally, you will also 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.
CBSE NCERT Solutions for 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’. The subject was originally developed to solve geometric problems involving triangles. It was studied by sea captains for navigation, surveyor to map out the new lands, by engineers and others.
Currently, 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, analyzing a musical tone and in many other areas. In earlier classes, you have studied the trigonometric ratios of acute angles as the ratio of the sides of a right angled triangle. You have also studied the trigonometric identities and application of trigonometric ratios in solving the problems related to heights and distances. In this Chapter, the concept of trigonometric ratios to trigonometric functions has been generalised and you will study their properties in a comprehensive way.
CBSE NCERT Solutions for Class 11 Maths Chapter 4: Principle Of Mathematical Induction
One key basis for mathematical thinking is deductive reasoning. In contrast to deduction, inductive reasoning depends on working with each case and developing a conjecture by observing incidences until you 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, you can say the word induction means the generalisation from particular cases or facts.
In algebra or in other disciplines 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.
CBSE NCERT Solutions for Class 11 Maths Chapter 5: Complex Numbers And Quadratic Equations
In earlier classes, you must have studied linear equations in one and two variables and quadratic equations in one variable. You had seen that the equation x2 + 1 = 0 has no real solution as x2 + 1 = 0 gives x2 = – 1 and square of every real number is non-negative. So, you need to extend the real number system to a larger system so that you can find the solution of the equation x2 = – 1. In fact, the main objective is to solve the equation ax2 + bx + c = 0, where D = b2 – 4ac < 0, which is not possible in the system of real numbers.
CBSE NCERT Solutions for Class 11 Maths Chapter 6: Linear Inequalities
In previous classes, you would 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 at most 60 tables or chairs or both. Here you 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, you 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, optimization problems, economics, psychology, etc.
CBSE NCERT Solutions for Class 11 Maths Chapter 7: Permutations And Combinations
Suppose you have a suitcase with a number lock. The number lock has 4 wheels each labelled with 10 digits from 0 to 9. The lock can be opened if 4 specific digits are arranged in a particular sequence with no repetition. Somehow, you have forgotten this specific sequence of digits. You remember only the first digit which is 7. In order to open the lock, how many sequences of 3-digits you may have to check with? To answer this question, you may, immediately, start listing all possible arrangements of 9 remaining digits taken 3 at a time. But, this method will be tedious, because the number of possible sequences may be large. Here, in this chapter, you shall learn some basic counting techniques which will enable you to answer this question without actually listing 3-digit arrangements.
CBSE NCERT Solutions for Class 11 Maths Chapter 8: Binomial Theorem
In prior classes, you learned how to find the squares and cubes of binomials like a + b and a – b. Using them, you could evaluate the numerical values of numbers like (98)2 = (100 – 2)2 , (999)3 = (1000 – 1)3 , etc. However, for higher powers like (98) 5, (101) 6, etc., the calculations become difficult by using repeated multiplication. This difficulty was overcome by a theorem known as the Binomial Theorem. It gives an easier way to expand (a + b) n, where n is an integer or a rational number. In this chapter, you will study the Binomial Theorem for positive integral indices only.
CBSE NCERT Solutions for Class 11 Maths Chapter 9: Sequences And Series
In mathematics, the word, “sequence” is used in much the same way as it is in ordinary English. When it is said that a collection of objects is listed in a sequence, it usually means that the collection is ordered in such a way that it has an identified first member, second member, third member and so on. For example, the population of human beings or bacteria at different times form a sequence. The amount of money deposited in a bank, over a number of years form a sequence.
Depreciated values of certain commodities occur in a sequence. Sequences have important applications in several spheres of human activities. Sequences, following specific patterns, are called progressions. In the previous class, you have studied Arithmetic Progression (A.P). In this Chapter, besides discussing A.P, Arithmetic mean, Geometric mean, the Relationship between A.M. and G.M., Special series in forms of a 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.
CBSE NCERT Solutions for Class 11 Maths Chapter 10: Straight Lines
You must now be familiar with two-dimensional coordinate geometry from earlier classes. Mainly, it is a combination of algebra and geometry. A systematic study of geometry by the use of algebra was first carried out by celebrated French philosopher and mathematician René Descartes, in his book ‘La Géométry, published in 1637. This book introduced the notion of the equation of a curve and related analytical methods into the study of geometry. The resulting combination of analysis and geometry is referred to now as Analytical geometry.
To recapitulate, the location of the points (6, – 4) and (3, 0) in the XY-plane is shown in Fig 10.1. We may note that the point (6, – 4) is at 6 units distance from the y-axis measured along the positive x-axis and at 4 units distance from the x-axis measured along the negative y-axis. Similarly, the point (3, 0) is at 3 units distance from the y-axis measured along the positive x-axis and has zero distance from the x-axis.
CBSE NCERT Solutions for Class 11 Maths Chapter 11: Conic Sections
In the preceding Chapter 10, you studied various forms of the equations of a line. In this chapter, you shall study 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, you will see how the intersection of a plane with a double napped right circular cone results in different types of curves.
CBSE NCERT Solutions for Class 11 Maths Chapter 12: Introduction to Three Dimensional Geometry
You may recall that to locate the position of a point in a plane, you 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. In actual life, you do not have to deal with points lying in a plane only. For example, consider the position of a ball thrown in space at different points of time or the position of an aeroplane as it flies from one place to another at different times during its flight. Similarly, if you were to locate the position of the lowest tip of an electric bulb hanging from the ceiling of a room or the position of the central tip of the ceiling fan in a room, you will not only require the perpendicular distances of the point to be located from two perpendicular walls of the room but also the height of the point from the floor of the room.
CBSE NCERT Solutions for 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 will bring you back the definition of derivative and study some algebra of derivatives. You will also obtain derivatives of certain standard functions.
CBSE NCERT Solutions for Class 11 Maths Chapter 14: Mathematical Reasoning
In this chapter, some basic ideas of Mathematical Reasoning will be discussed. As you 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, the process of reasoning, especially in the context of mathematics, will be talked about. In mathematical language, there are two kinds of reasoning – inductive and deductive. The inductive reasoning in the context of mathematical induction has already been discussed. In this chapter, you shall also learn about some fundamentals of deductive reasoning.
CBSE NCERT Solutions for Class 11 Maths Chapter 15: Statistics
You must be knowing that statistics deals with data collected for specific purposes. You can make decisions about the data by analyzing and interpreting it. In earlier classes, you have studied methods of representing data both graphically and in tabular form. This representation reveals certain salient features or characteristics of the data. You have also studied the methods of finding a representative value for the given data. This value is called the measure of central tendency.
CBSE NCERT Solutions for Class 11 Maths Chapter 16: Probability
In earlier classes, you studied the concept of probability as a measure of uncertainty of various phenomena. You have also obtained the probability of getting an even number in throwing a die as 3 6 i.e., 1 2. 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 the classical theory of probability.
Now that you have the detailed CBSE NCERT Solutions for Class 11 Maths for all chapters, we hope you make the best use of it. All the PDF comprising the questions have been solved by the best and top academicians at Embibe. You can rely on the NCERT Solutions for Class 11 Maths PDF to get the best results.
Along with solving the questions, you can also take the Class 11 Revision Test for free on Embibe. Also, if you plan to appear for JEE Main in the near future then you can take JEE Main Mock Test on Embibe to get the best out of your preparation. Taking the mock test and practising questions will prepare you for various other competitive exams.
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