NCERT SOLUTIONS FOR CLASS 11
Introduction about NCERT Solutions for Class 11 Maths
NCERT Solutions for class 11 given here have been put together by our content analysts who have many years of experience of creating content for CBSE board, ICSE board and all Indian state boards. The solutions have been designed to simplify all class 11 Math problems, which are given in the textbooks. All the 16 chapters as prescribed by CBSE have been included in NCERT Maths class 11 solutions.
Why students prefer NCERT Solutions for Class 11 Maths
Students prefer NCERT solutions to do their regular home assignment, mock tests and ace their final exams. In most of the common entrance tests conducted for admissions in Engineering institutes, the questions are designed as per the syllabus of textbooks. Therefore, the students prefer to practice these NCERT Solution exercises on a regular basis to score better marks in exams.
Topics Covered in NCERT Solutions for Class 11 Maths & Brief Detail About Them
NCERT Solutions of class 11 maths contains all chapter solutions in pdf. Solutions can be downloaded chapter wise. NCERT solutions for class 11 cover all the chapters including Sets, Relations and Functions, Trigonometric Functions, Principle of Mathematical Induction, Complex Numbers and Quadratic Equations, Linear Inequalities, Permutations and Combinations, Binomial Theorem, Sequences and Series, Straight lines, Conic Sections, Introduction to Three Dimensional Geometry, Limits and Derivatives, Mathematical Reasoning, Statistics, Probability.
These all the chapters are fully comprehensive well explained. It can really help you with your exams, providing you with the easiest and fastest method to solve the question, additionally, the concept of solutions has kept so simple and easy to understand so that it can be remembered for a lifetime to students hence it will also help you cracking other higherlevel exams.
Students can easily use the PDF of the chapterwise solutions and gain conceptual knowledge to solve the problems according to the NCERT Maths textbook for Class 11. This helps students enhance their confidence, which is required to master concepts and perform well in exams.
NCERT Solutions for Class 11 Maths Chapter 1 – Sets
 Sets and Their Representations:
 A set is a welldefined collection of objects.
 The empty set:
 A set that does not contain any element is called an empty set.
 Finite and infinite sets
 A set that consists of a definite number of elements is called a finite set, otherwise, the set is called an infinite set
 Equal sets
 Two sets A and B are said to be equal if they have exactly the same elements
 Subsets
 A set A is said to be a subset of a set B if every element of A is also an element of B. Intervals are subsets of R.
 Power set
 A power set of a set A is a collection of all subsets of A. It is denoted by P(A).
 Universal set
 Basic set is called the “Universal Set”. The universal set is usually denoted by U, and all its subsets by the letters A, B, C, etc.
 Venn diagrams
 The relationships between sets can be represented by means of diagrams which are known as Venn diagrams.
 Operations on sets
 The union of two sets A and B is the set of all those elements which are either in A or in B.
 The intersection of two sets A and B is the set of all elements which are common. The difference between two sets A and B in this order is the set of elements that belong to A but not to B.
 Complement of a set
 The complement of a subset A of universal set U is the set of all elements of U which are not the elements of A.
 Practical problems on union and intersection of two sets
 n (A ∪ B) = n (A) + n (B) – n (A ∩ B)
NCERT Solutions for Class 11 Maths Chapter 2 – Relations and Functions
 Cartesian Poduct of Sets
 Cartesin Product: Given two nonempty sets P and Q. The cartesian product P×Q is the set of all ordered pairs of elements from P and Q.
 Relations:
 Relation: A relation R from a set A to set B is a subset of the cartesian product A×B obtained by describing a relationship between the first element x and the second element y of the ordered pairs in A×
 Domain: The set of all first elements of the ordered pairs in a relation R from a set A to B is called the domain of the relation R.
 Range: The set of all second elements in a relation R from a set A to a set B is called the range of the relation R. The entire set B is called the codomain of the relation R. Note: Range ⊆
 Functions
 Function: A relation from set A to set B is said to be a function if every element of set A has one and only one image in set B.
 RealValued Function: A function that has either R or one of its subsets as its range is called a realvalued function. If its domain is either R or a subset of R, it is called a real function.
 Types of functions:
 Identity Function: f:R→R by y=f(x)=x for each x∈R is identity function.
 Constant Function: f:R→R by y=f(x)=c,x∈R
 Polynomial Function: f:R→R by f(x)=a_{0}+a_{1}x+a_{2}x^{2}+…+a_{n}x^{n}, where n is a nonnegative integer and a0,a1,a2,…,an∈R
 Rational Functions: Functions of the form f(x)/g(x), where f(x) and g(x) are rational functions and g(x)≠0.
 Modulus Function: f:R→R by f(x)=x={x−x if x≥0if x<0
 Algebra of Real Functions:
 Addition of two real functions: Let f:X→R and g:X→R be any two real functions, where X⊂R, then (f+g)(x)=f(x)+g(x), for all x∈X.
 Subtraction of two real functions: Let f:X→R and g:X→R be any two real functions, where X⊂R, then (f−g)(x)=f(x)−g(x), for all x∈X.
 Multiplication by a scalar: Let f:X→R and α is a scalar. Then (αf)(x)=αf(x),x∈X
Multiplication of two real functions: Let f:X→R and g:X→R be two real functions. Then fg:X→R by (fg)(x)=f(x)g(x), for all x∈X
NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions
 Angles
 Angle: Angle is a measure of rotation of a given ray about its initial point.
 Degree measure: If a rotation from the initial side to terminal side is 1/360 th a revolution, the angle is said to have a measure of one degree.
 Radian measure: Angle subtended at the centre by an arc of length 1 unit in a unit circle (circle of radius 1 unit) is said to have a measure of 1 radian.
 Relation between radian and real numbers: Radian measures and real numbers can be considered as one and the same.
 Relation between degree and radian
 Trigonometric Functions
 Sign of trigonometric functions
 Domain and range of trigonometric functions
 Trigonometric Functions of Sum and Difference of Two angles
 Trigonometric functions of sum of two angles: The basic results in this connection are called trigonometric identities.
 Trigonometric functions of a difference of two angles; The basic results in this connection are called trigonometric identities.
 Trigonometric Equations
 Trigonometric Equations: Equations involving trigonometric functions of a variable are called trigonometric equations.
 The principle of mathematical induction
 The principle of mathematical induction is one such tool that can be used to prove a wide variety of mathematical statements.
 Each such statement is assumed as P(n) associated with positive integer n, for which the correctness for the case n = 1 is examined. Then assuming the truth of P(k) for some positive integer k, the truth of P (k+1) is established.
 Complex Number
 Complex Number: Any number of the form a+ib, where a,b∈R and i^{2}=−1″i”iscalled”iota”, is a complex number. A complex number is denoted by z.
Here, a is called the real part and denoted by Re z, and b is called the imaginary part and denoted by Imz.

 Equality of complex numbers: Two complex numbers z_{1}=a+ib and z_{2}=c+idare equal if a=c and b=d.
 The Modulus and the Conjugate of a complex number.
 Modulus of a complex number: Let z=a+ib be a complex number. Then, modulus of z, denoted by z.
 Conjugate of a complex number: For any complex number z=a+ib, the conjugate, represented by z¯, is given by z¯=a−ib.
 Argand Plane and Polar Representation.
 The complex number x+iy corresponds to the ordered pair (x,y) can be shown geometrically as the unique point P(x,y) in the XY− plane and viceversa.
 The plane that has a complex number assigned to each of its points is called the complex plane or the Argand plane.
 In the Argand plane, the modulus of the complex number is the distance between the point P(x,y) and the origin O(0,0).
 The points on the xaxis correspond to the complex numbers of the form a+i0 and the points on the yaxis corresponds to the complex numbers of the form 0+ib.
 The xaxis and yaxis in the Argand plane are called the real axis and the imaginary axis.
 Representation of complex numbers and their conjugate.
 Polar form of the complex number.
 Square root of the complex number.
 Square root of the complex number.
NCERT Solutions for Class 11 Maths Chapter 6 – Linear Inequalities
 Inequalities
 Two real numbers or two algebraic expressions related by the symbols <, >, ≤ or ≥ form an inequality.
 Equal numbers may be added to (or subtracted from ) both sides of an inequality.
 Both sides of an inequality can be multiplied (or divided ) by the same positive number. But when both sides are multiplied (or divided) by a negative number, then the inequality is reversed.
 The values of x, which make an inequality a true statement, are called solutions of the inequality
 Algebraic solutions of linear inequalities in one variable and their graphical representation
 To represent x < a (or x > a) on a number line, put a circle on the number a and a dark line to the left (or right) of the number a.
 To represent x ≤ a (or x ≥ a) on a number line, put a dark circle on the number a and dark the line to the left (or right) of the number x.
 If inequality is having ≤ or ≥ symbol, then the points on the line are also included in the solutions of the inequality and the graph of the inequality lies left (below) or right (above) of the graph of the equality represented by a dark line that satisfies an arbitrary point in that part.
 If inequality is having < or > symbol, then the points on the line are not included in the solutions of the inequality and the graph of the inequality lies to the left (below) or right (above) of the graph of the corresponding equality represented by a dotted line that satisfies an arbitrary point in that part.
 Graphical solution of linear inequalities in two variables
 The solution region of a system of inequalities in the region satisfies all the given inequalities in the system simultaneously.
 Fundamental Principle of Counting
 Fundamental principle of counting If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of occurrence of the events in the given order is m × n.
 Permutations
 Permutations: A permutation is an arrangement in a definite order of a number of objects taken some or all at a time.
 Permutations when all the objects are distinct: The number of permutations of n different objects taken r at a time, where 0 < r ≤ n and the objects do not repeat is n ( n – 1) ( n – 2). . .( n – r + 1)
 Factorial notation
 Derivation of formula
 Permutations when all the objects are not distinct objects
 Combinations
 The number of combinations of n different things taken r at a time, denoted by nCr.
NCERT Solutions for Class 11 Maths Chapter 8 – Binomial Theorem
 Binomial Theorem for positive integral indices
 Coefficients are known as binomial coefficients.
 Number of terms in binomial expansion = n + 1
 In every term of the expansion, a sum of indices of a and b is n.
 General Term and Middle Terms
 General term: The (r + 1)^{th} term is called the general term of the expansion (a + b)^{n}.
 Middle terms: If n is even then the number of terms in the expansion will be n + 1. If n is odd then there will be two middle terms in the expansion.
NCERT Solutions for Class 11 Maths Chapter 9 – Sequences and Series
 Sequences
 Sequence
 Finite Sequence: A sequence containing a finite number of terms is called a finite sequence.
 Infinite Sequence: A sequence containing an infinite number of terms is called a finite sequence.
 Fibonacci Sequence: A sequence generated by the recurrence relation is called the Fibonacci sequence.
 Series
 Series: The sum expressed as a_{1} + a_{2} + a_{3} + … is called series.
 Finite Series: A series is called finite series if it has got a finite number of terms.
 Infinite Series A series is called finite series if it has got an infinite number of terms.
 Arithmetic Progression
 Arithmetic Progression: An arithmetic progress is a sequence in which terms increase or decrease regularly by the same constant.
 Standard form of an AP
 General form of an AP
 Properties of AP
 Sum of first n terms of an AP.
 Arithmetic Mean: The sequence a, A, b is in A.P.
 Geometric Progression
 Geometric progression: A sequence is said to be geometric progression if the ratio of any term to its preceding term is the same throughout.
 General term of a GP
 Finite or infinite GP
 Finite or infinite geometric series
 Sum to n terms of a GP
 Geometric mean: The sequence a, G, b is G.P.
 Relation between AM and GM
 Relation between AM and GM
 Sum to n terms of special series
 Sum of first n natural numbers
 Sum of squares of first n natural numbers
 Sum of cubes of first n natural numbers
 Infinite GP and its sum
 Infinite GP.
 Formula for finding sum to infinity
NCERT Solutions for Class 11 Maths Chapter 10 – Straight Lines
 Slope of a line:
 Slope of a line
 Slope of a line when coordinates of any two points on the line are given.
 Conditions of parallelism and perpendicularity of lines in terms of their slopes.
 Two lines are parallel if and only if their slopes are equal.
 Two lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.
 Angle between two lines.
 Collinearity of three points.
 Various forms of the equation of a line:
 Horizontal and vertical lines
 Point slope form of a line.
 Twopoint form of a line
 Slopeintercept form of a line
 Intercept form of a line
 Normal form of a line
 General Equation of a line
 Any equation of the form Ax+By+C=0, where A and B are not zero simultaneously is called a general linear equation or general equation of a line.
 Different forms of Ax+By+C=0
(i) Slopeintercept form
(ii) Intercept form
(iii) Normal form
NCERT Solutions for Class 11 Maths Chapter 11 – Conic Sections
 Sections of a cone
 Circle, ellipse, parabola, and hyperbola
 Degenerated conic sections
 Circle
 A circle is the set of all points in a plane that are equidistant from a fixed point in the plane.
 The equation of a circle with center (h, k) and the radius r
 Parabola
 A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point in the plane.
 The equation of the parabola with focus at (a, 0) a > 0 and directrix x = – a is y2 = 4ax.
 Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose endpoints lie on the parabola.
 Length of the latus rectum of the parabola y2 = 4ax is 4a.
 Ellipse
 An ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant
 Equation of an ellipse with foci on the xaxis
 Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose endpoints lie on the ellipse.
 Length of the latus rectum of the ellipse
 The eccentricity of an ellipse is the ratio between the distances from the center of the ellipse to one of the foci and to one of the vertices of the ellipse.
 Hyperbola
 A hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is a constant.
 The equation of a hyperbola with foci on the xaxis.
 Latus rectum of a hyperbola is a line segment perpendicular to the transverse axis through any of the foci and whose endpoints lie on the hyperbola.
 Length of the latus rectum of the hyperbola.
 The eccentricity of a hyperbola is the ratio of the distances from the center of the hyperbola to one of the foci and to one of the vertices of the hyperbola.
 Coordinate axes and coordinate planes in threedimensional shapes
 In three dimensions, the coordinate axes of a rectangular Cartesian coordinate system are three mutually perpendicular lines. The axes are called the x, y, and zaxes.
 The three planes determined by the pair of axes are the coordinate planes, called XY, YZ, and ZXplanes.
 The three coordinate planes divide the space into eight parts known as octants.
 Coordinates of a point in space
 The coordinates of a point P in threedimensional geometry are always written in the form of tripletlike (x, y, z). Here x, y, and z are the distances from the YZ, ZX, and XYplanes.
 Any point on xaxis is of the form (x, 0, 0)
 Any point on yaxis is of the form (0, y, 0)
 Any point on zaxis is of the form (0, 0, z)
 Distance between two points
 Section formula
 Section formula
 Midpoint formula
NCERT Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives
 Intuitive Idea of Derivative
 The expected value of the function as dictated by the points to the left of a point defines the left hand limit of the function at that point. Similarly the right hand limit
 Limits
 Limits: Limit of a function at a point is the common value of the left and right hand limits, if they coincide.
 Algebra of limits
 Limits of polynomials and rational functions
 Limits of Trigonometric Functions
 Derivatives
 Algebra of derivative of functions
 Derivative of polynomials and trigonometric function
NCERT Solutions for Class 11 Maths Chapter 14 – Mathematical Reasoning
 Statements
 A sentence is called a mathematically acceptable statement if it is either true or false but not both
 New Statements from old:
 Negation of a statement: Negation of a statement p: If p denote a statement, then the negation of p is denoted by ∼p
 Compound statements: A statement is a compound statement if it is made up of two or more smaller statements. The smaller statements are called component statements of the compound statement.
 Special Words/Phrases
 The word “And”
 The word “Or”
 Quantifiers
 Implications
 Contrapositive and converse: The contrapositive of a statement p ⇒ q is the statement ∼ q ⇒ ∼p. The converse of a statement p ⇒ q is the statement q ⇒ p ⇒ q together with its converse, gives p if and only if q.
 Validating Statements
 The following methods are used to check the validity of statements: (i) direct method (ii) contrapositive method (iii) method of contradiction (iv) using a counterexample.
NCERT Solutions for Class 11 Maths Chapter 15 – Statistics
 Measures of Dispersion
 Range
 Quartile deviation
 Mean deviation
 Standard deviation
 Range
 Range of a series = Maximum value – Minimum value
 Mean Deviation
 Mean deviation for ungrouped data
 Mean deviation for grouped data
 Mean deviation about mean
 Mean deviation about median
 Limitations of mean deviation
 Variance and Standard Deviation
 Standard deviation
 Standard deviation of a discrete frequency distribution
 Standard deviation of continuous frequency distribution
 Shortcut method to find variance and standard deviation
 Analysis of frequency distribution
 Comparison of two frequency distributions with same mean
NCERT Solutions for Class 11 Maths Chapter 16 – Probability
 Random Experiments
 Outcomes: The set of all possible outcome.
 Sample space: Elements of sample space
 Event
 Occurrence of an event
 Types of events
 Impossible and sure events: The empty set. The whole sample space is a sure event.
 Simple events: If an event E has only one sample point of a sample space.
 Compound event: If an event has more than one sample point.
 Algebra of events
 Complementary event: The set A′ or S – A
 The event A or B: The set A ∪ B
 Mutually exclusive events: A and B are mutually exclusive if A ∩ B = φ
 Exhaustive events: Events E_{1}, E_{2},…, En are mutually exclusive and exhaustive if E_{1} ∪ E_{2} ∪ …∪ E_{n} = S and E_{i} ∩ E_{j} = φ V i ≠ j
 Axiomatic Approach to Probability
 Probability of an event
 Probabilities of equally likely outcomes
 Probability of the event A or B
 Probability of event ‘not A’
Benefit of NCERT Solutions for Class 11 Maths
NCERT solutions for class 11 Maths will create better and effective learning for students. It will help in building a strong foundation of all the concepts for higherlevel classes and also for competitive exams.
NCERT Class 11th Maths solutions will help students to clear their doubts by offering an indepth understanding of the concepts. Through detailed explanations, students can learn the concepts which will enhance their thinking and learning abilities.
 It is very easy for students to access the solutions for every application from the chapters available.
 There are graphs and illustrations provided to students that help them understand the concepts better and retain them.
 These solutions are prepared by an expert team of Fliplearn that focuses on accuracy.
 The study material helps students to bridge the knowledge gap with the exercises and solutions.
 Simple and easily understandable solutions are provided.
 Detailed study material is available for class 11 students
Fliplearn is here to simplify your problems and make learning easy and enjoyable. Download the Fliplearn app to find more help and a personalized experience.
Frequently Asked Questions About NCERT Solutions for Class 11
How Fliplearn’s NCERT solutions assist us in scoring good marks in the exam?
The content analysts at Fliplearn have designed the NCERT Solutions in accordance with the syllabus designed by the CBSE board. The essential explanation is provided for major points to make the concepts easier for the students while learning. NCERT solutions are designed with the aim of helping students ace the exam without fear. The solutions mainly help students to improve their problemsolving abilities which are important for the exam.
What are the important concepts in chapter 11 of conic sections?
The chapter covers topics like circle, parabola, ellipse, hyperbola, and degenerate conic sections. In parabola, you will learn standard equations of parabola and latus rectum. In the case of an ellipse, you will learn the relationship between the semimajor axis, semiminor axis, and the distance of the focus from the center of the ellipse, Special cases of an ellipse, and latus rectum.
In this chapter, you will also learn eccentricity, standard equation, and latus rectum of Hyperbola. A conic section is one of the important chapters of class 11 maths.
What will I study in Chapter 4 Mathematical Induction of NCERT Solutions for Class 11 Maths?
Mathematical Induction is a technique that is used to prove whether a given statement is true or false. The important fact is that the theorem should be true for every given natural number. After covering the chapter students will be familiar with the following points.
 Proving a statement is the main motive.
 The proof should be true for all the values of natural numbers.
 For initial value, the statement should be true.
 For values till nth, the statement should be true.
 All the steps in the proof should be true and justified.
How many chapters are there in the class 11 Maths NCERT textbook?
There is a total of 16 chapters in class 11 Maths NCERT textbook. The name of the chapters are Sets (Chapter 1), Relations and Functions (Chapter 2), Trigonometric Functions (Chapter 3), Principle of Mathematical Induction (Chapter 4), Complex Numbers and Quadratic Equations (Chapter 5), Linear Inequalities (Chapter 6), Permutations and combination (Chapter 7), Binomial Theorem (Chapter 8), Sequence and Series (Chapter 9), Straight Lines (Chapter 10), Conic Sections (Chapter 11), Introduction to Three Dimensional Geometry (Chapter 12), Limits and Derivatives (Chapter 13), Mathematical Reasoning (Chapter 14), Statistics (Chapter 15), Probability (Chapter 16)
Is it required to solve each and every problem of NCERT Solutions for Class 11th Maths?
In the CBSE board, each and every problem irrespective of their understanding level are important for the exam. So the students are recommended to solve the NCERT textbook on a daily basis to gain a grip on the fundamental concepts. By regular practice, students will be able to analyze their areas of weakness and work on them for a better academic score. The stepwise explanation under each problem will help students to perform well in the annual exams.
NCERT Solutions for other Classes
NCERT Solutions is also available for other classes. Students preparing for class 6th, 7th, 8th, 9th, 10th and 12th will find it the best way to score good marks. NCERT Solutions for class 6th, 7th, 8th, 9th, 10th and 12th provides a plethora of study material and references that help students trust it the most.
NCERT Solution for Class 11 Maths
Addition 
202021 
Board 
CBSE Curriculum 
Subject 
Math 
PDF Download 
Yes 
Textbook Solutions 
Class 11 
Total Chapters 
16 
CLASSES