# NCERT Solutions Class 11 Maths

NCERT Solutions for Class 11 Maths provide a conceptual framework for all the topics of Class 11 Maths prescribed by CBSE Board. We have outlined all the important theorems and formulae with thorough explanations for students. NCERT Solutions for Maths are an essential aid for Class 11 Students. These Maths Solutions include answers to all the questions as per the latest CBSE Board Syllabus. Our subject-matter experts have designed these Maths NCERT Solutions for students of Class 11. Students can easily download NCERT Solutions free pdf.

These NCERT Solutions for Maths will help students in the preparation of Competitive Exams like JEE (Mains and Advanced), VITEEE and other state level exams. These Class 11 Solutions of NCERT are logically explainable as per the exercises given in the book.

EDUGROSS provides CBSE Class 11 Maths Solutions in PDF format which can be downloaded for free. If you have trouble in understanding a topic related to Maths, you can verify the answer to the questions given in the exercise of the book. By practicing the solutions that we have provided, students can aim for scoring higher in their Maths Board Exam.

Mathematics is said to be a methodical application of matter since the subject makes a man scientific or systematic. Mathematics helps us to keep our life in order and block disorder. Attributes such as reasoning power, creativity, abstract or spatial thinking, critical thinking, problem-solving ability and even effective communication skills are nurtured by Mathematics.

Mathematics is the rack of all creations without which the world cannot go on. Every human needs Mathematics in their daily life- be it a cook or a farmer, a carpenter or a mechanic, a shopkeeper or a doctor, an engineer or a scientist, a musician or a magician. Even small creatures like insects use Mathematics for their existence in the world.

##### 1) NCERT Solutions Class 11 Maths Chapter 1 Sets

In Mathematics, a set is a well-defined collection of distinct objects, considered as an object in its own right. The arrangement of the objects in the set does hold importance. A set may be denoted by placing its objects between a pair of curly braces. For example- the numbers 11, 5, and 7 are distinct objects when considered separately; when considered collectively, they form a single set of size three, written as {11, 5, 7} which could also be written as {7, 5, 11}, {5, 7, 11}, {7, 11, 5}, {5, 11, 7} or {11, 7, 5}.  Sets can also be denoted using capital Roman letters in italic such as P, Q, R.

NCERT Solutions Class 11 Maths Chapter 1 Sets Download free pdf. NCERT Solutions Class 11 Maths Chapter 1 Sets is provided here for students to learn better and for the help of the students in problem solving. The list of topics from this chapter are given below: –

• Introduction
• Sets and their Representations
• The Empty Set
• Finite and Infinite Sets
• Subsets
• Power Set
• Universal Set
• Venn Diagrams
• Operations on Sets
• Complement of a Set
• Practical Problems on Union and Intersection of Two Sets

Some important topics in ‘Sets’ are as follows-

• The union of two sets A and B are said to be contained elements that are either in set A and set B. The union of A and B is denoted as: ABAB.
• The intersection of two sets A and B are said to be contained elements that are common in both the sets. The intersection of A and B is denoted as: A∩BA∩B.
• The complement of a set A is the set of all elements given in the universal set U that are not contained in A. The complement of A is denoted as A′A′.
• For any two sets A and B, the following holds true:
• (AB)′ = A′∩B′
• (A∩B)′ = A′B′
• n(AB) = n(A) + n(B) − n(A∩B)

Chapter 1 Sets

##### 2) NCERT Solutions Class 11 Maths Chapter 2 Relations And Functions

Much of Mathematics is about finding a pattern – a recognisable connection between quantities that change. In our day-to-day life, we come across many patterns that characterise relations such as brother and sister, father and son, teacher and student. Also, in Mathematics, we come across many linkages such as number p is less than number r, line l is parallel to line m, set X is a subset of set Y. In all these, we notice that a relation involves pairs of objects in certain order. In this Chapter, we will learn how to connect 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 major in Mathematics since it captures the idea of a mathematically precise correspondence between one thing with the other.

NCERT Solutions Class 11 Maths Chapter 2 Relations And Functions Download free pdf. NCERT Solutions Class 11 Maths Chapter 2 Relations And Functions is provided here for students to learn better and for the help of the students in problem solving. The list of topics from this chapter are given below: –

• Cartesian Product of Sets
• Relations
• Functions

Important topics in ‘Relations and Functions’ are as follows-

• Ordered pair A pair of elements grouped together in a particular order.
• Cartesian product A × B of two sets A and B is given by A × B = {(a, b): a A, b B} In particular R × R = {(x, y): x, y R} and R × R × R = (x, y, z): x, y, z R}
• If (a, b) = (x, y), then a = x and b = y
• If n(A) = p and n(B) = q then n(A × B) = pq
• A × φ = φ
• In general, A × B ≠ B × A
• Relation A relation R from a set A to a 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 × B.
• The image of an element x under a relation R is given by y, where (x, y) R
• The domain of R is the set of all first elements of the ordered pairs in a relation R.
• The range of the relation R is the set of all second elements of the ordered pairs in a relation R.
• A is the domain and B is the co-domain of f.
• The range of the function is the set of images.

Chapter 2 Relations And Functions

##### 3) NCERT Solutions Class 11 Maths Chapter 3 Trigonometric Functions

In Mathematics, the trigonometric functions (also known as circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of lengths of two sides.

NCERT Solutions Class 11 Maths Chapter 3 Trigonometric Functions Download free pdf. NCERT Solutions Class 11 Maths Chapter 3 Trigonometric Functions are structured here for students to score higher in exam. The list of topics from this chapter are given below: –

• Angles
• Degree measure
• Relation between radian and real numbers
• Relation between degree and radian
• Notational Convention
• Trigonometric Functions
• Sign of trigonometric functions
• Domain and range of trigonometric functions
• Trigonometric Functions of Sum and Difference of Two Angles
• Trigonometric Equations

Some important formula from ‘Trigonometric Functions’ are given below-

• cos2x + sin2x = 1
• 1 + tan2x = sec2x
• 1 + cot2x = cosec2x
• cos (2nπ + x) = cos x
• sin (2nπ + x) = sin x
• sin (– x) = – sin x
• cos (– x) = cos x
• cos (x + y) = cos x cos y – sin x sin y
• cos (x – y) = cos x cos y + sin x sin y

Chapter 3 Trigonometric Functions

##### 4) NCERT Solutions Class 11 Maths Chapter 4 Principle Of Mathematical Induction

One unsurpassed ground for mathematical thinking is deductive reasoning. In contrary to deduction, inductive reasoning depends on working with different cases and developing a connective by observing incidences until each and every case have been observed. Simply, we can say the word ‘induction’ means the generalisation from particular cases or facts. The principle of mathematical induction is one such tool which 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.

NCERT Solutions Class 11 Maths Chapter 4 Principle Of Mathematical Induction Download free pdf. NCERT Solutions Class 11 Maths Chapter 4 Principle Of Mathematical Induction is provided here for students to learn better and for the help of the students in problem solving. The list of topics from this chapter are given below: –

• Motivation
• The Principle of Mathematical Induction

Chapter 4 Principle Of Mathematical Induction

##### 5) NCERT Solutions Class 11 Maths Chapter 5 Complex Numbers And Quadratic Equations

A number of the form x + iy, where x and y are real numbers, is called a complex number; x is called the real part and y is called the imaginary part of the complex number.

NCERT Solutions Class 11 Maths Chapter 5 Complex Numbers And Quadratic Equations Download free pdf. NCERT Solutions Class 11 Maths Chapter 5 Complex Numbers And Quadratic Equations are structured here for students to score higher in exam. The list of topics from this chapter are given below: –

• Complex Numbers
• Algebra of Complex Numbers
• Addition of two complex numbers
• Difference of two complex numbers
• Multiplication of two complex numbers
• Division of two complex numbers
• Power of i
• The square roots of a negative real number
• Identities
• The Modulus and the Conjugate of a Complex Number
• Argand Plane and Polar Representation
• Polar representation of a complex number

Some important formula from ‘Complex Numbers And Quadratic Equations’ are given below-

• z1 + z2 = (a + c) + i (b + d)
• z1 z2 = (ac – bd) + i (ad + bc)
• For any integer k, i 4k = 1, i 4k + 1 = i, i 4k + 2 = – 1, i 4k + 3 = – i
• The conjugate of the complex number z = a + ib, denoted by z, is given by z = a – ib.

Chapter 5 Complex Numbers And Quadratic Equations

##### 6) NCERT Solutions Class 11 Maths Chapter 6 Linear Inequalities

We have not only studied equations in one variable and two variables but also solved some statement problems by translating them in the form of equations. Thus, 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 162 cm. Your classroom can occupy at most 50 tables or chairs or both. Here, we get certain statements involving a sign ‘’ (greater than), ‘≤’ (less than or equal) and ≥ (greater than or equal) which are known as inequalities.

NCERT Solutions Class 11 Maths Chapter 6 Linear Inequalities Download free pdf. NCERT Solutions Class 11 Maths Chapter 6 Linear Inequalities is provided here for students to learn better and for the help of the students in problem solving. The list of topics from this chapter are given below: –

• Inequalities
• Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
• Graphical Solution of Linear Inequalities in Two Variables
• Solution of System of Linear Inequalities in Two Variables

Some important theorems from ‘Linear Inequalities’ are given below-

• Equal numbers may be added to (or subtracted from) both sides of an equation.
• Both sides of an equation may be multiplied (or divided) by the same non-zero number
• Equal numbers may be added to (or subtracted from) both sides of an inequality without affecting the sign of 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 sign of inequality is reversed.

Chapter 6 Linear Inequalities

##### 7) NCERT Solutions Class 11 Maths Chapter 7 Permutations And Combinations

Permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order does matter, a combination when the order doesn’t matter. Fundamental concept of counting is if an event can occur in m different ways, following which another event can occur in n different ways, then the total number of occurrences of the events in the given order is m × n.

NCERT Solutions Class 11 Maths Chapter 7 Permutations And Combinations Download free pdf. NCERT Solutions Class 11 Maths Chapter 7 Permutations And Combinations is provided here in the simplest and understanding pattern for students in getting more efficiency. The list of topics from this chapter are given below: –

• Fundamental Principle of Counting
• Permutations
• Permutations when all the objects are distinct
• Factorial notation
• Derivation of the formula for nPr
• Permutations when all the objects are not distinct objects
• Combinations

Some important formula from ‘Permutations And Combinations’ are given below-

• n! = 1 × 2 × 3 × …× n
• n! = n × (n – 1)!

Chapter 7 Permutations And Combinations

##### 8) NCERT Solutions Class 11 Maths Chapter 8 Binomial Theorem

The coefficients of the expansions are arranged in an array. This array is called Pascal’s triangle. In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial (x + y)n into a sum involving terms of the form axbyc, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b.

NCERT Solutions Class 11 Maths Chapter 8 Binomial Theorem Download free pdf. NCERT Solutions Class 11 Maths Chapter 8 Binomial Theorem is provided here for students to learn better and for the help of the students in problem solving. The list of topics from this chapter are given below: –

• Binomial Theorem for Positive Integral Indices
• Pascal’s Triangle
• Binomial theorem for any positive integer n
• General and Middle Terms

Some important formula from ‘Binomial Theorem’ are given below-

• The expansion of a binomial for any positive integral n is given by Binomial Theorem, which is (a + b)n = nC0 an + nC1 an – 1b + nC2 an – 2 b2 + …+ nCn – 1a bn – 1 + nCn bn
• The general term of an expansion (a + b)n is Tr + 1 = nCr an – r br

Chapter 8 Binomial Theorem

##### 9) NCERT Solutions Class 11 Maths Chapter 9 Sequences And Series

A sequence means an arrangement of a number in a definite order according to some rule. Moreover, we define a sequence as a function whose domain is the set of natural numbers or some subsets of the type (1, 2, 3….k). A sequence containing a finite number of terms is called a finite sequence. A sequence is called infinite if it is not a finite sequence.

A sequence x1, x2, x3, …, xn is called arithmetic sequence or arithmetic progression if xn + 1 = xn + d, n ∈ N, where x1 is called the first term and the constant term d is called the common difference of the A.P. By letting a1 = a, we obtain a geometric progression, a, ar, ar2, ar3, …. where a is called the first term and r is called the common ratio of the G.P.

NCERT Solutions Class 11 Maths Chapter 9 Sequences And Series Download free pdf. NCERT Solutions Class 11 Maths Chapter 9 Sequences And Series is provided here in the simplest and understanding pattern for students in getting more efficiency in Maths. The list of topics from this chapter are given below: –

• Sequences
• Series
• Arithmetic Progression (A.P.)
• Arithmetic mean
• Geometric Progression (G.P.)
• General term of a G.P.
• Sum to n terms of a G.P.
• Geometric Mean (G.M.)
• Relationship Between A.M. and G.M
• Sum to n Terms of Special Series

Some important formula from ‘Sequence And Series’ are given below-

• Sequence of Arithmetic Progression:  a, a+d, a+2d, ……, a+(n-1)d
• Sequence of Geometric Progression:  a, ar, ar2, …., ar(n-1)
• Common Difference:  d = a2 – a1   (Successive term – Preceding term)
• Common ratio:  r = ar(n-1)/ar(n-2) (Successive term/Preceding term)
• General Term (nth Term) of Arithmetic Progression:  an = a + (n-1)d
• General Term (nth Term) of Geometric Progression:  an = ar(n-1)
• nth term from the last term of Arithmetic Progressionan = l – (n-1)d
• nth term from the last term of Geometric Progression:  an = 1/r(n-1)
• Sum of first n terms of Arithmetic Progression:  sn= n/2(2a + (n-1)d)
• Sum of first n terms of Geometric Progression:  sn= a(1 – rn)/(1 – r) if r < 1
• Sum of first n terms of Geometric Progression:  sn= a(rn -1)/(r – 1) if r > 1

[Here, a = first term, d = common difference, r = common ratio, n = position of term, l = last term]

Chapter 9 Sequences And Series

##### 10) NCERT Solutions Class 11 Maths Chapter 10 Straight Lines

By definition, a straight line is the set of all points between and extending beyond two points. The two properties of straight lines in Euclidean geometry are that they have only one dimension, length, and they extend in two directions forever. Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is known as the general linear equation or general equation of a line.

NCERT Solutions Class 11 Maths Chapter 10 Straight Lines Download free pdf. NCERT Solutions Class 11 Maths Chapter 10 Straight Lines is provided here in the simplest and understanding pattern for students in getting more efficiency in Maths. The list of topics from this chapter are given below: –

• Slope of a Line
• Slope of a line when coordinates of any two points on the line are given
• Conditions for parallelism and perpendicularity of lines in terms of their slopes
• Angle between two lines
• Collinearity of three points
• Various Forms of the Equation of a Line
• Horizontal and vertical lines
• Point-slope form
• Two-point form
• Slope-intercept form
• Intercept – form
• Normal form
• General Equation of a Line
• Different forms of Ax + By + C = 0
• Distance of a Point from a Line
• Distance between two parallel lines

Some important points from ‘Straight Lines’ are given below-

• Two lines are parallel if and only if their slopes are equal.
• Two lines are perpendicular if and only if product of their slopes is –1.
• Three points A, B and C are collinear, if and only if slope of AB = slope of BC.
• Equation of the horizontal line having distance a from the x-axis is either y = a or y = – a
• Equation of the vertical line having distance b from the y-axis is either x = b or x = – b
• The point (x, y) lies on the line with slope m and through the fixed point (xo , yo )

Chapter 10 Straight Lines

##### 11) NCERT Solutions Class 11 Maths Chapter 11 Conic Sections

A circle is the set of all points in a plane that are equidistant from a fixed point in the plane. 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. Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose end points lie on the hyperbola. 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. Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose end points lie on the ellipse.

NCERT Solutions Class 11 Maths Chapter 11 Conic Sections Download free pdf. NCERT Solutions Class 11 Maths Chapter 11 Conic Sections is provided here in the simplest and understanding pattern for students in getting more efficiency in Maths. The list of topics from this chapter are given below: –

• Sections of a Cone
• Circle, ellipse, parabola and hyperbola
• Degenerated conic sections
• Standard equations of circle
• Standard equations of parabola
• Standard equations of an ellipse
• Latus rectum
• Relationship between semi-major axis, semi-minor axis and the distance of the focus from the centre of the ellipse
• Special cases of an ellipse

Some important points from ‘Conic Sections’ are given below-

• The equation of a circle with centre (h, k) and the radius r is (x – h)2 + (y – k)2 = r2
• Length of the latus rectum of the parabola y2 = 4ax is 4a
• The equation of the parabola with focus at (a, 0) a > 0 and directrix x = – a is y2 = 4ax

Chapter 11 Conic Sections

##### 12) NCERT Solutions Class 11 Maths Chapter 12 Introduction To Three-Dimensional Geometry

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 z-axes. The three planes determined by the pair of axes are the coordinate planes, called XY, YZ and ZX-planes. The three coordinate planes divide the space into eight parts known as octants.

NCERT Solutions Class 11 Maths Chapter 12 Introduction To Three-Dimensional Geometry Download free pdf. NCERT Solutions Class 11 Maths Chapter 12 Introduction To Three-Dimensional Geometry is provided here for students to learn better and for the help of the students in problem solving. The list of topics from this chapter are given below: –

• Coordinate Axes and Coordinate Planes in Three-Dimensional Space
• Coordinates of a Point in Space
• Distance between Two Points
• Section Formula

Some important points from ‘Introduction To Three-Dimensional Geometry’ are given below-

• The coordinates of a point P in three-dimensional geometry is always written in the form of triplet like (x, y, z). Here x, y and z are the distances from the YZ, ZX and XY-planes.
• Any point on x-axis is of the form (x, 0, 0)
• Any point on y-axis is of the form (0, y, 0)
• Any point on z-axis is of the form (0, 0, z)
• The coordinates of the mid-point of the line segment joining two points P(x1, y1, z1 ) and Q(x2, y2, z2 ) are ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2)
• The coordinates of the centroid of the triangle, whose vertices are (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) are ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3, (z1 + z2 + z3)/3)

Chapter 12 Introduction To Three-Dimensional Geometry

##### 13) NCERT Solutions Class 11 Maths Chapter 13 Limits And Derivatives

In Mathematics, a limit is defined as a value that a function approaches as the input and it produces some value. Limits are essential in Calculus and Mathematical analysis and are used to define integrals, derivatives, and continuity. 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. Limit of a function at a point is the common value of the left- and right-hand limits, if they coincide.

NCERT Solutions Class 11 Maths Chapter 13 Limits And Derivatives Download free pdf. NCERT Solutions Class 11 Maths Chapter 13 Limits And Derivatives is provided here in the simplest and understanding pattern for students in getting more efficiency in Maths. The list of topics from ‘Limits and Derivatives’ are given below: –

• Intuitive Idea of Derivatives
• Limits
• Algebra of limits
• Limits of polynomials and rational functions
• Limits of Trigonometric Functions
• Derivatives
• Algebra of derivative of functions
• Derivative of polynomials and trigonometric functions

Chapter 13 Limits And Derivatives

##### 14) NCERT Solutions Class 11 Maths Chapter 14 Mathematical Reasoning

A mathematically acceptable statement is a sentence which is either true or false. Mathematical reasoning is the critical skill that enables a student to make use of all other mathematical skills. Mathematical reasoners are able to reflect on solutions to problems and determine whether or not they make sense. They appreciate the pervasive use and power of reasoning as a part of Mathematics.

NCERT Solutions Class 11 Maths Chapter 14 Mathematical Reasoning Download free pdf. NCERT Solutions Class 11 Maths Chapter 14 Mathematical Reasoning is provided here in the simplest and understanding pattern for students in getting more efficiency in Maths. The list of topics from this chapter are given below: –

• Statements
• New Statements from Old
• Negation of a statement
• Compound statements
• Special Words/Phrases
• The word ‘And’
• The word ‘Or’
• Quantifiers
• Implications
• Contrapositive and Converse
• Validating Statements

The following methods are used to check the validity of statements-

• Direct method
• Contrapositive method
• Using a counter example

Chapter 14 Mathematical Reasoning

##### 15) NCERT Solutions Class 11 Maths Chapter 15 Statistics

Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real-life studies. Statistics studies methodologies to gather, review, analyze and draw conclusions from data.

NCERT Solutions Class 11 Maths Chapter 15 Statistics Download free pdf. NCERT Solutions Class 11 Maths Chapter 15 Statistics is provided here in the simplest and understanding pattern for students in getting more efficiency. The list of topics from this chapter are given below: –

• Measures of Dispersion
• Range
• Mean Deviation
• Mean deviation for ungrouped data
• Mean deviation for grouped data
• Shortcut method for calculating mean deviation about mean
• Limitations of mean deviation
• Variance and Standard Deviation
• Standard Deviation
• Standard deviation of a discrete frequency distribution
• Standard deviation of a continuous frequency distribution
• Shortcut method to find variance and standard deviation
• Analysis of Frequency Distributions
• Comparison of two frequency distributions with same mean

Some important points from ‘Statistics’ are given below-

• The different types of measures of dispersion are:
1. Range
2. Quartile deviation
3. Mean deviation
4. Standard deviation.
• Range = Maximum Value – Minimum Value
• Mean Deviation = Sum of absolute values of deviations from ‘a’ / Number of observations
• The data can be grouped into two ways namely,
1. Discrete frequency distribution
2. Continuous frequency distribution
• To find the mean deviation for the continuous frequency distribution, assume that the frequency in each class is centred at its midpoint. After finding the midpoint, proceed further to find the mean deviation similar to the discrete frequency distribution.

Chapter 15 Statistics

##### 16) NCERT Solutions Class 11 Maths Chapter 16 Probability

Probability simply means possibility. It is a branch of Mathematics that deals with the occurrence of a random event. The value of probability is defined from zero to one. Probability has been introduced to predict how likely events are to happen.

Probability is the branch of Mathematics concerning numerical descriptions of how likely it is that a proposition is true. This is the main probability theory that is also used in the probability distribution where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

NCERT Solutions Class 11 Maths Chapter 16 Probability Download free pdf. NCERT Solutions Class 11 Maths Chapter 16 Probability is provided here for students to learn better and for the help of the students in problem solving. The list of topics from this chapter are given below: –

• Random Experiments
• Outcomes and sample space
• Event
• Occurrence of an event
• Types of events
• Algebra of events
• Mutually exclusive events
• Exhaustive events
• 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’

Some important points of ‘Probability’ are as follows-

• Sample space: The set of all possible outcomes
• Sample points: Elements of sample space
• Event: A subset of the sample space
• Impossible event: The empty set
• Sure event: The whole sample space
• Complementary event or ‘not event’: The set A′ or S – A
• Event A or B: The set A B
• Event A and B: The set A ∩ B
• Event A and not B: The set A – B
• Mutually exclusive event: A and B are mutually exclusive if A ∩ B = φ

Chapter 16 Probability

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• NCERT Solutions provide a step-by-step explanation to every question given in the textbooks. It is one of the most valuable aids to students in their home assignments and exams as well.
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