# NCERT Solutions Class 11 Maths

**NCERT Solutions for Class 11 Maths** provides a conceptual framework for all the subjects of Class 11 Maths as prescribed by the CBSE Board. We have designed all the important theorems and formulas with a complete explanation for the students. NCERT Solutions for Mathematics is an essential aid for class 11 students. These Maths Solutions include answers to all questions as per the latest CBSE Board Syllabus. Our subject experts have prepared these maths NCERT solutions for class 11 students. Students can easily **download** NCERT Solutions **Free PDF.**

These NCERT Solutions for maths will help students prepare for competitive exams like JEE (Mains and Advanced), VITEEE, and other state-level exams. These NCERT Solutions for Class 11 are logically explainable as per the exercises given in the book.

Study tutee provides CBSE Class 11 Maths Solutions in PDF format which can be downloaded for free of cost. If you have trouble understanding a topic related to maths, you can verify the answers to the questions given in the exercises in the book. By practicing the solutions provided by us, students can aim to score high in their Maths Board Exams.

Mathematics is said to be a systematic application of matter because the subject makes man scientific or systematic. Mathematics helps us to keep our lives organized and prevent clutter. Qualities 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 racket of all creations without which the world cannot run. Every human being needs mathematics in his 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.

###### List of Chapters Available in Class 11 Maths NCERT Solutions Free PDF

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

In mathematics, a set is a well-defined collection of distinct objects, treated as an object in itself. The arrangement of the items in the set matters. A set can be represented by placing its objects between a pair of curly braces. For example- the numbers 11, 5, and 7 are different things when considered separately; When considered collectively, they form a single set of size three, written {11, 5, 7}, which can be called {7, 5, 11}, {5, 7, 11}, {Can also be written as 7. 11, 5.}, {5, 11, 7} or {11, 7, 5}. Sets can also be represented in italics using capitalized Roman letters such as **P, Q, R.**

Download NCERT Solutions for Class 11 Maths Chapter 1 Set in Free Pdf. The NCERT Solutions for Class 11 Maths Chapter 1 Set is given here to help the students learn and solve the problem in a better way. The list of topics of this chapter is 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 ‘SET’ are as follows-**

**The union of two sets A and B is called an element which is either in set A and set B. The union of A and B is represented as****A****∪****BA****∪****B****.****The intersection of two sets A and B is called the element which is common to both sets. The intersection of A and B is represented 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 in A. A’s complement is represented as A′A′.****For any two sets A and B, the following is true:****(A****∪****B)′ = A′∩B′****(A∩B)′ = A′****∪****B′****n(A****∪****B) = n(A) + n(B) − n(A∩B)**

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

Much of mathematics is about finding a pattern – a recognizable relationship between quantities that changes. In our daily lives, we see many patterns that characterize relationships such as brother and sister, father and son, teacher and student. Also, in mathematics, we find many linkages such that the number p is less than the number r, the line l is parallel to the line m, the set X is a subset of the set Y. In all these, we see that the pairs of objects in a relation are in a certain order. In this chapter, we will learn how to pair pairs of objects from two sets and then introduce the relationship between the two objects in the pair. Finally, we will learn about the special relations that qualify a function. The concept of function is prominent in mathematics because it captures the idea of a mathematically precise correspondence between one thing and another.

Download NCERT Solutions for Class 11 Maths Chapter 2 Relation and Functions in Free Pdf. Here are the NCERT Solutions for Class 11 Maths Chapter 2 Relationships and Functions to help students learn and problem solve in a better way. The list of topics of this chapter is given below: –

- Cartesian Product of Sets
- Relations
- Functions

**The important topics in ‘Relationship and Functions’ are as follows-**

**Ordered pair A pair of elements grouped in a particular order.****The**

Cartesian product of two sets A and B is given A × B = {(a, b): a**∈****A, b****∈****B} specifically 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****The relation R from set A to set B is a subset of the Cartesian product A × B, obtained by describing the 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 the first elements of the ordered pairs in a relation to R.****The range R of the relation is the set of all other elements of the ordered pairs concerning R.****A is the domain and B is the co-domain of f.****The limit of the function is the set of images.**

**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 that relate an angle of a right-angled triangle to ratios of lengths of two sides.

Download NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions in Free PDF Download. The NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions are structured here to help students score high in the examination. The list of topics of this chapter is given below: –

- Angles
- Degree measure
- Radian 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 formulas from ‘Trigonometric Function’ are given below-**

**cos**^{2}x + sin^{2}x = 1**1 + tan**^{2}x = sec^{2}x**1 + cot**^{2}x = cosec^{2}x**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**

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

An unsurpassed basis of mathematical thinking is deductive reasoning. Unlike a deduction, inductive reasoning relies on developing conjunction by working with different cases and observing events until each case is observed. Simply put, we can say that the word ‘induction’ means generalization from particular cases or facts. The principle of mathematical induction is a tool that can be used to prove a variety of mathematical statements. Each such statement is treated as P(n) associated with a positive integer n, for which the correctness of the n = 1 condition is checked. Then assuming the truth of P(k) for any positive integer k, the truth of P(k+1) is established.

Download NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction in PDF for free. NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction is given here to help students learn and problem solve in a better way. The list of topics of this chapter is given below: –

- Motivation
- The 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.

Download NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations in Free Pdf. NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are here structured to help students score high in the examination. The list of topics of this chapter is 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 formulas from ‘Complex Numbers and Quadratic Equations’ are given below-**

**z**_{1}+ z_{2}= (a + c) + i (b + d)**z**_{1}z_{2}= (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.**

**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 into equations. Thus, a natural question arises: ‘Is it always possible to translate a statement problem as an equation? For example, all the students in your class are less than 162 cm tall. Your classroom can have up to 50 tables or chairs, or both. Here, we get some statements that have the sign “(greater than), “≤” (less than or equal to), and (greater than or equal to), which are called an inequality.

Download NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities in PDF for free. NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities are given here to help students learn and problem-solve better. The list of topics of this chapter is 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 can be added to (or subtracted from) both sides of the equation.****Both sides of an equation can be multiplied (or divided) by the same non-zero number.****Equal numbers can be added (or subtracted) to both sides of the inequality without affecting the inequality sign.****Both sides of the inequality can be multiplied (or divided) by the same positive number. But when both sides are multiplied or divided by a negative number, the inequality sign is reversed.**

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

Permutations and combinations are various ways in which items can be selected from a set, usually without replacement, to form subsets. This selection of subsets is called a permutation when order matters, a combination when order does not matter. The basic concept of computation is that if an event can occur in m different ways, followed by another event in n different ways, then the total number of events in the given sequence is m × n.

NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations **Free PDF Download.** The NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations are provided here in a simple and understandable pattern for the students to gain more proficiency. The list of topics of this chapter is given below: –

- Fundamental Principle of Counting
- Permutations
- Permutations when all the objects are distinct
- Factorial notation
- Derivation of the formula for
^{n}P_{r} - Permutations when all the objects are not distinct objects
- Combinations

**Some important formulas from ‘Permutation and Combination’ are given below-**

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

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

The coefficients of expansion 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 the powers of a binomial. According to the theorem, it is possible to extend the polynomial (*x* + *y*)* ^{n}* to a sum involving terms of the form

*ax*,

^{b}y^{c}where the exponents b and cb + c = n are non-negative integers, and the coefficients of each are . is one. The term is a specific positive integer that depends on n and b.

Download NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Free Pdf. NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem is provided here to help the students in better learning and problem-solving. The list of topics of this chapter is given below: –

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

**Some important formulas of Binomial Theorem are given below-**

**The expansion of the binomial for any positive integral n is given by the binomial theorem, which is (a + b)**^{n}=^{n}C_{0}a^{n}+^{n}C_{1}a^{n – 1}b +^{n}C_{2}a^{n – 2 }b^{2}+ …+^{n}C_{n – 1}a b^{n – 1}+^{n}C_{n}b^{n}**The general term of the expansion (a + b)**^{n}is T_{r + 1}=^{n}C_{r}a^{n – r}b^{r}

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

Sequence means the arrangement of a number in a certain order according to some rule. Furthermore, we define a sequence as a function whose domain is the set of natural numbers or some subset of the type (1, 2, 3…. k). The sequence in which the number of terms is limited is called a finite sequence. A sequence is said to be infinite if it is not a finite sequence.

A sequence x_{1}, x_{2}, x_{3}, …, x_{n} is called an arithmetic sequence or an arithmetic progression if x_{n + 1} = x_{n} + d, n ∈ N, where x_{1} is called the first term and the constant d is called the common difference. Giving A.P. By letting a_{1} = a, we obtain a geometric progression, a, ar, ar^{2}, ar^{3}, …. where a is called the first term and r is called the common ratio of the G.P.

Download NCERT Solutions for Class 11 Maths Chapter 9 Sequence and Series Free Pdf. NCERT Solutions for Class 11 Maths Chapter 9 Sequence & Series is provided here in the most simple and understandable pattern for the students to get more proficiency in Mathematics. The list of topics of this chapter is 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 formulas from ‘Sequence and Series’ are given below-**

**Order of Arithmetic Progression: a, a+d, a+2d, ……, a+(n-1)d****Order of geometric progression: a, ar, ar**^{2}, …., ar^{(n-1)}**Common Difference:****d = a**_{2}– a_{1 }**(****Successive term – Preceding term)****Common ratio: r = ar**^{(n-1)}/ar^{(n-2) }(Successive term/Preceding term)**General Term (nth Term) of Arithmetic Progression: a**_{n}= a + (n-1)d**General Term (nth Term) of Geometric Progression: a**_{n}= ar^{(n-1)}**nth term from the last term of****Arithmetic Progression****:****a**_{n}= l – (n-1)d**nth term from the last term of****Geometric Progression****:****a**_{n}= 1/r^{(n-1)}**Sum of first n terms of Arithmetic Progression: s**_{n}= n/2(2a + (n-1)d)**Sum of first n terms of Geometric Progression: s**_{n}= a(1 – r^{n})/(1 – r) if r < 1**Sum of first n terms of Geometric Progression: s**_{n}= a(r^{n}-1)/(r – 1) if r > 1

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

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

By definition, a straight line is the set of all points between and after two points. 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, not zero is also known as a general linear equation or a general equation of a line.

Download NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines in free pdf. NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines are provided here in a simple and understandable pattern for the students to get more proficiency in Maths. The list of topics of this chapter is 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 Line’ 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 (x**_{o}, y_{o})

**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. The latus rectum of a parabola is a line segment perpendicular to the axis of the parabola through the focus and whose endpoint lies on the hyperbola. An ellipse is the set of all points in a plane whose sum of distances from two fixed points in the plane is a constant. The latus rectum of an ellipse is a line segment that is perpendicular to the principal axis through any of the foci and whose endpoint lies on the ellipse.

Download NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Free Pdf. NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections are provided here in the most simple and understandable pattern for the students to get more proficiency in Mathematics. The list of topics of this chapter is 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 radius r is (x – h)**^{2}+ (y – k)^{2}= r^{2}**The length of the latus rectum of the parabola y**^{2}= 4ax is 4a**The equation of the parabola with focus at (a, 0) a > 0 and directrix x = – a is y**^{2}= 4ax

**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-axis. The three planes determined by the pair of axes are the coordinate planes, called the XY, YZ, and ZX planes. Three coordinate planes divide space into eight parts called octaves.

NCERT Solutions Class 11 Maths Chapter 12 Introduction to Three-Dimensional Geometry **PDF Free download** NCERT Solutions Class 11 Maths Chapter 12 Introduction to Three-Dimensional Geometry helps students to learn and solve problems in a better way. The list of topics of this chapter is 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-**

**In three-dimensional geometry, the coordinates of a point P are always written as triples (x, y, z). Here x, y, and z are the distances from the YZ, ZX, and XY planes.****Any point on the x-axis is of the form (x, 0, 0).****Any point on the y-axis is of the form (0, y, 0)****Any point on the z-axis is of the form (0, 0, z)****The coordinates of the mid-point of the line segment joining two points P(x**_{1}, y_{1}, z_{1}) and Q(x_{2}, y_{2}, z_{2}) are ((x_{1}+x_{2})/2, (y_{1}+y_{2})/2, (z_{1}+z_{2})/2)**The coordinates of the centroid of a triangle whose vertices (x**_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2}) and (x_{3}, y_{3}, z_{3}) are ((x_{1 }+ x_{2 }+ x_{3})/3, (y_{1 }+ y_{2}+ y_{3})/3, (z_{1 }+ z_{2 }+ z_{3})/3)

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

In mathematics, a limit is defined as the value that a function reaches as input and which produces some value. Limits are essential in calculus and mathematical analysis and are used to define integrals, derivatives, and continuity. The expected value of a function determined by the points to the left of a point defines the leftmost limit of the function at that point. Similarly, the right-hand range. The limit of a function at some point is the common value of the left- and right-hand limits, if they coincide.

Download NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Free Pdf. NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives is provided here in a simple and understandable pattern for the students to get more proficiency in Maths. Below is the list of topics from ‘Limits and Derivatives’: –

- 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

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

A mathematically acceptable statement is a sentence that is either true or false. Mathematical reasoning is an important skill that enables a student to use all other mathematical skills. Mathematical reasoners can reflect on solutions to problems and determine whether they make sense. They appreciate the widespread use and power of logic as a part of mathematics.

Download NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning in Free Pdf. NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning is provided herein the most simple and understandable pattern for the students to get more proficiency in Maths. The list of topics of this chapter is 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
- By Contradiction

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

**Direct method****Contrapositive method****Method of contradiction****Using a counter example**

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

Statistics is a form of mathematical analysis that uses quantitative models, representations, and summaries for a given set of experimental data or real-life studies. Methods of statistical study to collect, review, analyze and draw conclusions of data.

Download NCERT Solutions for Class 11 Maths Chapter 15 Statistics in Free Pdf. The NCERT Solutions for Class 11 Maths Chapter 15 Statistics is provided here in the most simple and easy-to-understand pattern for the students to gain more proficiency. The list of topics of this chapter is 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-**

**There are different types of measures of dispersion :**

**Range****Quartile deviation****Mean deviation****Standard deviation.**

**Range = Maximum Value – Minimum Value****Mean Deviation = Sum of absolute values of deviations from ‘a’ / Number of observations****Data can be classified in two ways, namely,**

**Discrete frequency distribution****Continuous frequency distribution**

**To find the mean deviation of a continuous frequency distribution, assume that the frequency in each class is centered at its midpoint. After finding the midpoint, proceed to find the mean deviation similar to the discrete frequency distribution.**

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

Chance simply means probability. It is a branch of mathematics that deals with the occurrence of a random event. The value of probability is defined as zero to one. Probability is introduced to estimate the probability of occurrence of events.

Probability is the branch of mathematics that deals with numerical descriptions of how likely it is that a proposition is true. This is the main probability theory that is also used in probability distributions where you will learn the probability of the outcomes of a random experiment. To find the probability that an event will occur, we must first find the total number of possible outcomes.

Download NCERT Solutions for Class 11 Maths Chapter 16 Probability in PDF. NCERT Solutions for Class 11 Maths Chapter 16 Probabilities are given here to help students learn and solve problems in a better way. The list of topics of this chapter is 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 the sample space****Event: A subset of the sample space****Impossible event: 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**

**Benefits of Solving Class 11 Maths NCERT Solutions**

- NCERT Solutions provides step by step explanation of every question given in the textbooks. It is one of the most valuable aids to the students in their homework and exams as well.
- Solving these NCERT solutions will help the students to clear all their doubts.
- These NCERT solutions are designed as per the syllabus of the subject concerned and thus, provide proper guidance along with the entire learning process.
- NCERT solutions help in clearing difficult concepts as these NCERT solutions are prepared using proper explanations.
- To score maximum marks in the exam, students need to practice these NCERT solutions as it consists of different types of questions for practice purpose. This will help the students to solve the wrong questions easily.
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