NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning (Ex 14.3) Exercise 14.3
Home » NCERT Solutions » NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning (Ex 14.3) Exercise 14.3

CBSE Important Questions›

CBSE Previous Year Question Papers›
 CBSE Previous Year Question Papers
 CBSE Previous Year Question Papers Class 12
 CBSE Previous Year Question Papers Class 10

CBSE Revision Notes›

CBSE Syllabus›

CBSE Extra Questions›

CBSE Sample Papers›
 CBSE Sample Papers
 CBSE Sample Question Papers For Class 5
 CBSE Sample Question Papers For Class 4
 CBSE Sample Question Papers For Class 3
 CBSE Sample Question Papers For Class 2
 CBSE Sample Question Papers For Class 1
 CBSE Sample Question Papers For Class 12
 CBSE Sample Question Papers For Class 11
 CBSE Sample Question Papers For Class 10
 CBSE Sample Question Papers For Class 9
 CBSE Sample Question Papers For Class 8
 CBSE Sample Question Papers For Class 7
 CBSE Sample Question Papers For Class 6

ISC & ICSE Syllabus›

ICSE Question Paper›
 ICSE Question Paper
 ISC Class 12 Question Paper
 ICSE Class 10 Question Paper

ICSE Sample Question Papers›
 ICSE Sample Question Papers
 ISC Sample Question Papers For Class 12
 ISC Sample Question Papers For Class 11
 ICSE Sample Question Papers For Class 10
 ICSE Sample Question Papers For Class 9
 ICSE Sample Question Papers For Class 8
 ICSE Sample Question Papers For Class 7
 ICSE Sample Question Papers For Class 6

ICSE Revision Notes›
 ICSE Revision Notes
 ICSE Class 9 Revision Notes
 ICSE Class 10 Revision Notes

ICSE Important Questions›

Maharashtra board›

RajasthanBoard›
 RajasthanBoard

Andhrapradesh Board›
 Andhrapradesh Board
 AP Board Sample Question Paper
 AP Board syllabus
 AP Board Previous Year Question Paper

Telangana Board›

Tamilnadu Board›

NCERT Solutions Class 12›
 NCERT Solutions Class 12
 NCERT Solutions Class 12 Economics
 NCERT Solutions Class 12 English
 NCERT Solutions Class 12 Hindi
 NCERT Solutions Class 12 Maths
 NCERT Solutions Class 12 Physics
 NCERT Solutions Class 12 Accountancy
 NCERT Solutions Class 12 Biology
 NCERT Solutions Class 12 Chemistry
 NCERT Solutions Class 12 Commerce

NCERT Solutions Class 10›

NCERT Solutions Class 11›
 NCERT Solutions Class 11
 NCERT Solutions Class 11 Statistics
 NCERT Solutions Class 11 Accountancy
 NCERT Solutions Class 11 Biology
 NCERT Solutions Class 11 Chemistry
 NCERT Solutions Class 11 Commerce
 NCERT Solutions Class 11 English
 NCERT Solutions Class 11 Hindi
 NCERT Solutions Class 11 Maths
 NCERT Solutions Class 11 Physics

NCERT Solutions Class 9›

NCERT Solutions Class 8›

NCERT Solutions Class 7›

NCERT Solutions Class 6›

NCERT Solutions Class 5›
 NCERT Solutions Class 5
 NCERT Solutions Class 5 EVS
 NCERT Solutions Class 5 English
 NCERT Solutions Class 5 Maths

NCERT Solutions Class 4›

NCERT Solutions Class 3›

NCERT Solutions Class 2›
 NCERT Solutions Class 2
 NCERT Solutions Class 2 Hindi
 NCERT Solutions Class 2 Maths
 NCERT Solutions Class 2 English

NCERT Solutions Class 1›
 NCERT Solutions Class 1
 NCERT Solutions Class 1 English
 NCERT Solutions Class 1 Hindi
 NCERT Solutions Class 1 Maths

JEE Main Question Papers›

JEE Main Syllabus›
 JEE Main Syllabus
 JEE Main Chemistry Syllabus
 JEE Main Maths Syllabus
 JEE Main Physics Syllabus

JEE Main Questions›
 JEE Main Questions
 JEE Main Maths Questions
 JEE Main Physics Questions
 JEE Main Chemistry Questions

JEE Main Mock Test›
 JEE Main Mock Test

JEE Main Revision Notes›
 JEE Main Revision Notes

JEE Main Sample Papers›
 JEE Main Sample Papers

JEE Advanced Question Papers›

JEE Advanced Syllabus›
 JEE Advanced Syllabus

JEE Advanced Mock Test›
 JEE Advanced Mock Test

JEE Advanced Questions›
 JEE Advanced Questions
 JEE Advanced Chemistry Questions
 JEE Advanced Maths Questions
 JEE Advanced Physics Questions

JEE Advanced Sample Papers›
 JEE Advanced Sample Papers

NEET Eligibility Criteria›
 NEET Eligibility Criteria

NEET Question Papers›

NEET Sample Papers›
 NEET Sample Papers

NEET Syllabus›

NEET Mock Test›
 NEET Mock Test

NCERT Books Class 9›
 NCERT Books Class 9

NCERT Books Class 8›
 NCERT Books Class 8

NCERT Books Class 7›
 NCERT Books Class 7

NCERT Books Class 6›
 NCERT Books Class 6

NCERT Books Class 5›
 NCERT Books Class 5

NCERT Books Class 4›
 NCERT Books Class 4

NCERT Books Class 3›
 NCERT Books Class 3

NCERT Books Class 2›
 NCERT Books Class 2

NCERT Books Class 1›
 NCERT Books Class 1

NCERT Books Class 12›
 NCERT Books Class 12

NCERT Books Class 11›
 NCERT Books Class 11

NCERT Books Class 10›
 NCERT Books Class 10

Chemistry Full Forms›
 Chemistry Full Forms

Biology Full Forms›
 Biology Full Forms

Physics Full Forms›
 Physics Full Forms

Educational Full Form›
 Educational Full Form

Examination Full Forms›
 Examination Full Forms

Algebra Formulas›
 Algebra Formulas

Chemistry Formulas›
 Chemistry Formulas

Geometry Formulas›
 Geometry Formulas

Math Formulas›
 Math Formulas

Physics Formulas›
 Physics Formulas

Trigonometry Formulas›
 Trigonometry Formulas

CUET Admit Card›
 CUET Admit Card

CUET Application Form›
 CUET Application Form

CUET Counselling›
 CUET Counselling

CUET Cutoff›
 CUET Cutoff

CUET Previous Year Question Papers›
 CUET Previous Year Question Papers

CUET Results›
 CUET Results

CUET Sample Papers›
 CUET Sample Papers

CUET Syllabus›
 CUET Syllabus

CUET Eligibility Criteria›
 CUET Eligibility Criteria

CUET Exam Centers›
 CUET Exam Centers

CUET Exam Dates›
 CUET Exam Dates

CUET Exam Pattern›
 CUET Exam Pattern
Mathematics is a subject that necessitates constant practise. Students are expected to practise questions and problems provided in the prescribed NCERT textbooks for Mathematics when preparing for the exams. Students are also recommended toseek out other sources like past years’ papers, sample question papers, and other kinds of welldesigned practise assessments. Practising with the help of a wide variety of academic resources would have a positive effect on the academic performance of students. It would also give them a advantage of familiarising themselves with the pattern of questions that could appear in the examinations. Once the students have acquired this extent of reading comprehension abilities, they will be able to figure out the appropriate line of action to be followed after being presented with particular types of problems. The system of examinations that is prevalent in thenational education system is regulated and monitored by the NCERT which is a thorough and complex one. A distinct schema of mark distribution characterises the question papers, and students are expected to frame their answers while keeping this scheme in mind.
The Class 11 Mathematics curriculum has undergone extensive revision by the Central Board of Secondary Education (CBSE), one of India’s most prestigious educational boards, in order to give students a solid basis for the advanced range of courses.
The NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.3 have been offered in a methodical way. The rigorous chapterbychapter organisation of these answers guarantees that students may use their time wisely. The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 include detailed explanations that will help students understand each topic’s underlying ideas. Specialists have simplified even the most complex topics in NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 to enable seamless learning.Additionally, each and every chapter’s solutions for Class 11 adhere to the NCERT (CBSE Board) guidelines and syllabus.
With NCERT Solutions, getting good grades is an achievable goal. The NCERT Solutions for Class Class 11 Maths Chapter 14 Exercise 14.3 cover every exercise from the Class 11 Mathematics textbook. The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 discuss the depth of the chapter in great detail while adhering to the most recent curriculum. Students will be able to learn from the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 how various principles are used in actual situations. The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 would also help the students in Class 12 as they get ready for the competitive exams. Students’ approaches to answering questions in entrance exams like JEE will improve as they tackle more challenging topics. While preparing for the various entrance tests, students can refer to the solutions for the crucial Mathematics Class 11 problems on the Extramarks’ website.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning (Ex 14.3) Exercise 14.3
The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 were created by some of Extramarks’ top subject experts.Extramarks provides a PDF version of Class 11 Maths Chapter 14 Exercise 14.3 to help students with their preparation.Test takers can refer to the NCERT Solutions for Class 11 Maths, Chapter 14, Exercise 14.3, which can be downloaded from the official website.Furthermore, students can attend live classes on the platform provided by some of the country’s top academicians to clear up any doubts they have about important topics such as the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3.
Students who wish to know the chapters they will be studying can refer to the Class 11 Mathematics Syllabus. There are 16 chapters in the Mathematics textbook for Class 11. In comparison to Class 10, students may feel that the syllabus is extensive. However, with Extramarks’ assistance, students can quickly grasp each subject and perform well on their Mathematics examinations.
Access NCERT Solutions for Class 11 Maths Chapter 14 – Mathematical Reasoning
All 16 chapters of the NCERT answers for Mathematics Class 11 are included in a single set. Students have the option of downloading individual sets or the entire set at once. Relations & Functions, Trigonometric Functions, Mathematical Induction Principle, Complex Numbers and Quadratic Equations, among other chapters, are treated. Every chapter has been thoroughly explained by subject specialists so that students can comprehend it.
The systematic NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 are organised topicwise. Additionally, the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 assists with time management for the final examination. The detailed explanations of the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 will help students understand each topic underlying idea. Students can prepare for the exam by practising the questions from each chapter. The main goal is to perform well on the examination.
For CBSE students preparing for exams, using the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 Class 11 Math is thought to be the best alternative. There are numerous exercises in this chapter. The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 are available on Extramarks’ website in PDF format. Students have the option of downloading these solutions at their convenience or studying them straight from Extramarks’ website or mobile application.
There are numerous exercises in this chapter that contain questions in addition to the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3. Experts have responded to all of the student’s inquiries. These NCERT Solutions are guaranteed to be of the highest quality, and anyone can use them to study for exams. It is crucial to comprehend all the concepts in the textbooks and work through the questions that are provided in NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 in order to receive the greatest grades possible in the class.
For the Class 11 Mathematics examination, students can refer to NCERT Solutions. Experts create the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 in an easytounderstand language. Additionally, the majority of the exam’s questions will be either from or directly related to the NCERT textbooks. Students must therefore completely revise the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 in order to adequately prepare for the Class 11 Mathematics exam. On the Extramarks’ website, students can access the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 in PDF format.
Due to the vast differences between the Class 11 Mathematics curriculum and what they studied in Class 10, students frequently struggle to keep up. Additionally, students feel that they are unable to understand the topics because of the large array of new concepts that are taught to them in the Class 11 Mathematics curriculum. The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 are skillfully created to explain all the ideas. Students can sign up on the Extramarks’ website and be part of live classes led by professionals if they have any questions about any subject.
The Class 11 NCERT Mathematics books have 16 chapters and a total of 53 exercises. On Extramarks’ website, students can obtain the solutions to every exercise. Top subject experts have developed the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3. They have made sure that the answers are accurate and are presented simply. With these solutions in their possession, students will be able to complete their NCERT coursework and become examready.
Here are a few key chapters from chapters of the NCERT Solutions for Class 11 Math, which can all be found on the Extramarks website and mobile application:
 Concept of Subset, Superset, and Power Set
 Cartesian Product of Sets
 Concept of Relations
 RealValued Functions
 Signs of Trigonometric Functions
 Trigonometric Functions and Their Graphs
 Trigonometric Identities and equations
 Modulus and Conjugate of a Complex Number
 Polar Representation of Complex Numbers
 General and Middle Term of a Binomial Expansion
 Concept of Permutations when All Objects are Distinct
 Concept of Permutations when All Objects are Not Distinct
 Concept of Combinations
 Solving Linear Inequalities in One Variable
 Solving a System of Linear Inequalities in Two Variables
 Sum of n Terms of an Arithmetic Progression
 Properties of Arithmetic Progressions and the Concept of Arithmetic Mean
 nth term and Sum of n Terms of a Geometric Progression
 Concept of Geometric Mean and Its Relation with Arithmetic Mean
 Sum of n Terms of Special Series
 Angle between Two Lines
 Pointslope and Twopoint Form of Straight Lines
 SlopeIntercept Form of Straight Lines
 Intercept Form of Straight Lines
 Normal form of Straight Lines
 Distance of a Point from a Line and Distance between Two Parallel Lines
 Circle
 Parabola
 Ellipse
 Hyperbola
 Distance between Two Points in Three Dimensional Space
 Section Formula
 Limit of a Polynomial and a Rational Function
 Limit of a Trigonometric Function
 Derivative of a Function
 Derivative of Trigonometric and Polynomial Functions
 Negation of a Statement.
 Implications.
 Validity of “Ifthen” and “If and only if” Statements.
 Validation of a Statement by Method of Contradiction and by Giving a Counterexample.
 Mean Deviation for Continuous Frequency Distribution.
 Variance and Standard Deviation of Continuous Frequency Distribution.
 Coefficient of Variation.
 Finding Probability Using Complement of a Known Event.
 Algebra of Events and Mutually Exclusive and Exhaustive Events.
 Probability of an Event.
NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning
Students can use critical thinking in Mathematics by using the skill of Mathematical Reasoning. It calls for the application of logical, cognitive reasoning. Students can use these abilities to answer a mathematical question by applying the subject’s fundamentals. The students can find the answer and determine whether it makes sense with the use of Mathematical Reasoning.
Teachers use this idea in the classroom to help students comprehend the subject well. It develops a pattern of thoughts that aids in the resolution of challenging problems. This technique establishes a connection between figures or circumstances. Students explain that connection and make deductions. When a learner forgets a certain formula or topic, Mathematical Reasoning is often helpful.
Mathematical Reasoning is not just useful in the classroom; it is also very useful in daytoday situations. Students who are adept at this notion go further in life. Every situation calls for the capacity for logical thought, which allows students to advance overall. These students go on to succeed as Managers, Business Owners, and Leaders. Bill Gates, Stephen Hawking, Isaac Newton, and Johannes Kepler are a few instances of wellknown individuals with strong critical thinking abilities.
Although everyone is born with the ability to do well in Mathematics, these skills can be developed with the right instructions and methods. There are many tests and evaluations available on Extramarks to determine a student’s Mathematical Reasoning. When identified, Extramarks can help them with the development of their skills. Teachers can devise techniques to increase a student’s competence, and teachers can help students with low reasoning abilities develop high abilities.
Experts compile the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 to familiarise students with the concepts and increase learning speed. As a result, the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 helps the students implement effective time management techniques for better examination outcomes. All of the practise questions in the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 will allow students to hone their mathematical abilities. Students can register on the Extramarks’ website for a free webinar session offered by Extramarks featuring the top Mathematics tutors in India. Additionally, students will benefit from access to conceptual films and live masterclasses.
Additionally, all PDFs of the study materials and solutions, including the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 will be available to students. Online Tests will also be made available to them on account of the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3. They will be prepared with all the necessary standard study materials, which will make learning simpler for them.
Below is a list of all the Chapters and their solutions that are being made available to the students by Extramarks:
 Chapter 1 – Sets
 Chapter 2 – Relations and Functions
 Chapter 3 – Trigonometric Functions
 Chapter 4 – Principal 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 Derivations
 Chapter 14 – Mathematical Reasoning
 Chapter 15 – Statistics
 Chapter 16 – Probability
Each of the topics from the list above is discussed in a way that is easy to comprehend. Therefore, any student in class 11 mayrapidly master the principles and get a deeper comprehension of them. There is lots of information regarding the topics and subtopics, which will not only assist students in getting ready for their board exams but also give them the confidence to get ready for the JEE and other engineering entrance exams.
By using the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3, students can obtain all of the arithmetic index pages for each subject and improve their preparation.For further help with students’ Mathematics preparation, they can obtain a variety of classspecific Mathematics sample papers, question papers, formulas, and other study aids from the Extramarks’ website and mobile application.
Extramarks provides NCERT Solutions for all classes. Students from all classes can download the NCERT Solutions Class 1, NCERT Solutions Class 2, NCERT Solutions Class 3, NCERT Solutions Class 4, NCERT Solutions Class 5, NCERT Solutions Class 6, NCERT Solutions Class 7, NCERT Solutions Class 8, NCERT Solutions Class 9, NCERT Solutions Class 10, NCERT Solutions Class 11, and NCERT Solutions Class 12 from the Extramarks’ website.
The Class 11 Mathematics index page provided here lists every chapter and each of its subtopics from the NCERT Class 11 Math textbook. All of the CBSE’s recommended curriculum concepts are included in the topics listed on this index page. These themes from the CBSE math curriculum are explained simply to aid pupils in grasping the material better.
It goes without saying that Class 11 is a significant year because the topics covered on the syllabus are necessary for competitive exams like the JEE in addition to being important for the Class 11 examination. These topicspecific index pages can help students conveniently navigate through all the topics.
Students can utilise Extramarks’ NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 to effectively prepare for their Mathematics Examinations. The NCERT Class 11 Maths textbook has a total of 16 chapters. Sets is the first chapter, followed by Relations and Functions, Trigonometric Functions, the Principle of Mathematical Induction, Complex Numbers and Quadratic Equations, Linear Inequalities, Permutations and Combinations, the Binomial Theorem, Sequences and Series, Straight Lines, Conic Sections, Introduction to Three Dimensional Geometry, Limits and Conditions, and the Binomial Theorem (Chapter 16). On the website of Extramarks, students may access NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3.
Q.1 For each of the following compound statements first identify the connecting words and then break it into component statements.
(i) All rational numbers are real and all real numbers are not complex.
(ii) Square of an integer is positive or negative.
(iii) The sand heats up quickly in the Sun and does not cool down fast at night.
(iv) x = 2 and x = 3 are the roots of the equation 3x^{2} – x – 10 = 0.
Ans.
(i) The connecting word of given components statements is “and”. The component statements are:
p: All rational numbers are real.
q: All real numbers are not complex.
(ii) The connecting word of given components statements is “or”. The component statements are:
p: Square of an integer is positive.
q: Square of an integer is negative.
(iii) The connecting word of given components statements is “and”. The component statements are:
p: The sand heats up quickly in the Sun.
q: The sand does not cool down fast at night.
(iv) The connecting word of given components statements is “and”. The component statements are:
p: x = 2 is the roots of the equation 3x^{2 }– x – 10= 0.
q: x = 3 is the roots of the equation 3x^{2} – x – 10= 0.
Q.2 Identify the quantifier in the following statements and write the negation of the statements.
(i) There exists a number which is equal to its square.
(ii) For every real number x, x is less than x + 1.
(iii) There exists a capital for every state in India.
Ans.
(i) The quantifier is “There exists” in the given statement.
Negation: There does not exist a number which is equal to its square.
(ii) The quantifier is “For every” in the given statement.
Negation: For every real number x, x is not less than x + 1.
(iii) The quantifier is “There exists” in the given statement.
Negation: There does not exist a capital for every state in India.
Q.3 Check whether the following pair of statements are negation of each other. Give reasons for your answer.
(i) x + y = y + x is true for every real numbers x and y.
(ii) There exists real numbers x and y for which x + y = y + x.
Ans.
No, the following pair of statements are not negation of each other. The negation of statement (i) is:
$\mathrm{x}+\mathrm{y}\ne \mathrm{y}+\mathrm{x}\text{}\mathrm{is}\text{}\mathrm{true}\text{}\mathrm{for}\text{}\mathrm{every}\text{}\mathrm{real}\text{}\mathrm{numbers}\text{}\mathrm{x}\text{}\mathrm{and}\text{}\mathrm{y}.$
While the sense of given statement (ii) is different.
Q.4 State whether the “Or” used in the following statements is “exclusive “or” inclusive.
Give reasons for your answer.
(i) Sun rises or Moon sets.
(ii) To apply for a driving licence, you should have a ration card or a passport.
(iii) All integers are positive or negative.
Ans.
(i) Here “Or” is exclusive because both events do not happen simultaneously.
(ii) Here “Or” is inclusive because for applying a driving licence, a person can have both a ration card and a passport.
(iii) Here “Or” is exclusive because all integers are neither positive nor negative.
Please register to view this section
FAQs (Frequently Asked Questions)
1. How do the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 help students?
Subject matter specialists create the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 in accordance with CBSE requirements. Each chapter includes a thorough explanation and covers all the important details to make sure the subject is clear. The answer will assist students in honing their problemsolving abilities.
2. Where can students access the PDF of the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3?
Students can access the PDF format of the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 on the Extramarks’ website and mobile application. The NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 are available at Extramarks in PDF format. Students can download the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 PDF notes to boost their exam preparation. The themes covered in the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3 in PDF format have been presented in a stepbystep manner, enabling students to get familiar with all the ideas covered in the Class 11 Mathematics syllabus. Students only need to log in to the official website to download the PDF notes for NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.3. Additionally, academicians and subject experts created the solutions. As a result, pupils may trust them without hesitation.