NCERT Solutions for Class 11 Maths Chapter 16 Probability (Ex 16.2) Exercise 16.2

Both public and private schools receive secondary education from the Central Board of Secondary Education, which is headquartered in New Delhi. CBSE is governed and administered by the Indian government. Since 1961, the National Council of Educational Research and Training has been working to improve the quality of school education in the country. This organisation provides advisory and assistance services to the State Governments and the Central Government. In addition to model textbooks, supplementary materials, newsletters, journals, educational kits, and multimedia digital products, they also create and publish educational materials. For the students studying in Class 11, a minimum score of 33% must be achieved on both the theory and practical examinations in order to be promoted to Class 12.

The study of Mathematics is an important part of the academic curriculum for students who have chosen to study it. As part of their course curriculum, all Commerce and Science stream students are required to take Mathematics. The Exercises Question And Answers For Class 11 Mathematics are designed to simplify all the problems found in the CBSE textbooks for Class 11. All the exercises, questions, and answers in NCERT Class 11 Mathematics are organised systematically and cover the entire curriculum. Along with Probability, other chapters include Sets, the Principle of Mathematical Induction, Linear Inequalities, Trigonometric Functions, the Binomial Theorem, Limits and Derivatives, among others.

Class 11 Mathematics covers Probability in Chapter 16. Probability had been studied previously by the students in preceding classes. Therefore, they are familiar with the concepts discussed in the chapter. The frequency with which unexpected events occur can be defined as Probability. Exercise 16.2 in the textbook focuses on the occurrence of events, the types of events, and event algebra, among other topics. There are numerous examples of each type of event provided in the textbook. For students to be adequately prepared, it is essential that they complete  exercise 16.2. Probability is one of the most fascinating and rewarding chapters of statistics. Through the use of Extramarks’ NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2, students can better prepare for the exam.

Through the provision of comprehensive learning, NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.2 helps students develop better mathematical skills as well as logical and reasoning abilities. In order to facilitate learning, the solutions to difficult problems have been simplified and explained. The solutions For Class 11 Mathematics should be practised by the students in preparation for the Class 11 Mathematics examination. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 are designed to provide students with answers to all the questions to assist them in understanding the questions better.

In the majority of competitive engineering examinations and other college entrance tests, textbook syllabuses are used as the basis for the examinations. Therefore, it is recommended that students practise these NCERT Solutions regularly in order to achieve higher test scores. In addition, students are encouraged to practise solving the exemplar problems and solutions on the Extramarks’ website. With the help of these solutions, students can gain a better understanding of the importance of studying Class 11 Mathematics. Several study materials are available through Extramarks to assist students in becoming familiar with the concepts covered in this chapter.

NCERT Solutions are also included in the CBSE exam preparation study materialsBefore taking the final examination, students should review the NCERT Solutions Class 11 Mathematics at least twice.Extramarks offers solutions not only for Mathematics but also for other chapters and classes. Using Extramarks’ website, students in Class 1 through Class 12 have easy access to these solutions. For all subjects, the solutions have been curated by experts and are considered to be an invaluable resource. For various classes, students can access 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, and NCERT Solutions Class 12 on the Extramarks’ website and learning platform.

NCERT Solutions for Class 11 Maths Chapter 16 Probability (Ex 16.2) Exercise 16.2

On the Extramarks website, the students can easily find NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.2. During the preparation for the final Mathematics Class 11 exam, students should pay particular attention to Class 11 Maths Chapter 16 Exercise 16.2 e.g. questions. Extramarks’ website and mobile app provide students with access to a variety of study materials. The website provides a variety of study resources to help students prepare well, which include past years’ papers, revision notes, sample papers, and extra questions. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 can be downloaded from Extramarks and used to assist students in preparing for their exams.

Experts prepare solutions based on the most recent CBSE syllabus to assist students with their studies. In order to help them understand the questions, NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 can be used. As well as solutions, there is also a clear explanation so that students can comprehend them. By accessing the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2, students can prepare for the Class 11 examination at any time and from any location. In addition to accessing the online version of the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2, students may also download a PDF copy.

NCERT Solutions for Class 11 Maths Chapter 16 Probability Exercise 16.2

For answers to questions in the Class 11 Mathematics textbook, students should refer to the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2. It is also imperative that students understand the concepts presented in this chapter. Because the NCERT book frequently contains exam questions, practising exercises from it is generally beneficial. There are a number of questions contained in this chapter that may be challenging for students. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 are available at Extramarks. To prepare for the examination, students should refer to authentic and original solutions. In order to access reliable study materials like NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 should utilise Extramarks’ learning platform. Through the use of NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2, students can accelerate their learning process and improve their academic performance. These solutions help them gain a deeper understanding of the problems. The Extramarks website provides students with the opportunity to solve practise modules in order to improve their understanding of the concepts.

For students preparing for exams or working on homework assignments, the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 is a valuable resource. A thorough understanding of theorems and numericals is necessary for passing the Class 11 and competitive examinations. Using the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 is an effective method of preparing for exams. By studying the Extramarks solutions, students are able to effectively understand any problem. There are comprehensive solutions to all the problems in NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2. Extramarks provides solved examples at the end of each chapter to assist students in understanding the concepts. With the help of NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2, students can practise and revise concepts more effectively. For students to score well in the NCERT Class 11 Mathematics Examination, they should apply a logical approach. When studying, having  NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 available can be extremely useful for reviewing material quickly. Students can gain a thorough understanding of Class 11 Mathematics Chapter 16 by regularly reviewing NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2.

Students should use NCERT Solutions Class 11 to improve their understanding of Class 11 Mathematics Chapter 16. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 contains exercises and examples that assists students in understanding the concept better. Throughout the course, students are prepared for the CBSE final examination based on the curriculum. There are many textbook questions that are frequently asked during competitive examinations, such as the JEE and others. Thus, it serves as a valuable study resource for their preparation. Detailed explanations of all questions significantly enhance concept-based learning. In order to improve retention and understanding, the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 use simple language. Students can track their progress by practising additional practise questions for each subject.

In addition to these NCERT Solutions for Class 11 Maths Exercise 16.2, students may also refer to other study materials on the website. With the assistance of these study materials, students are able to gain a deeper understanding of the topics and concepts discussed in class. There is a comprehensive understanding of the subject provided by these NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.2. Using the exercise questions and examples provided in Class 11 Mathematics is essential to understanding the concepts presented. The solutions can be used by students to prepare for the CBSE Class 11 final exams based on the CBSE curriculum. There are many competitive exams that contain questions based on the NCERT Class 11 Mathematics Chapter 16, including JEE, BITSAT, and others.

Exercise 16.2

The topic of probability is covered in Chapter 16 of Class 11 Mathematics. The students had previously studied probability in previous classes. This has resulted in their familiarity with the concept of the chapter. A measure of the frequency with which unanticipated events occur. There are several topics discussed in Exercise 16.2 in the textbook. These topics include the occurrence of events, the types of events, event algebra, and others. Throughout the textbook, a variety of examples are provided for each type of event. In exercise 16.2 of Class 11 Mathematics, there are a total of seven questions divided into sub-parts. It is advised that students study diligently and refer to the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 in order to cross-check their answers. It is imperative that students complete the exercise in order to be adequately prepared for the chapter. The study of probability is an enthralling and rewarding experience. In this way, students can prepare for their exams more effectively by using NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2.

NCERT Solutions for Class 11 Maths Chapter 16 Probability Exercise 16.2

For a deeper understanding of the concepts presented in Class 11 Mathematics NCERT Solutions, students should refer to the examples provided in Class 11 Maths Exercise 16.2. The answers to each exercise are provided in detail, so students can follow the steps in order to complete them. It is evident that some questions and patterns are repeated among them. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 have been prepared by highly qualified professionals to meet the needs of students preparing for CBSE examinations. The Extramarks’ NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 helps students  achieve high levels of effectiveness because of this. It is critical to thoroughly understand the concepts involved in NCERT exercise 16.2 in order to be able to solve it. In order to facilitate students’ understanding of how to solve complex problems, each step of the method is explained in a simple manner. According to the CBSE examination mark distribution, the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 provide step-by-step solutions. This chapter has been updated according to the most recent CBSE guidelines. In order to achieve a higher grade, students will be required to solve a variety of problems in this chapter.

The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 should be reviewed by students before taking the CBSE exams. The NCERT solutions provided by Extramarks for grades 1-12 must be downloaded in PDF format. This PDF file contains detailed explanations of the solutions to NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2. This source of information has been considered trustworthy by many students. To improve their understanding of the subject and their performance on examinations, students should regularly review NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2. When solutions are arranged according to chapter content, students are not required to search through their textbooks for answers. Students who are studying for exams or working on homework assignments can find the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 to be a valuable resource. A thorough understanding of concepts and numericals is required in order to pass the Class 11 and competitive exams.

For the preparation of exams, NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 are useful educational resources. The Extramarks solutions provide students with an effective means of understanding any problem. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 provide comprehensive solutions to all the problems described in the chapter. Extramarks provides solved examples at the end of each chapter so that students can better understand the concepts. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 provide students with the opportunity to practise and revise concepts more effectively. In order to score well in the NCERT Class 11 Mathematics Examination, students must apply a logical approach. When studying, having NCERT solutions available is extremely helpful for obtaining a quick review of the material. It is recommended that students review NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 on a regular basis in order to gain a thorough understanding of all the questions covered in the chapter.

Q.1 A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?

Ans.
Here, E = {4}, F = {2, 4, 6}
E ∩ F = {4}
Since, E ∩ F ≠

ϕ

So, E and F are not mutually exclusive events.

Q.2 A die is thrown. Describe the following events:

(i) A: a number less than 7
(ii) B: a number greater than 7
(iii) C: a multiple of 3
(iv) D: a number less than 4
(v) E: an even number greater than 4
(vi) F: a number not less than 3

Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F′, F′

Ans.
Here,
(i) A = {1, 2, 3, 4, 5, 6}
(ii) B = {} = Φ
(iii) C = {3, 6}
(iv) D = {1, 2, 3}
(v) E = {6}
(vi) F = {3, 4, 5, 6}

A ∪ B = {1, 2, 3, 4, 5, 6},
A ∩ B = {} = Φ
B ∪ C = {3, 6}
E ∩ F = {6}
D ∩ E = {} = Φ
A – C = {1, 2, 4, 5}
D – E = {1, 2, 3}
E ∩ F’ = {6} ∩ [{1, 2, 3, 4, 5, 6} – {3, 4, 5, 6}]
= {6} ∩ {1, 2}
= {} = Φ
F’ = {1, 2}

Q.3 An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

A: the sum is greater than 8,
B: 2 occurs on either die
C: the sum is at least 7 and a multiple of 3.

Which pairs of these events are mutually exclusive?

Ans.

S={(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

A = {(3, 6), (4, 5), (4, 6),(5, 4), (5, 5),(5, 6), (6, 3),(6, 4), (6, 5),(6, 6)}
B = {(1, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (4, 2), (5, 2), (6, 2)}
C = {(3, 6), (4, 5), (5, 4), (6, 3), (6, 6)}
Since, A ∩ B =

ϕ

. So, A and B are mutually exclusive.
And B ∩ C =

ϕ

. So, B and C are mutually exclusive.

Q.4 Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”, C denote the event” three tails show and D denote the event ‘a head shows on the first coin”.
Which events are (i) mutually exclusive? (ii) simple? (iii) Compound?

Ans.

S={(HHH),(HHT),(HTH),(THH),(HTT),(THT),(TTH),(TTT)}A={(HHH)}B={(HHT),(HTH),(THH)}C={(TTT)}D={(HTT),(HHH),(HHT),(HTH),(HHT)}(i) Since,​ A∩B = ϕ, so, A and B are Mutually exclusive.     Since,​ A∩C = ϕ so, A and C are Mutually exclusive.     Since,​ B∩C = ϕ so, B and C are Mutually exclusive.     Since,​ C∩D = ϕ so, C and D are Mutually exclusive.(ii) A and C are simple events because they have single element. (iii) Compound events are B and D.

Q.5 Three coins are tossed. Describe

(i) Two events which are mutually exclusive.
(ii) Three events which are mutually exclusive and exhaustive.
(iii) Two events, which are not mutually exclusive.
(iv) Two events which are mutually exclusive but not exhaustive.
(v) Three events which are mutually exclusive but not exhaustive.

Ans.

S={(HHH),(HHT),(HTH),(THH),(HTT),(THT),(TTH),(TTT)}(i) Two mutually exclusive events are: {(HHH)} and {(TTT)}.(ii) Three events which are mutually exclusive and  exhaustive:  A={(HHH),(HHT)}      B={(HTH),(THH)}  and     C=  {(HTT),(THT),(TTH),(TTT)}∵A∩B=ϕ,B∩C=ϕ,A∩C=ϕ and A∪B∪C=S(iii) D={(HHH),(HHT),(HTH),(THH),(HTT)}and  E={(HTH),(THH),(HTT),(THT),(TTH)}∵D∩E≠ϕ, so, D and E are not mutually exclusive.iv F={(HHH),(HHT),(HTH),(THH),(HTT),(THT),}       G={(TTH)}Since, F∩G=ϕ but F∪G=SSo, F and G are exclusive but not exhaustive.(v) H={(HHH),(HHT)}         K={(HTH),(THH)}         L={(HTT),(THT)}∵ H∩K=ϕ, H∩L=ϕ      K∩L=ϕ and H∪K∪L≠SSo, H, K and L are mutually exclusive but not exhaustive.

Q.6 Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5.

Describe the events
(i) A′ (ii) not B ,
(iii) A or B (iv) A and B
(v) A but not C (vi) B or C
(vii) B and C (viii) A ∩ B′∩C′

Ans.

S={(1,1),  (1,2),  (1,3),(1,4),(1,5),(1,6)(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}A={(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}B={(1,1),  (1,2),  (1,3),(1,4),(1,5),(1,6)(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}C={(1,1),  (1,2),  (1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)}

(i) A’=S−A                      ={(1,1),  (1,2),  (1,3),(1,4),(1,5),(1,6)(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}=B(ii) not B=S−B                      ={(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}=Aiii A or B=A∪B                      ={(1,1),  (1,2),  (1,3),(1,4),(1,5),(1,6)(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}=S(iv) A and B=A∩B  =ϕ(v) A but not C=A−C                                ={(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}−{(1,1),  (1,2),  (1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)}

MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbba9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@01D7@                                 ={(2,4),(2,5),(2,6),(4,2),(4,3),(4,4),(4,5),(4,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}(vi) B or C=B∪C                                ={(1,1),  (1,2),  (1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}(vii) B and C=B∩C                                ={(1,1),(1,2),(1,3),(1,4),(3,1),(3,2)}(viii) A∩B‘=A∩(S−B)                                =A∩A[From (ii)]                               =A                               ={(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}                         C‘=(S−C)                               ={(1,5),(1,6),(2,4),(2,5),(2,6),(3,3),(3,4),(3,5),(3,6),(4,2),(4,3),(4,4),(4,5),(4,6)(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}        A∩B‘∩C‘={(2,4),(2,5),(2,6),(4,2),(4,3),(4,4),(4,5),(4,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Q.7 Refer to question 6 above, state true or false: (Give reason for your answer)

(i) A and B are mutually exclusive
(ii) A and B are mutually exclusive and exhaustive
(iii) A = B′
(iv) A and C are mutually exclusive
(v) A and B′ are mutually exclusive.
(vi) A′, B′, C are mutually exclusive and exhaustive.

Ans.
1. True, because A ∩ B = Φ
2. True, because A ∩ B = Φ and A È B = S.
3. True, because B’= S – B = A.
4. False, because A ∩ C ≠ Φ
5. False, because A ∩ B’ = A ∩ A ≠ Φ [Here, B’ = A]
6. False, because A’ ∩ B’ = Φ, B’ ∩ C ≠ Φ

Please register to view this section

FAQs (Frequently Asked Questions)

1. What are some ways in which the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 can assist students?

Students who are enrolled in the Class 11 Mathematics get the benefit from the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 for a number of reasons. The reasons are listed below:

  • The textbook exercises are intended to assist students in solving problems in Chapter 16 of Class 11 Mathematics by providing answers to the questions.
  • The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 provides students with all formulas that they will need in order to gain a thorough understanding of the subject.
  • Several of the most knowledgeable subject experts in the field have been involved in the development of these NCERT solutions.
  • As well as being useful in preparing for competitive exams such as JEE Main, Olympiads, and other exams, the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 may also assist in the preparation for other competitive exams.
  • Students can use these solutions to gain a better understanding of question patterns, mark distributions, and other topics.

2. Provide a brief description of the unique features of the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2.

A large part of the NCERT solutions is prepared by subject experts who are knowledgeable about the concepts in depth. A simple, easy-to-understand language is used to describe each step in order to assist students in understanding how to solve complex problems. These solutions are based on the CBSE examination mark distribution. Based on the most recent CBSE guidelines, the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 cover all the essential topics. In preparation for the CBSE examinations, students are encouraged to use the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2.

3. Why are Extramarks' NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2 different from other solutions?

Students are able to improve their fundamental skills by reviewing NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2. It is essential for students to understand both the basic concepts and the advanced sections of Chapter 16 Exercise 16.2. For a more comprehensive understanding of Chapter 16 Probability of NCERT Class 11 Mathematics, students are recommended to refer to the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.2. If they are adequately prepared, they are capable of answering even the most challenging questions in this section. Aside from this, the solutions assist the students in clarifying any doubts they may have as well as clarify the concepts discussed in the chapter. In preparation for the Class 11 Mathematics examination, students benefit greatly from having answers available to score well.