NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning (Ex 14.4) Exercise 14.4

The National Council of Educational Research and Training is known as NCERT. The NCERT is an educational institution that was founded as an autonomous agency by the Ministry of Education, which is part of the Government of India, in 1961. The nation’s top academics and researchers make up NCERT. The primary reason for NCERT’s establishment was to create a uniform educational framework for all students in the country. It sought to foster cultural diversity throughout this enormous country and advance unification through education.

The Central Board of Secondary Education’s Academic, Training, Innovation, and Research unit’s mission is to provide balanced academic activities in Board-affiliated schools while achieving academic excellence through the creation of policies and their operational planning. By completing the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4, students can efficiently prepare for their exams. The Central Board of Secondary Education’s academic division offers a curriculum, a scheme of study, academic standards, texts, support materials, extracurricular activities, and capacity-building programmes. The unit complies with the many laws and regulations that the Government of India occasionally approves, as well as the more general goals outlined in the National Curriculum Framework-2005. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 are based on the questions in the NCERT books.

The end of each chapter in NCERT textbooks includes practise questions for students at all levels, as well as those in Class 11. Extramarks has the solutions to all these questions. Extramarks provides study resources like NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4. These solutions are based on the themes covered in the preceding chapter. All of  the NCERT books’ solutions, including the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4, are available for Class 11 students as well as others on the Extramarks website.

The subject-matter experts at Extramarks are aware of the significance of all classes, not simply those in higher secondary. Students can always benefit from tools like the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 and many others, regardless of what class they are in. The subject specialists are well-versed in their fields, and they cover all levels, from Class 1 to Class 12. For all of these classes, students can access the answers to the questions in their NCERT books on the Extramarks website –

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The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 along with other resources available on the Extramarks website, are very user-friendly. The experts in individual subjects are responsible for coming up with these resources. The experts prepare the tools like the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 keeping in mind their usability for the students. The students can easily access the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 by simply visiting the Extramarks website. There are several other tools that the students can access on the Extramarks website, along with the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4. All these tools can be of great help to the students when preparing for their final examinations.

Extramarks has various resources that can be helpful for the students, not only from an examination point of view but for other purposes as well. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 are the answers to the questions that are asked in the Class 11 Maths Chapter 14 Exercise 14.4. All the chapters in the NCERT Mathematics books are divided into various exercises. The students can find the answers to all these exercises on the Extramarks website. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 are the solutions to one particular exercise, but students can easily access solutions to all the other exercises in Chapter 14 and other chapters as well.

The students are also advised to keep in mind that theory also plays an important part when it comes to the final examinations. There is a common misconception that the theory part of Mathematics is of no use. The students need to understand the importance of the theory and the formulas, equations, and theorems that are in it, as these are what help the students understand the topic better and  solve the Mathematical problems with more efficiency. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 can also help the students practise the NCERT questions and be more efficient in solving the Mathematical problems in the examinations.

Class 11 students are well familiar with the subject of Mathematics and might already have their own strategies to excel in the subject. The tools such as the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 along with other tools questions on a particular topic, etc.,can facilitate their strategies and help them perform even better. Students are advised to make use of these tools as much as possible. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 can be referred to when students want to practise the questions from Class 11 Maths Exercise 14.4 .

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning (Ex 14.4) Exercise 14.4 

Many students can find Mathematics to be a very difficult subject to prepare for. What is important for the students to remember is that Mathematics is also a subject that is relevant in everyday life. If looked at from that perspective, it can be a fun subject to study and prepare for the examinations. With the use of various interactive resources available on the Extramarks website for the students to take help from, the students can learn to tackle the subject more effectively. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 are this one example of such resources that are available on the Extramarks website. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 can help the students with their practice and self study of the mathematical problems. There are also tools that can help them understand the theory parts of the subject as well. The more time students spend with tools such as the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4, the higher their chances of scoring well in the final examinations.

Access NCERT Solutions for Class 11 Maths Chapter 14 – Mathematical Reasoning Exercise 14.4 

Mathematical Reasoning is one of the easier topics in Mathematics, and the doubts that arise from  this topic are straightforward to resolve. Because this chapter covers a subject that is also covered in the chapter on Semiconductors in Physics, the information that the students gain in this chapter may be useful to them in other subjects as well. This chapter is significant from the perspective of exams because it is easy to score well on it. Students may be able to answer a question in under a minute if they have mastered the concept. Students can get to learn a new chapter, but they mostly have no trouble learning and comprehending this chapter. The use of the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 can make it even easier for the students to understand this chapter.

Comparatively speaking to other chapters, this one is brief overall. Students can use resources like the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 to be prepared for this chapter. The answers are especially for exercise 4.4, however, students can also visit the Extramarks website for the answers to all the other exercises as well. No matter the chapter’s level of difficulty, all Mathematics topics require practice. Students’ chances of doing well in their exams increase as they spend more time working through Mathematical problems. The Extramarks website has a number of resources that students can use to help them with their final exams, class tests, and other assessments. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 are just one of such tools that the students can take help from.

Exercise 14.4 

Students in Class 11 occasionally do not understand the relevance of Class 11. This is due to the students’ mindset, which holds that the board examinations are the only tests they should take seriously. Students in Class 11 occasionally lag behind because Classes 10 and 12—the classes before and following Class 11—have board exams. Because they place less value on Class 11 than they do on Class 10 and Class 12. The students are advised to use the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 in order to effectively prepare for the Class 11 exams and do well in their tests. The students are advised to give the Class 11 examinations enough and equal importance.

The students must comprehend the importance of Class 11, since what they learn there creates the foundation for what will be taught in Class 12. Laying a firm foundation with the help of what is taught in Class 11 can be helped by the resources on the Extramarks website, like the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4. The outcomes of the Class 11 exams are significant because they provide the students the self-confidence they need to succeed in Class 12. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 can help students prepare for their Class 11 Mathematics examinations sincerely. There are similar tools on the website for all the other subjects of Class 11. The students are advised to take help from them to excel in all the subjects.

NCERT Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Exercise 14.4 

Students may find a variety of uses for the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.4. Students might utilise these solutions to help them study for their upcoming class test. Students can use these solutions to help them grasp the themes in Chapter 14. If they are required to give a presentation on those topics, this can prove to be very beneficial. The students can also use additional beneficial resources along with the NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.4 , that are accessible on the Extramarks website for activities like class presentations and other similar tests and assignments. Students in Class 11 are encouraged to take their exams seriously because doing so would help them feel more confident and perform excellently in their Board Exams in Class 12.

NCERT Solutions for Class 11 Maths Chapter 14 Exercise 14.4

Asking questions is a virtue that many students possess. This is a habit that students are advised to inculcate. The more questions a student has, the more clarity they may get about a topic. Asking questions can also mean that the student has an interest in the subject and wishes to understand it in-depth. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 are the answers to the Mathematical problems that are given at the end of NCERT Mathematics book. But there are some questions that the students may have that are not part of the book. The experts at Extramarks understand the importance of helping  students clear their doubts before examinations. 

A student with less doubt is more confident in their preparation and has a higher chance of performing well in their final examinations. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 can also be very helpful in boosting the students’ confidence in their preparations. At Extramarks, the students can find the Frequently Asked Questions section where they may get their doubts cleared by the subject specialists.

Q.1 Rewrite the following statement with “if-then” in five different ways conveying the same meaning.
If a natural number is odd, then its square is also odd.

Ans.
The given statement can be written in 5 different ways as follows:

(i) A natural number is odd implies that its square is odd.
(ii) A natural number is odd only if its square is odd.
(iii) For a natural number to be odd it is necessary that its square is odd.
(iv) For the square of a natural number to be odd, it is sufficient that the number is odd
(v) If the square of a natural number is not odd, then the natural number is not odd.

Q.2 Write the contrapositive and converse of the following statements.

(i) If x is a prime number, then x is odd.
(ii) If the two lines are parallel, then they do not intersect in the same plane.
(iii) Something is cold implies that it has low temperature.
(iv) You cannot comprehend geometry if you do not know how to reason deductively.
(v) x is an even number implies that x is divisible by 4.

Ans.
(i) Contrapositive:
If x is not odd, then x is not a prime number.
Converse: If the number x is odd, then x is a prime number.

(ii) Contrapositive:
If the two lines intersect in the same plane, then they are not parallel.
Converse: If two lines do not intersect in the same plane, then they are parallel.

(iii) Contrapositive:
If something has not low temperature, then it is not cold.
Converse: If something is at low temperature, then it is cold.

(iv) Contrapositive:
If you do know how to reason deductively, then you can comprehend geometry.
Converse: If you do not know how to reason deductively, then you cannot comprehend geometry.

(v) Contrapositive:
x is not divisible by 4, then x is not an even number.
Converse: If x is divisible by 4, then x is an even number.

Q.3 Write each of the following statements in the form “if-then”

(i) You get a job implies that your credentials are good.
(ii) The Banana trees will bloom if it stays warm for a month.
(iii) A quadrilateral is a parallelogram if its diagonals bisect each other.
(iv) To get an A+ in the class, it is necessary that you do all the exercises of the book.

Ans.
(i) If your credentials are good, then you get a job.
(ii) If it stays warm for a month, then the banana trees will bloom.
(iii) If diagonals of a quadrilateral bisect each other, then it is a parallelogram.
(iv) If you do all the exercises of the book, the you will get A+ in the class.

Q.4 Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.
(a) If you live in Delhi, then you have winter clothes.
(i) If you do not have winter clothes, then you do not live in Delhi.

(ii) If you have winter clothes, then you live in Delhi.
(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

(i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.

(ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Ans.
(a) (i) Given statement is Contrapositive of statement (a).
(ii) Given statement is Converse of statement (a).

(b) (i) Given statement is Contrapositive of statement (b).
(ii) Given statement is Converse of statement (b).

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FAQs (Frequently Asked Questions)

When the students are preparing for Mathematics examinations, they are advised to spend the maximum of their time to practice the Mathematical problems that are present in the NCERT book itself.  Tools like the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 can be helpful in this regard.  The final examination question papers are mostly similar to the questions that are given in the NCERT book itself. If the students are thorough with the Mathematical problems given in the book, they have a higher chance of performing excellently in the examinations. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 can be helpful in practicing the questions in this particular exercise. But the students can find the answers to all the exercises in the NCERT books at Extramarks.

Another point that the student can remember is to keep in mind the syllabus and the guidelines that are given by the NCERT and CBSE. The students should make use of tools like the NCERT syllabus available on the Extramarks website to keep in mind what topics are a part of it. Solving questions that are not  part of the syllabus but are similar to the topics that are part of it can be helpful for the students to practise the topic. But with the limited time the students have for  preparation before the examinations, it is advised to stick to the syllabus itself and not end up getting confused.

The tools such as the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 and many other resourceful tools that are available on the Extramarks website are created by subject specialists. They are experts on a subject and are highly knowledgeable in their respective fields. The students can confidently rely on  tools such as the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 as they are prepared, keeping in mind the guidelines from the NCERT and CBSE. There are many such resources available on  Extramarks website along with the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 . The students are advised to make the most of these tools when preparing for their examinations.

The students are advised not to spend their precious time browsing all the abundant number of educational websites that are available on the internet. The students should rather spend their time practising the subject matter of their syllabus. They can easily take help from all the resources available on the Extramarks website to save time and avoid any confusion or disturbance in their preparation. All these resources are prepared by subject specialists and can be trusted. The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 are one such tool that the students can rely on.

There are various uses of the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 . Students can take help from the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 when solving their homework related to the exercise. Students can also use the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 to get conceptual clarity on the topics covered in Chapter 14. This can help the students prepare any class presentations or project reports, etc., if needed.

The NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 can be of great use to go through right before the examinations. This can help students perform a quick revision and feel confident in their preparation. The students that are confident when writing their paper have a higher chance of excelling in their examinations.

Another benefit of taking help from the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 is that the students can get access to this tool and many others by a simple click. The students can refer to the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 at their own convenience. Students can refer to the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 with the help of computers or even mobile phones. This ensures that the students can take help from the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 whenever and wherever they wish to.

The students can take help from the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4 through the website as well as the mobile application of Extramarks. The tools are prepared by the subject experts, keeping in mind their easy accessibility as well as usability . Therefore, it is highly convenient for the students to refer to the NCERT Solutions for Class 11 Maths Chapter 14 exercise 14.4.