# NCERT Solutions for Class 10 Maths Chapter 4 Exercise 4.2

Mathematics is an important discipline and has considerable relevance for other disciplines as well. Students need to focus well on the curriculum of Mathematics. Practising topics of Mathematics is useful for developing analytical thinking and reasoning abilities in students. They can improve their understanding of other subjects by using mathematical concepts.Students can get admission into prestigious colleges in India if they have a strong foundation in basic mathematical principles. It is advised for them to develop better problem-solving skills in order to practise questions in an effective manner. Class 10 students of the Central Board of Secondary Education (CBSE) are advised to keep practising questions of Mathematics chapters to score well in Mathematics. It is crucial for students to access study materials from reliable sources. The Central Board of Secondary Education (CBSE) is responsible for governing the examinations of Class 10 and Class 12. The CBSE Board works under the supervision of the Ministry of Education and is responsible for improving the level of secondary education in India. It is preferred by many Indian students as it has a verycomprehensive curriculum for all the subjects.

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The main topic discussed in Chapter 4 is Quadratic Equations. It is one of the crucial topics of Algebra. Students must practise questions of Chapter 4 in a thorough manner as they can appear in the board examination of Mathematics. To solve questions effectively it is necessary to get well versed in the theory of the topics. Learning formulae, derivations, theorems, etc., is also important for solving questions. Students can get easy solutions to exercises with the help of the Extramarks learning portal. Students of all classes can obtain NCERT Solutions for all the subjects from the Extramarks website and mobile application. Students often overlook the theoretical proportion of Mathematics which should be retained in order to gain proficiency in the subject. It is crucial to retain important concepts as they provide a base for practising questions set up on the topics. The questions in Class 10 Maths Chapter 4 Exercise 4.2 can be solved with the help of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2. Students must download the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 from the Extramarks website and mobile application. All of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 are given in simple language so that students understand them very well.

Solving exercise questions is beneficial for scoring well in the Mathematics examination as most of the questions that appear in the Mathematics question paper are taken from them or based on them. It is necessary for students to learn time management skills to be able to solve questions properly within the allotted time. Regular practise and good calculation speed can enable students to manage their time appropriately while solving questions in the Mathematics examination. To learn theory and practising questions related to Chapter 4, students must rely on the NCERT textbook of Mathematics. They will be able to learn the theory of Chapter 4 in an efficient manner if they read the NCERT textbook. All the questions of Chapter 4 given in the textbook are very significant for the preparation for the Mathematics examination. Students should practise them regularly. The NCERT textbook contains authentic information and is prescribed by the CBSE Board itself. All the questions of Chapter 4 given in the NCERT textbook can be practised well with the assistance of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2.

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Coursebooks for all CBSE Board classes are published by the National Council of Educational Research and Training (NCERT). The NCERT books are written with the intention of providing students with well-balanced knowledge. Additionally, NCERT offers training programmes for primary and secondary school teachers. Moreover, NCERT is also responsible for conducting research in various fields concerning Indian school education. Research aids in identifying essential adjustments to the way schools operate their classes. In order to address the issues that India’s school-based learning is currently dealing with, NCERT collaborates with numerous education departments and colleges in India. There are many units of NCERT operating in different parts of the country for the proper functioning of the organisation.

It is important for students to become well versed in all the topicsbefore the examinations. Revision is necessary for scoring well in a subject like Mathematics. All students need to understand the importance of practise when preparing for the Mathematics examination. Most of the questions at the Class 10 level are crucial for preparation for competitive examinations like JEE, NTSE, CUET, etc. Class 10 Mathematics topics lay the foundation to prepare students for these examinations. Students must go through each chapter of Class 10 Mathematics thoroughly.

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## NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations

Students can increase the speed of their calculations with the help of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2. They can easily score well in Mathematics if they refer to the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 on a routine basis. It is crucial for students to retain formulae, definitions, and theorems for a longer time to be able to perform well in the examinations. Class 10 students must revise them consistently to retain them for a long time. The NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 are also beneficial for revising important formulae, definitions and theorems. It is important to be confident in order to solve questions in an efficient manner. Class 10 students can boost their confidence with the help of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2.

Practising questions with the help of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 is helpful in motivating students to practise more. Students will learn to find the roots of given quadratic equations with the assistance of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2. All questions of Exercise 4.2 are important from the perspective of the board examination, and students are encouraged to practise them from time to time. Derivations are very important for students to learn. Paying attention to the derivations of Chapter 4 will help students in solving problems of the chapter. Students must revise the derivations of Chapter 4 consistently. The NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 are useful in revising the derivations of Chapter 4. Students can compare their own solutions with the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 and make necessary changes if required.Before attempting to solve questions, students must first understand their requirements. The NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 are helpful in understanding the requirements of each question of Class 10 Maths Ch 4 Ex 4.2.

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### Important Points to Learn Before Solving Exercise 4.2

Students of Class 10 can easily download the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 in PDF format from the Extramarks website and mobile application. Students can refer to the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 in offline mode as well. Along with practising questions with the assistance of NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2, students are also required to practice past years’ papers and sample papers of Mathematics from time to time. Solving past years’ papers helps in knowing the marks distribution and question paper pattern of Mathematics. The NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 could prove to be indispensable with regard to writing well-coordinated solutions. To achieve higher marks in the Mathematics examination, NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 are extremely important. Students can easily find solutions for Exercise 4.2 questions with the use of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2.

### Access NCERT Solutions for Class 10 Maths Chapter 4 – Quadratic Equations

Students can easily practice questions included in Exercise 4.2 with the help of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2. These solutions are created in accordance with the latest syllabus of Mathematics. All the solutions are explained well. It is important to keep assessing the ongoing preparation in order to make necessary adjustments in the examination preparation strategy. The NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 are crucial for self-assessment.

### Class 10 Maths Chapter 4 – Exercise 4.2

All the questions of Exercise 4.2 are based on the topic Solution of a Quadratic Equation by Factorisation. It is necessary to learn the theory of the topic in order to practise questions based on it. There are 6 questions in Exercise 4.2 and to solve them, it is important for students to revise the method of factorisation of quadratic equations that they learned in Class 9. Students having problems in solving questions of the Maths Class 10 Chapter 4 Exercise 4.2 are recommended to make use of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2. Students are required to practise questions on a daily basis to prepare adequately for the upcoming examinations. All the topics must be well practised before the examination. Chapter 4 Exercise 4.2 Class 10 Mathematics Solutions

Students who are facing difficulties in finding accurate and concise NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 can conveniently access them from the Extramarks learning platform. The NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 are very useful in enhancing preparation for the Mathematics examination. With the help of these solutions, students can improve their overall understanding of Chapter 4. It is recommended that students keep referring to them when practising questions of Exercise 4.2.

### Benefits of Chapter 4 Exercise 4.2 Class 10 Mathematics Solved Solutions.

There are many benefits of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2. These are essential for learning time management skills, problem-solving skills, formulas,etc. Students need to refer to them from time to time. It is possible that Class 10 students can get stuck when trying to solve questions of Exercise 4.2. The NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 are designed to assist students in solving all the questions of Exercise 4.2. The solutions are available on Extramarks in PDF format, therefore students can refer to them in the absence of an internet connection as well.

### NCERT Solutions for Class 10 Maths Chapter 4 Exercises

Class 10 students can also access NCERT Solutions for all the exercises of Chapter 4 from the Extramarks learning platform. They can access NCERT Solutions exercise-wise according to their need and preference. There are 4 exercises in the Quadratic Equations chapter and all of them can be solved with the assistance of Extramarks. Students of the Central Board of Secondary Education can get NCERT Solutions for every academic discipline on Extramarks. Students in Class 12 can utilise the NCERT Solutions Class 12 to aid with their board examination preparation. To assist them to study for their final examinations, students in Class 11 can download the NCERT Solutions Class 11 from the Extramarks learning portal. The NCERT Solutions Class 10 are accessible on Extramarks. On the Extramarks website and Learning App, Class 10 can easily access the NCERT Solutions Class 10 for all subjects. The NCERT Solutions Class 9 for Mathematics, English, Hindi, and other subjects are available to Class 9 students via the Extramarks website and mobile application. In order to answer exercise questions for textbooks of English, Mathematics, Hindi, and other subjects, Class 8 students must have access to the NCERT Solutions Class 8. Students in Class 7 can obtain the NCERT Solutions Class 7 on Extramarks to efficiently study for their annual examinations. Students in Class 6 can use the NCERT Solutions Class 6 to practise exercise questions from all chapters of each subject in their course.

**Q.1 **

$\begin{array}{l}\text{Find the roots of the following quadratic equations}\\ \text{by factorisation:}\\ \text{(i)}{\mathrm{x}}^{2}-3\mathrm{x}-10=0\text{(ii)}2{\mathrm{x}}^{2}+\mathrm{x}-6=0\\ \text{(iii)}\sqrt{2}{\mathrm{x}}^{2}+7\mathrm{x}+5\sqrt{2}=0{\text{(iv) 2x}}^{2}-\mathrm{x}+\frac{1}{8}=0\\ {\text{(v) 100x}}^{2}-20\mathrm{x}+1=0\end{array}$

**Ans.**

$\begin{array}{l}\text{(i)}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\mathrm{x}}^{2}-3\mathrm{x}-10=0\\ \Rightarrow \text{\hspace{0.17em}}{\mathrm{x}}^{2}-5\mathrm{x}+2\mathrm{x}-10=0\\ \Rightarrow \text{\hspace{0.17em} x(}\mathrm{x}-5)+2(\mathrm{x}-5)=0\\ \Rightarrow \text{\hspace{0.17em} (}\mathrm{x}-5\left)\right(\mathrm{x}+2)=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}-5=0\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}+2=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}=5\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}=-2\\ \text{Therefore, roots of the equation}{\mathrm{x}}^{2}-3\mathrm{x}-10=0\text{are 5 and \u20132.}\\ \text{(ii)}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}2{\mathrm{x}}^{2}+\mathrm{x}-6=0\\ \Rightarrow \text{\hspace{0.17em} 2}{\mathrm{x}}^{2}+4\mathrm{x}-3\mathrm{x}-6=0\\ \Rightarrow \text{\hspace{0.17em} 2}\mathrm{x}\text{(}\mathrm{x}+2)-3(\mathrm{x}+2)=0\\ \Rightarrow \text{\hspace{0.17em} (2}\mathrm{x}-3\left)\right(\mathrm{x}+2)=0\\ \Rightarrow \text{\hspace{0.17em} 2}\mathrm{x}-3=0\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}+2=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}=\frac{3}{2}\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}=-2\\ \text{Therefore, roots of the equation}2{\mathrm{x}}^{2}+\mathrm{x}-6=0\text{are}\frac{3}{2}\text{and \u20132.}\\ \text{(iii)}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\sqrt{2}{\mathrm{x}}^{2}+7\mathrm{x}+5\sqrt{2}=0\text{}\\ \Rightarrow \text{\hspace{0.17em}}\sqrt{2}{\mathrm{x}}^{2}+2\mathrm{x}+5\mathrm{x}+5\sqrt{2}=0\\ \Rightarrow \text{\hspace{0.17em}}\sqrt{2}\mathrm{x}\text{(}\mathrm{x}+\sqrt{2})+5(\mathrm{x}+\sqrt{2})=0\\ \Rightarrow \text{\hspace{0.17em} (}\sqrt{2}\mathrm{x}+5\left)\right(\mathrm{x}+\sqrt{2})=0\\ \Rightarrow \text{\hspace{0.17em}}\sqrt{2}\mathrm{x}+5=0\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}+\sqrt{2}=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}=-\frac{5}{\sqrt{2}}\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}=-\sqrt{2}\\ \text{Therefore, roots of the equation}\sqrt{2}{\mathrm{x}}^{2}+7\mathrm{x}+5\sqrt{2}=0\\ \text{are}-\frac{5}{\sqrt{2}}\text{and \u2013}\sqrt{2}\text{.}\\ \text{(iv)}\\ {\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}2x}}^{2}-\mathrm{x}+\frac{1}{8}=0\text{}\\ \Rightarrow {\text{\hspace{0.17em} 16x}}^{2}-8\mathrm{x}+1=0\text{}\\ \Rightarrow {\text{\hspace{0.17em} 16x}}^{2}-4\mathrm{x}-4\mathrm{x}+1=0\\ \Rightarrow \text{\hspace{0.17em} 4x(4x}-1)-1(4\mathrm{x}-1)=0\\ \Rightarrow \text{\hspace{0.17em} (4x}-1\left)\right(4\mathrm{x}-1)=0\\ \Rightarrow \text{\hspace{0.17em} 4x}-1=0\text{or\hspace{0.17em}\hspace{0.17em}}4\mathrm{x}-1=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}=\frac{1}{4}\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}=\frac{1}{4}\\ {\text{Therefore, roots of the equation 2x}}^{2}-\mathrm{x}+\frac{1}{8}=0\text{are}\frac{1}{4}\text{and}\frac{1}{4}\text{.}\\ \text{(v)}\\ {\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}100x}}^{2}-20\mathrm{x}+1=0\text{}\\ \Rightarrow {\text{\hspace{0.17em} 100x}}^{2}-10\mathrm{x}-10\mathrm{x}+1=0\\ \Rightarrow \text{\hspace{0.17em} 10x(10x}-1)-1(10\mathrm{x}-1)=0\\ \Rightarrow \text{\hspace{0.17em} (10x}-1)\text{(10x}-1)=0\\ \Rightarrow \text{\hspace{0.17em} 10x}-1=0\text{or\hspace{0.17em}\hspace{0.17em}}10\mathrm{x}-1=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}=\frac{1}{10}\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}=\frac{1}{10}\\ {\text{Therefore, roots of the equation 100x}}^{2}-20\mathrm{x}+\; 1=0\text{are}\frac{1}{10}\text{and}\frac{1}{10}\text{.}\end{array}$

**Q.2 ** Solve the problems given in Example 1.

(i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. We would like to find out the number of toys produced on that day.

**Ans.**

$\begin{array}{l}\text{(i)}\\ \text{John and Jivanti together have 45 marbles.}\\ \text{So, let the number of marbles John had be x.}\\ \text{Then, number of marbles Jivanti had}=45-\mathrm{x}\\ \text{Both of them lost 5 marbles each, then}\\ \text{number of marbles left with John}=\mathrm{x}-5\\ \text{and}\\ \text{number of marbles left with Jivanti}=45-\mathrm{x}-5=40-\mathrm{x}\\ \text{The product of the number of marbles they now have is 124}.\\ \text{Therefore,}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}(\mathrm{x}-5)(40-\mathrm{x})=\text{124}\\ \Rightarrow \text{\hspace{0.17em}}40\mathrm{x}-{\mathrm{x}}^{2}-200+5\mathrm{x}-124=0\text{}\\ \Rightarrow \text{\hspace{0.17em}}{\mathrm{x}}^{2}-45\mathrm{x}+324=0\\ \Rightarrow \text{\hspace{0.17em}}{\mathrm{x}}^{2}-36\mathrm{x}-9\mathrm{x}+324=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}(\mathrm{x}-36)-9(\mathrm{x}-36)=0\\ \Rightarrow \text{\hspace{0.17em}}(\mathrm{x}-9)(\mathrm{x}-36)=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}-9=0\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}-36=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}=9\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}=36\\ \text{So, if John had 9 marbles then Jivanti had 36 marbles}\\ \text{and if John had 36 marbles then Jivanti had 9 marbles.}\\ \text{(ii)}\\ \text{Let the number of toys produced be x.}\\ \text{Given that cost of production of each toy is}\\ \text{55 minus the number of toys produced in a day.}\\ \therefore \text{Cost of production of each toy =}\u20b9\text{(55}-\text{x)}\\ \text{Given that total cost of production of the toys in a day}=\text{\hspace{0.17em}}\u20b9\text{750}\\ \text{Therefore,}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(55}-\text{x)}\mathrm{x}=\text{750}\\ \Rightarrow \text{\hspace{0.17em}}-{\mathrm{x}}^{2}+55\mathrm{x}-750=0\text{}\\ \Rightarrow \text{\hspace{0.17em}}{\mathrm{x}}^{2}-55\mathrm{x}+750=0\\ \Rightarrow \text{\hspace{0.17em}}{\mathrm{x}}^{2}-25\mathrm{x}-30\mathrm{x}+750=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}(\mathrm{x}-25)-30(\mathrm{x}-25)=0\\ \Rightarrow \text{\hspace{0.17em}}(\mathrm{x}-30)(\mathrm{x}-25)=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}-30=0\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}-25=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}=30\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}=25\\ \text{So, number of toys is either 25 or 30.}\end{array}$

**Q.3** Find two numbers whose sum is 27 and product is 182.

**Ans.**

$\begin{array}{l}\text{Let the numbers are x and y, then we have}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{x}+\mathrm{y}=27\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}...\left(1\right)\\ \text{and}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{xy}=182\\ \Rightarrow \mathrm{x}(27-\mathrm{x})=182\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}[\text{Putting the value of y from equation\hspace{0.17em}\hspace{0.17em}(1)]}\\ \Rightarrow 27\mathrm{x}-{\mathrm{x}}^{2}-182=0\\ \Rightarrow {\mathrm{x}}^{2}-27\mathrm{x}+182=0\\ \Rightarrow {\mathrm{x}}^{2}-13\mathrm{x}-14\mathrm{x}+182=0\\ \Rightarrow \mathrm{x}(\mathrm{x}-13)-14(\mathrm{x}-13)=0\\ \Rightarrow (\mathrm{x}-13)(\mathrm{x}-14)=0\\ \Rightarrow \mathrm{x}-13=0\text{or}\mathrm{x}-14=0\\ \Rightarrow \mathrm{x}=13\text{or}\mathrm{x}=14\\ \text{Putting}\mathrm{x}=13\text{in equation (1), we get}\mathrm{y}=14\\ \text{and}\\ \text{Putting}\mathrm{x}=14\text{in equation (1), we get}\mathrm{y}=13\\ \text{So, the two numbers are 13 and 14.}\end{array}$

**Q.4 ** Find two consecutive positive integers, sum of whose squares is 365.

**Ans.**

$\begin{array}{l}\text{Let the two consecutive positive integers are}\mathrm{x}\text{and}\mathrm{x}+1\text{and}\\ \text{sum of their square, is 365.}\\ \text{Therefore,}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\mathrm{x}}^{2}+{\left(\mathrm{x}+1\right)}^{2}=365\\ \Rightarrow \text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{x}}^{2}+{\mathrm{x}}^{2}+2\mathrm{x}+1-365=0\\ \Rightarrow 2{\mathrm{x}}^{2}+2\mathrm{x}-364=0\\ \Rightarrow {\mathrm{x}}^{2}+\mathrm{x}-182=0\\ \Rightarrow {\mathrm{x}}^{2}+14\mathrm{x}-13\mathrm{x}-182=0\\ \Rightarrow \mathrm{x}(\mathrm{x}+14)-13(\mathrm{x}+14)=0\\ \Rightarrow (\mathrm{x}+14)(\mathrm{x}-13)=0\\ \Rightarrow \mathrm{x}+14=0\text{or}\mathrm{x}-13=0\\ \Rightarrow \mathrm{x}=-14\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}or}\mathrm{x}=13\\ \text{Integers are positive. So, we take}\mathrm{x}=13\\ \text{Thus the consecutive positive integers are 13 and 14.}\end{array}$

**Q.5 ** The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

**Ans.**

$\begin{array}{l}\text{Let the base of a right triangle is}\mathrm{x}\text{cm. Then its altitude is}\\ (\mathrm{x}-7)\text{cm. It is given that hypotenuse of the triangle is 13 cm.}\\ \text{Using Pythagoras theorem, we have}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\mathrm{x}}^{2}+{\left(\mathrm{x}-7\right)}^{2}={13}^{2}\\ \Rightarrow \text{}{\mathrm{x}}^{2}+{\mathrm{x}}^{2}-14\mathrm{x}+49=169\\ \Rightarrow \text{2}{\mathrm{x}}^{2}-14\mathrm{x}+49-169=0\\ \Rightarrow \text{2}{\mathrm{x}}^{2}-14\mathrm{x}-120=0\\ \Rightarrow \text{}{\mathrm{x}}^{2}-7\mathrm{x}-60=0\\ \Rightarrow \text{}{\mathrm{x}}^{2}-12\mathrm{x}+5\mathrm{x}-60=0\\ \Rightarrow \text{}\mathrm{x}(\mathrm{x}-12)+5(\mathrm{x}-12)=0\\ \Rightarrow \text{}(\mathrm{x}-12)(\mathrm{x}+5)=0\\ \Rightarrow \text{}\mathrm{x}-12=0\text{or}\mathrm{x}+5=0\\ \Rightarrow \text{}\mathrm{x}=12\text{or}\mathrm{x}=-5\\ \text{Length can not be negative. Thus,}\\ \text{base}=\mathrm{x}=12\text{cm}\\ \text{and}\\ \text{altitude}=\mathrm{x}-7=12-7=5\text{cm.}\end{array}$

**Q.6** A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ₹ 90, find the number of articles produced and the cost of each article.

**Ans.**

$\begin{array}{l}\text{Let the number of pottery articles produced be x.}\\ \text{Cost of production of each article is 3 more than twice}\\ \text{the number of articles produced in a day.}\\ \therefore \text{Cost of production of each article}=\text{\hspace{0.17em}\hspace{0.17em}}\u20b9\text{(}2\mathrm{x}+3\text{)}\\ \text{Total cost of production of the rticles in a day}=\text{\hspace{0.17em}}\u20b99\text{0}\\ \text{Therefore,}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(}2\mathrm{x}+3\text{)}\mathrm{x}=\text{90}\\ \Rightarrow \text{\hspace{0.17em} 2}{\mathrm{x}}^{2}+3\mathrm{x}-90=0\text{}\\ \Rightarrow \text{\hspace{0.17em} 2}{\mathrm{x}}^{2}+15\mathrm{x}-12\mathrm{x}+90=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}(2\mathrm{x}+15)-6(2\mathrm{x}+15)=0\\ \Rightarrow \text{\hspace{0.17em}}(2\mathrm{x}+15)(\mathrm{x}-6)=0\\ \Rightarrow \text{\hspace{0.17em}}2\mathrm{x}+15=0\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}-6=0\\ \Rightarrow \text{\hspace{0.17em}}\mathrm{x}=-\frac{15}{2}\text{or\hspace{0.17em}\hspace{0.17em}}\mathrm{x}=6\\ \text{So, number of articles produced in a day is 6.}\\ \text{Cost of each article}=2\times 6+3=\text{\hspace{0.17em}\hspace{0.17em}}\u20b915\end{array}$

## FAQs (Frequently Asked Questions)

### 1. Where can students get access to the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2?

Students can easily download the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 from Extramarks in PDF format. All the questions of Exercise 4.2 can be solved precisely with the help of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2. Students will be able to prepare well for the upcoming Mathematics examination with the aid of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2.

### 2. How can students prepare well for the Mathematics examination?

To prepare well for the Mathematics examination, students are advised to keep practising exercises on a regular basis. Solving problems given in the sample papers helps in boosting the confidence of students. Students are encouraged to solve past years’ papers in Mathematics as well. They should refer to the revision notes from time to time. Students of Class 10 should put the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 to use to prepare for the Mathematics examination. Students can access the NCERT Solutions for all the chapters in Class 10 Mathematics from the Extramarks learning platform. The NCERT Solutions are very useful in practising questions that can appear in the question paper of Mathematics.

### 3. Is Extramarks a credible source for accessing the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2?

The NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 available on Extramarks are designed by knowledgeable instructors of Mathematics. Students can trust the credibility of the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 as they are updated from time to time. All the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 are properly reviewed periodically for any inconsistencies.

### 4. Are the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 accessible in PDF format?

Students of Class 10 can download the NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 in PDF format on the Extramarks website and mobile application. The NCERT Solutions For Class 10 Maths Chapter 4 Exercise 4.2 can also be referred to in offline mode after they are downloaded.