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Class 10 Maths Case Study Questions of Chapter 1 Real Numbers

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Case study Questions in the Class 10 Mathematics Chapter 1 are very important to solve for your exam. Class 10 Maths Chapter 1 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 1 Real Numbers

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In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Real Numbers Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths Chapter 1 Real Numbers

Case Study/Passage-Based Questions

Case Study 1: Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. (i) For what value of n, 4 n ends in 0?

Answer: (d) no value of n

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, a n is a rational number?

Answer: (c) for all n > 1

(iii) If x and yare two odd positive integers, then which of the following is true?

Answer: (d) both (a) and (b)

(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is

Answer: (a) always true

(v) If n is any odd integer, then n2 – 1 is divisible by

Answer: (d) 8

Case Study 2: HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM Based on the above information answer the following questions.

(i) If two positive integers x and y are expressible in terms of primes as x =p 2 q 3 and y=p 3 q, then which of the following is true? (a) HCF = pq 2 x LCM (b) LCM = pq 2 x HCF (c) LCM = p 2 q x HCF (d) HCF = p 2 q x LCM

Answer: (b) LCM = pq2 x HCF

ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p? (a) p is odd (b) p is even (c) p is not prime (d) both (b) and (c)

Answer: (d) both (b) and (c)

(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively. (a) 3 (b) 1 (c) 34 (d) 17

Answer: (d) 17

(iv) Find the least positive integer that on adding 1 is exactly divisible by 126 and 600. (a) 12600 (b) 12599 (C) 12601 (d) 12500

Answer: (b) 12599

(v) If A, B and C are three rational numbers such that 85C – 340A = 109, 425A + 85B = 146, then the sum of A, B and C is divisible by (a) 3 (b) 6 (c) 7 (d) 9

Answer: (a) 3

Case Study 3: Real numbers are an essential concept in mathematics that encompasses both rational and irrational numbers. Rational numbers are those that can be expressed as fractions, where the numerator and denominator are integers and the denominator is not zero. Examples of rational numbers include integers, decimals, and fractions. On the other hand, irrational numbers are those that cannot be expressed as fractions and have non-terminating and non-repeating decimal expansions. Examples of irrational numbers include √2, π (pi), and e. Real numbers are represented on the number line, which extends infinitely in both positive and negative directions. The set of real numbers is closed under addition, subtraction, multiplication, and division, making it a fundamental number system used in various mathematical operations and calculations.

Which numbers can be classified as rational numbers? a) Fractions b) Integers c) Decimals d) All of the above Answer: d) All of the above

What are rational numbers? a) Numbers that can be expressed as fractions b) Numbers that have non-terminating decimal expansions c) Numbers that extend infinitely in both positive and negative directions d) Numbers that cannot be expressed as fractions Answer: a) Numbers that can be expressed as fractions

What are examples of irrational numbers? a) √2, π (pi), e b) Integers, decimals, fractions c) Numbers with terminating decimal expansions d) Numbers that can be expressed as fractions Answer: a) √2, π (pi), e

How are real numbers represented? a) On the number line b) In complex mathematical formulas c) In algebraic equations d) In geometric figures Answer: a) On the number line

What operations are closed under the set of real numbers? a) Addition, subtraction, multiplication b) Subtraction, multiplication, division c) Addition, multiplication, division d) Addition, subtraction, multiplication, division Answer: d) Addition, subtraction, multiplication, division

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 1 Real Numbers with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Real Numbers Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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CBSE Class 10 Maths: Case Study Questions of Chapter 1 Real Numbers PDF Download

Case study Questions in the Class 10 Mathematics Chapter 1 are very important to solve for your exam. Class 10 Maths Chapter 1 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 10 Maths Chapter 1 Real Numbers

Real Numbers Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths Chapter 1 Real Numbers

Case Study/Passage-Based Questions

Question 1:

Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. (i) For what value of n, 4 n ends in 0?

Answer: (d) no value of n

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, a n is a rational number?

Answer: (c) for all n > 1

(iii) If x and yare two odd positive integers, then which of the following is true?

Answer: (d) both (a) and (b)

(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is

Answer: (a) always true

(v) If n is any odd integer, then n2 – 1 is divisible by

Answer: (d) 8

Question 2:

Answer: (b) LCM = pq2 x HCF

Answer: (d) both (b) and (c)

(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively. (a) 3 (b) 1 (c) 34 (d) 17

Answer: (d) 17

(iv) Find the least positive integer that on adding 1 is exactly divisible by 126 and 600. (a) 12600 (b) 12599 (C) 12601 (d) 12500

Answer: (b) 12599

(v) If A, B and C are three rational numbers such that 85C – 340A = 109, 425A + 85B = 146, then the sum of A, B and C is divisible by (a) 3 (b) 6 (c) 7 (d) 9

Answer: (a) 3

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Case Study Questions for Class 10 Maths Chapter 1 Real Numbers

Last modified on: 10 months ago
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Question 1:

(ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p? (a) p is odd (b) p is even (c) p is not prime (d) both (b) and (c)

(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively. (a) 3 (b) 1 (c) 34 (d) 17

(iv) Find the least positive integer which on adding 1 is exactly divisible by 126 and 600. (a) 12600 (b) 12599 (C) 12601 (d) 12500

(v) If A, B and C are three rational numbers such that 85C – 340A = 109, 425A + 85B = 146, then the sum of A, B and C is divisible by (a) 3 (b) 6 (c) 7 (d) 9

Question 2:

To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.

(i) What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B? (a) 144 (b) 128 (c) 288 (d) 272

(ii) If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is (a) 2 (b) 4 (c) 6 (d) 8

(iii) 36 can be expressed as a product of its primes as (a) (b) (c) (d)

(iv) 7 is a (a) Prime number (b) Composite number (c) Neither prime nor composite (d) None of the above

(v) If p and q are positive integers such that p = a and q= b, where a , b are prime numbers, then the LCM (p, q) is (a) ab (b) a 2 b 2 (c) a 3 b 2 (d) a 3 b 3

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CBSE 10th Standard Maths Subject Real Number Case Study Questions With Solution 2021

By QB365 on 21 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get more marks in Exams

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, a n is a rational number?

(iii) If x and yare two odd positive integers, then which of the following is true?

(iv) The statement 'One of every three consecutive positive integers is divisible by 3' is

(v) If n is any odd integer, then n2 - 1 is divisible by

Real numbers are extremely useful in everyday life. That is probably one of the main reasons we all learn how to count and add and subtract from a very young age. Real numbers help us to count and to measure out quantities of different items in various fields like retail, buying, catering, publishing etc. Every normal person uses real numbers in his daily life. After knowing the importance of real numbers, try and improve your knowledge about them by answering the following questions on real life based situations. (i) Three people go for a morning walk together from the same place. Their steps measure 80 cm, 85 cm, and 90 cm respectively. What is the minimum distance travelled when they meet at first time after starting the walk assuming that their walking speed is same?

(ii) In a school Independence Day parade, a group of 594 students need to march behind a band of 189 members. The two groups have to march in the same number of columns. What is the maximum number of columns in which they can march?

(iii) Two tankers contain 768litres and 420 litres of fuel respectively. Find the maximum capacity of the container which can measure the fuel of either tanker exactly.

(iv) The dimensions of a room are 8 m 25 cm, 6 m 75 crn and 4 m 50 cm. Find the length of the largest measuring rod which can measure the dimensions of room exactly.

(v) Pens are sold in pack of 8 and notepads are sold in pack of 12. Find the least number of pack of each type that one should buy so that there are equal number of pens and notepads

In a classroom activity on real numbers, the students have to pick a number card from a pile and frame question on it if it is not a rational number for the rest of the class. The number cards picked up by first 5 students and their questions on the numbers for the rest of the class are as shown below. Answer them. (i) Suraj picked up $\sqrt{8}$ and his question was - Which of the following is true about $\sqrt{8}$ ?

(ii) Shreya picked up 'BONUS' and her question was - Which of the following is not irrational?

(iii) Ananya picked up $\sqrt{5}$ -. $\sqrt{10}$ and her question was - $\sqrt{5}$ -. $\sqrt{10}$ _________is number.

(iv) Suman picked up $\frac{1}{\sqrt{5}}$ and her question was - $\frac{1}{\sqrt{5}}$ is __________ number.

(v) Preethi picked up $\sqrt{6}$ and her question was - Which of the following is not irrational?

Decimal form of rational numbers can be classified into two types. (i) Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form $\frac{p}{\sqrt{q}}$ where p and q are co-prime and the prime faetorisation of q is of the form 2 n ·5 m , where n, mare non-negative integers and vice-versa. (ii) Let x = $\frac{p}{\sqrt{q}}$ be a rational number, such that the prime faetorisation of q is not of the form 2 n 5 m , where n and m are non-negative integers. Then x has a non-terminating repeating decimal expansion. (i) Which of the following rational numbers have a terminating decimal expansion?

(ii) 23/(2 3 x 5 2 ) =

(iii) 441/(2 2 x 5 7 x 7 2 ) is a_________decimal.

(iv) For which of the following value(s) of p, 251/(2 3 x p 2 ) is a non-terminating recurring decimal?

(v) 241/(2 5 x 5 3 ) is a _________decimal.

HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM. Based on the above information answer the following questions. (i) If two positive integers x and yare expressible in terms of primes as x = p2q3 and y = p3 q, then which of the following is true?

(ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p?

(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively.

(iv) Find the least positive integer which on adding 1 is exactly divisible by 126 and 600.

(v) If A, Band C are three rational numbers such that 85C - 340A :::109, 425A + 85B = 146, then the sum of A, B and C is divisible by

*****************************************

Cbse 10th standard maths subject real number case study questions with solution 2021 answer keys.

(i) (d) : For a number to end in zero it must be divisible by 5, but 4 n = 22 n is never divisible by 5. So, 4 n never ends in zero for any value of n. (ii) (c) : We know that product of two rational numbers is also a rational number. So, a 2 = a x a = rational number a 3 = a 2 x a = rational number a 4 = a 3 x a = rational number ................................................ ............................................... a n = a n-1 x a = rational number. (iii) (d): Let x = 2m + 1 and y = 2k + 1 Then x 2 + y 2 = (2m + 1) 2 + (2k + 1) 2 = 4m 2 + 4m + 1 + 4k 2 + 4k + 1 = 4(m 2 + k 2 + m + k) + 2 So, it is even but not divisible by 4. (iv) (a): Let three consecutive positive integers be n, n + 1 and n + 2. We know that when a number is divided by 3, the remainder obtained is either 0 or 1 or 2. So, n = 3p or 3p + lor 3p + 2, where p is some integer. If n = 3p, then n is divisible by 3. If n = 3p + 1, then n + 2 = 3p + 1 + 2 = 3p + 3 = 3(p + 1) is divisible by 3. If n = 3p + 2, then n + 1 = 3p + 2 + 1 = 3p + 3 = 3(p + 1) is divisible by 3. So, we can say that one of the numbers among n, n + 1 and n + 2 Wi always divisible by 3. (v) (d): Any odd number is of the form of (2k +1), where k is any integer. So, n 2 - 1 = (2k + 1)2 -1 = 4k 2 + 4k For k = 1, 4k 2 + 4k = 8, which is divisible by 8. Similarly, for k = 2, 4k 2 + 4k = 24, which is divisible by 8. And for k = 3, 4k 2 + 4k = 48, which is also divisible by 8. So, 4k 2 + 4k is divisible by 8 for all integers k, i.e., n 2 - 1 is divisible by 8 for all odd values of n.

(i) (b): Here 80 = 2 4 x 5, 85 = 17 x 5 and 90 = 2 x 3 2 x 5 L.C.M of 80, 85 and 90 = 2 4 x 3 x 3 x 5 x 17 = 12240 Hence, the minimum distance each should walk when they at first time is 12240 cm. (ii) (c): Here 594 = 2 x 3 3 x 11 and 189 = 3 3 x 7 HCF of 594 and 189 = 3 3 = 27 Hence, the maximum number of columns in which they can march is 27. (iii) (c) : Here 768 = 2 8 x 3 and 420 = 2 2 x 3 x 5 x 7 HCF of 768 and 420 = 2 2 x 3 = 12 So, the container which can measure fuel of either tanker exactly must be of 12litres. (iv) (b): Here, Length = 825 ern, Breadth = 675 cm and Height = 450 cm Also, 825 = 5 x 5 x 3 x 11 , 675 = 5 x 5 x 3 x 3 x 3 and 450 = 2 x 3 x 3 x 5 x 5 HCF = 5 x 5 x 3 = 75 Therefore, the length of the longest rod which can measure the three dimensions of the room exactly is 75cm. (v) (a): LCM of 8 and 12 is 24. $\therefore $ The least number of pack of pens = 24/8 = 3 $\therefore $ The least number of pack of note pads = 24/12 = 2

(i) (b): Here $\sqrt{8}$ = 2 $\sqrt{2}$ = product of rational and irrational numbers = irrational number (ii) (c): Here, $\sqrt{9}$ = 3 So, 2 + 2 $\sqrt{9}$ = 2 + 6 = 8 , which is not irrational. (iii) (b): Here. $\sqrt{15}$ and $\sqrt{10}$ are both irrational and difference of two irrational numbers is also irrational. (iv) (c): As $\sqrt{5}$ is irrational, so its reciprocal is also irrational. (v) (d): We know that $\sqrt{6}$ is irrational. So, 15 + 3. $\sqrt{6}$ is irrational. Similarly, $\sqrt{24}$ - 9 = 2. $\sqrt{6}$ - 9 is irrational. And 5 $\sqrt{150}$ = 5 x 5. $\sqrt{6}$ = 25 $\sqrt{6}$ is irrational.

(i) (c): Here, the simplest form of given options are 125/441 = 5 3 /(3 2 x 7 2 ), 77/210 = 11/(2 x 3 x 5), 15/1600 = 3/(2 6 x 5) Out of all the given options, the denominator of option (c) alone has only 2 and 5 as factors. So, it is a terminating decimal. (ii) (b): 23/(2 3 x 5 2 ) = 23/200 = 0.115 (iii) (a): 441/(2 2 x 5 7 x 7 2 ) = 9/(2 2 x 5 7 ), which is a terminating decimal. (iv) (d): The fraction form of a non-terminating recurring decimal will have at least one prime number other than 2 and 5 as its factors in denominator. So, p can take either of 3, 7 or 15. (v) (a): Here denominator has only two prime factors i.e., 2 and 5 and hence it is a terminating decimal.

(i) (b): LCM of x and y = p 3 q 3 and HCF of x and y = p 2 q Also, LCM = pq 2 x HCF. (ii) (d): Number of marbles = 5m + 2 or 6n + 2. Thus, number of marbles, p = (multiple of 5 x 6) + 2 = 30k + 2 = 2(15k + 1) = which is an even number but not prime (iii) (d): Here, required numbers = HCF (398 - 7, 436 - 11,542 -15) = HCF (391,425,527) = 17 (iv) (b): LCMof126and600 = 2 x 3 x 21 x 100= 12600 The least positive integer which on adding 1 is exactly divisible by 126 and 600 = 12600 - 1 = 12599 (v) (a): Here 8SC - 340A = 109 and 425A + 85B = 146 On adding them, we get 85A + 85B + 85C = 255 ~ A + B + C = 3, which is divisible by 3.

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Case Study Questions Class 10 Maths with Solutions PDF Download

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Case Study on Real Numbers Class 10 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Real Numbers Class 10 Maths can use this page to download the PDF file.

The case study questions on Real Numbers are based on the CBSE Class 10 Maths Syllabus, and therefore, referring to the Real Numbers case study questions enable students to gain the appropriate knowledge and prepare better for the Class 10 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Real Numbers Class 10 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Real Numbers, therefore, they prepared a set of solutions along with the case study questions on Real Numbers.

The case study on Real Numbers Class 10 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Real Numbers case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Real Numbers Case Study Questions on Class 10 Maths?

There are three major reasons why one should solve Real Numbers case study questions on Class 10 Maths - all those major reasons are discussed below:

To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 10 Maths students, therefore, it is important to solve Real Numbers Case study questions as it will help better prepare for the Class 10 board exam preparation.
Develop Problem-Solving Skills: Class 10 Maths Real Numbers case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 10 students develop their problem-solving skills, which are essential for success in any profession rather than Class 10 board exam preparation.
Understand Real-Life Applications: Several Real Numbers Class 10 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Real Numbers as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Real Numbers?

Students can choose their own way to answer Case Study on Real Numbers Class 10 Maths, however, we believe following these three steps would help a lot in answering Class 10 Maths Real Numbers Case Study questions.

Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Real Numbers questions quickly.
Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Real Numbers Class 10 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 10 Real Numbers?

A few essential things to know to solve Case Study Questions on Class 10 Real Numbers are -

Basic Formulas of Real Numbers: One of the most important things to know to solve Case Study Questions on Class 10 Real Numbers is to learn about the basic formulas or revise them before solving the case-based questions on Real Numbers.
To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 10 Maths Real Numbers case study questions.
Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

Where to Find Case Study on Real Numbers Class 10 Maths?

Use Selfstudys.com to find Case Study on Real Numbers Class 10 Maths. For ease, here is a step-wise procedure to download the Real Numbers Case Study for Class 10 Maths in PDF for free of cost.

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Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

Real Numbers Case Study Question
Polynomials Case Study Question
Pair of Linear Equations in Two Variables Case Study Question
Quadratic Equations Case Study Question
Arithmetic Progressions Case Study Question
Triangles Case Study Question
Coordinate Geometry Case Study Question
Introduction to Trigonometry Case Study Question
Some Applications of Trigonometry Case Study Question
Circles Case Study Question
Area Related to Circles Case Study Question
Surface Areas and Volumes Case Study Question
Statistics Case Study Question
Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

Find the production in the 1 st year.
Find the production in the 12 th year.
Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

Find the distance between Lucknow (L) to Bhuj(B).
If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

Find the distance PA.
Find the distance PB
Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

What is the length of the line segment joining points B and F?
The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

If the first circular row has 30 seats, how many seats will be there in the 10th row?
For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

$ch 1 case study class 10 maths$

Draw a neat labelled figure to show the above situation diagrammatically.

$ch 1 case study class 10 maths$

What is the speed of the plane in km/hr.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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CBSE Case Study Questions for Class 10 Maths Real Numbers Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Real Numbers in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 10 Maths Real Numbers PDF

Mcq set 1 -, mcq set 2 -, checkout our case study questions for other chapters.

Chapter 2: Polynomials Case Study Questions
Chapter 3: Pair of Linear Equations in Two Variables Case Study Questions
Chapter 4: Quadratic Equation Case Study Questions
Chapter 5: Arithmetic Progressions Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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Class 10 Maths Chapter 1 MCQ

Class 10 Maths Chapter 1 Real Numbers MCQ (Multiple Choice Objective Questions) with answers and complete explanation case study type questions for the first term examination 2024-25. The answers of 10th Maths Chapter 1 MCQ are given with explanation, so that students can understand easily. This page of Class 10 Maths MCQ contains the questions released by CBSE as well as extra questions for practice.

Case Study – 1

What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?

Factors of 32 = 2 х 2 х 2 х 2 х 2 = 2⁵ Factors of 36 = 2 х 2 х 3 х 3 = 2² х 3² LCM of 32 and 36 = 2⁵ х 3² = 32 х 9 = 288 Hence, the correct option is (C).

View Answer

If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32, 36) is

Factors of 32 = 2 х 2 х 2 х 2 х 2 = 2⁵ Factors of 36 = 2 х 2 х 3 х 3 = 2² х 3² LCM of 32 and 36 = 2⁵ х 3² = 32 х 9 = 288 HCF (32, 36) = (32 х 36) / LCM = (32 х 36) / 288 = 4 Hence, the correct option is (B).

36 can be expressed as a product of its primes as

Factors of 36 = 2 х 2 х 3 х 3 = 2² х 3² Hence, the correct option is (A).

7 х 11 х 13 х 15 + 15 is a

7 х 11 х 13 х 15 + 15 = 15 х (7 х 11 х 13 + 1) = 15 х (Integer) It has more than two factor. So, it is a composite number. Hence, the correct option is (B).

If p and q are positive integers such that p = ab² and q = a²b, where a, b are prime numbers, then the LCM (p, q) is

p = ab² q = a²b LCM = highest powers of common factors of ab² and a²b = a²b² Hence, the correct option is (B).

Case Study – 2

A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English, and Mathematics are 60, 84, and 108 respectively.

Class 10 Maths Chapter 1 Real Numbers MCQ

In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are

Factors of 60 = 2 х 2 х 3 х 5 = 2² х 3 х 5 Factors of 84 = 2 х 2 х 3 х 7 = 2² х 3 х 7 Factors of 108 = 2 х 2 х 3 х 3 х 3 = 2² х 3³ HCF of 60, 84, and 108 = 2² х 3 = 12 Hence, the correct option is (B).

What is the minimum number of rooms required during the event?

Factors of 60 = 2 х 2 х 3 х 5 = 2² х 3 х 5 Factors of 84 = 2 х 2 х 3 х 7 = 2² х 3 х 7 Factors of 108 = 2 х 2 х 3 х 3 х 3 = 2² х 3³ HCF of 60, 84, and 108 = 2² х 3 = 12 Number of room required for Hindi participants = 60/12 = 5 Number of room required for English participants = 84/12 = 7 Number of room required for Mathematics participants = 108/12 = 9 Total number of room required = 5 + 7 + 9 = 21 Hence, the correct option is (D).

The LCM of 60, 84, and 108 is

Factors of 60 = 2 х 2 х 3 х 5 = 2² х 3 х 5 Factors of 84 = 2 х 2 х 3 х 7 = 2² х 3 х 7 Factors of 108 = 2 х 2 х 3 х 3 х 3 = 2² х 3³ LCM of 60, 84, and 108 = 2² х 3³ х 5 х 7 = 4 х 27 х 5 х 7 = 3780 Hence, the correct option is (A).

The product of HCF and LCM of 60, 84, and 108 is

Factors of 60 = 2 х 2 х 3 х 5 = 2² х 3 х 5 Factors of 84 = 2 х 2 х 3 х 7 = 2² х 3 х 7 Factors of 108 = 2 х 2 х 3 х 3 х 3 = 2² х 3³ HCF of 60, 84, and 108 = 2² х 3 = 12 LCM of 60, 84, and 108 = 2² х 3³ х 5 х 7 = 4 х 27 х 5 х 7 = 3780 Product of HCF and LCM of 60, 84, and 108 = 12 х 3780 = 45360 Hence, the correct option is (D).

108 can be expressed as a product of its primes as

Factors of 108 = 2 х 2 х 3 х 3 х 3 = 2² х 3³ Hence, the correct option is (D).

Case Study – 3

Rohit Singh is a worker in a petrol pump. He along with the other co-workers, use to transfer petrol from tanker to storage. On Monday, there were two tankers containing 850 litres and 680 litres of petrol respectively.

Case study based MCQ for 10th Maths chapter 1

What is the maximum capacity of a container which can measure the petrol of either tanker in exact number of time?

The maximum capacity of the container is the HCF of 850 and 680. Factors of 850 = 2 х 5 х 5 х 17 = 2 х 5² х 17 Factors of 680 = 2 х 2 х 2 х 5 х 17 = 2³ х 5 х 17 HCF of 850 and 680 = 2 х 5 х 17 = 170 Hence, the correct option is (C).

If the product of two positive integers is equal to the product of their HCF and LCM is true then, the LCM (850, 680) is

Factors of 850 = 2 х 5 х 5 х 17 = 2 х 5² х 17 Factors of 680 = 2 х 2 х 2 х 5 х 17 = 2³ х 5 х 17 HCF of 850 and 680 = 2 х 5 х 17 = 170 LCM (850, 680) = (850 х 680) / HCF = (850 х 680) / 170 = 3400 Hence, the correct option is (D).

680 can be expressed as a product of its primes as

Factors of 680 = 2 х 2 х 2 х 5 х 17 = 2³ х 5 х 17 Hence, the correct option is (C).

2 х 3 х 5 х 11 х 17 + 11 is a

2 х 3 х 5 х 11 х 17 + 11 = 11 х (2 х 3 х 5 х 17 + 1) = 11 х (Integer) It has more than two factor. So, it is a composite number. Hence, the correct option is (B).

If p and q are positive integers such that p = a³b² and q = a²b³, where a, b are prime numbers, then the LCM (p, q) is

p = a³b² q = a²b³ LCM = highest powers of common factors of a³b² and a²b³ = a³b³ Hence, the correct option is (B).

Case Study – 4

A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience. Observe the following factor tree and answer the following:

Class 10 Maths Case study MCQ Factor tree

What will be the value of x?

X = 5 х 2783 = 13915 Hence, the correct option is (B).

What will be the value of y?

Y = 2783/253 = 11 Hence, the correct option is (C).

What will be the value of z?

Z = 253/11 = 23 Hence, the correct option is (B).

According to Fundamental Theorem of Arithmetic 13915 is a

Because 13915 can be written into the product of primes. 13915 = 5 х 11 х 11 х 23 = 5 х 11² х 23 Hence, the correct option is (A).

The prime factorisation of 13915 is

13915 = 5 х 11 х 11 х 23 = 5 х 11² х 23 Hence, the correct option is (C).

Case Study – 5

We all know that morning walk is good for health. In a morning walk, three friends Anjali, Sofia, and Angelina step of together. There steps measure 80 cm, 85 cm, and 90 cm. respectively.

What is the minimum distance each should walk so that they can cover the distance in complete steps?

The minimum distance covered by each in complete steps must be the LCM of 80 cm, 85 cm, and 90 cm. Factors of 80 = 2 х 2 х 2 х 2 х 5 = 2⁴ х 5 Factors of 85 = 5 х 17 Factors of 90 = 2 х 3 х 3 х 5 = 2 х 3² х 5 LCM of 80, 85, and 90 = 2² х 3² х 5 х 17 = 12240 Now, 12240 cm = 122 m 40 cm Hence, the correct option is (B).

What is the minimum number of steps taken by any of the three friends, when they meet again?

Factors of 80 = 2 х 2 х 2 х 2 х 5 = 2⁴ х 5 Factors of 85 = 5 х 17 Factors of 90 = 2 х 3 х 3 х 5 = 2 х 3² х 5 LCM of 80, 85, and 90 = 2² х 3² х 5 х 17 = 12240 The step size of Angelina is maximum among these three. So, she will take minimum number of steps to cover the same distance. Number of steps = 12240/90 = 136 Hence, the correct option is (D).

The HCF of 80, 85, and 90 is

Factors of 80 = 2 х 2 х 2 х 2 х 5 = 2⁴ х 5 Factors of 85 = 5 х 17 Factors of 90 = 2 х 3 х 3 х 5 = 2 х 3² х 5 HCF of 80, 85, and 90 = 5 Hence, the correct option is (A).

The product of HCF and LCM of 80, 85, and 90 is

Factors of 80 = 2 х 2 х 2 х 2 х 5 = 2⁴ х 5 Factors of 85 = 5 х 17 Factors of 90 = 2 х 3 х 3 х 5 = 2 х 3² х 5 HCF of 80, 85, and 90 = 5 LCM of 80, 85, and 90 = 2² х 3² х 5 х 17 = 12240 Therefore, the product of HCF and LCM of 80, 85, and 90 = 12240 х 5 = 61200 Hence, the correct option is (C).

90 can be expressed as a product of its primes as

Factors of 108 = 2 х 3 х 3 х 5 = 2 х 3² х 5 Hence, the correct option is (D).

Class 10 Maths Chapter 1 MCQ are given below. There are total of 5 questions with four choices. Only one option is correct and the explanation of correct answer is given below the questions. Every time the students will get a new set of five questions with different levels of questions. For any further discussion, please join the Discussion Forum.

Euclid’s division lemma represents the pair of integers 25 & 7.

Because 7 goes into 25 thrice and leaves remainder 4, where 0 < 4 <7.

m^2 -1 is divisible by 8, if m is

Square of an odd integer will be always odd and m^2 – 1 will be even and will be divisible by 8 for an odd integer.

If the HCF of 408 and 1032 is expressible in form 1032 × 2 + 408 × P, then value of p is

HCF of 408 and 1032 is 24. So, 1032 × 2 + 408 × (-5) = 2064 – 2040 = 24

When a number is divided by 7, its remainder is always

According to Euclid’s Division Lemma, If a = 7q + r, then r should be less than 7. In other words, remainder should always be less than divisor.

If HCF (16, y) = 8 and LCM (16, y) = 48, then the value of y is

We know that: HCF × LCM = 16 × y So, 8 × 48 = 16 × y y = 8 × 48/16 = 24

What are the important topics in Class 10 Maths Chapter 1 MCQ?

Euclid’ division lemma and the Fundamental Theorem of Arithmetic are the two main topics in 10th Maths chapter 1 Real Numbers. Now questions are designed on the basis of case study. So practice MCQ questions based on daily life events which will be more helpful in CBSE exams.

In which of the four exercise of 10th Maths Chapter 1, are Case Study MCQ asked?

There are questions from each exercise of Chapter 1 of 10th Maths, but most of the MCQs can be formed from Exercise 1.4. Now CBSE introduces the questions based on CASE STUDY which may be asked from any section of class 10 Maths chapter 1.

How many MCQ are required to be perfect in Chapter 1 of Class 10 Maths?

If your concepts are clear, the MCQs provide more confidence in that section. More practice means more to retain and better understanding with the concepts of topics.

How many questions from Chapter 1 of Class 10 Maths asked in CBSE Board?

There is no classification of number of questions from the different chapters. There may be one, more than one or none from Chapter 1 Real Numbers of Class 10 Maths.

We are adding more questions frequently, so that students can have a good practice of Class 10 Maths Chapters. If you have suggestion or feedback about this page or website improvement, you are welcome. Important questions with solutions and answers will be added very soon for each chapter of class 10 Maths.

Download NCERT Books and Offline Apps 2024-25 based on new CBSE Syllabus. Ask your doubts related to NIOS or CBSE Board and share your knowledge with your friends and other users through Discussion Forum.

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Chapter 1 Class 10 Real Numbers

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Updated for NCERT 2023-2024 Book.

Answers to all exercise questions and examples are solved for Chapter 1 Class 10 Real numbers. Solutions of all these NCERT Questions are explained in a step-by-step easy to understand manner

In this chapter, we will study

What is a Real Number
What is Euclid's Division Lemma , and
How to find HCF (Highest Common Factor) using Euclid's Division Algorithm
Then, we study Fundamental Theorem of Arithmetic, which is basically Prime Factorisation
And find HCF and LCM using Prime Factorisation
We also use the formula of HCF and LCM of two numbers a and b HCF × LCM = a × b
Then, we see what is an Irrational Number
and Prove numbers irrational (Like Prove √ 2, √ 3 irrational)
We revise our concepts about Decimal Expansion (Terminating, Non-Terminating Repeating, Non Terminating Non Repeating)
And find out Decimal Expansion of numbers without performing long division

Click on an NCERT Exercise below to get started.

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Concept wise.

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Math Article
Real Numbers For Class 10

Real Numbers Class 10 Notes: Chapter 1

Cbse real numbers class 10 notes:- download pdf here, class 10 maths chapter 1 real number notes.

CBSE Class 10 Maths Chapter 1 Real Numbers Notes are provided here in detail. As we all know, any number, excluding complex numbers, is a real number. Positive and negative integers, irrational numbers, and fractions are all examples of real numbers. To put it another way, any number found in the real world is a real number. Numbers can be found all around us. Natural numbers are being used to count objects, integers are used to measure temperature, rational numbers are used to represent fractions, irrational numbers are used to calculate the square root of a number, etc. These various types of numbers form a collection of real numbers. Here, we are going to learn what a real number is, Euclid’s division algorithm, the fundamental theorem of arithmetic, methods of finding LCM and HCF and the complete explanation of rational and irrational numbers with examples.

Real Numbers

Positive integers, negative integers, irrational numbers, and fractions are all examples of real numbers. In other words, we can say that any number is a real number, except for complex numbers. Examples of real numbers include -1, ½, 1.75, √2, and so on. In general,

Real numbers constitute the union of all rational and irrational numbers.
Any real number can be plotted on the number line.

To know more about real numbers, visit here .

Students can refer to the short notes and MCQ questions along with a separate solution pdf of this chapter for quick revision from the links below.

Real Numbers Short Notes
Real Numbers MCQ Practice Questions
Real Numbers MCQ Practice Solutions

Euclid’s Division Lemma

Euclid’s Division Lemma states that given two integers a and b , there exists a unique pair of integers q and r such that a = b × q + r a n d 0 ≤ r < b .
This lemma is essentially equivalent to : dividend = divisor × quotient + remainder
In other words, for a given pair of dividend and divisor, the quotient and remainder obtained are going to be unique.

For more information on Euclid’s Division Lemma, watch the below video

To know more about Euclid’s Division Lemma, visit here .

Euclid’s Division Algorithm

Euclid’s Division Algorithm is a method used to find the H.C.F of two numbers, say a and b where a> b.
We apply Euclid’s Division Lemma to find two integers q and r such that a = b × q + r a n d 0 ≤ r < b .
If r = 0, the H.C.F is b; else, we apply Euclid’s division Lemma to b (the divisor) and r (the remainder) to get another pair of quotient and remainder.
The above method is repeated until a remainder of zero is obtained. The divisor in that step is the H.C.F. of the given set of numbers.

For more information on Euclid’s Division Algorithm, watch the below video

The Fundamental Theorem of Arithmetic

Prime Factorisation

Prime Factorisation is the method of expressing a natural number as a product of prime numbers.
Example: 36 = 2 × 2 × 3 × 3 is the prime factorisation of 36.

Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic states that the prime factorisation for a given number is unique if the arrangement of the prime factors is ignored.
Example: 36 = 2 × 2 × 3 × 3 OR, 36 = 2 × 3 × 2 × 3
Therefore, 36 is represented as a product of prime factors (Two 2s and two 3s) ignoring the arrangement of the factors.

To know more about the Fundamental Theorem of Arithmetic, visit here .

Method of Finding LCM

As we know, the smallest of the common multiples of two or more numbers is called the lowest common multiple (LCM). Example: To find the Least Common Multiple ( L.C.M ) of 36 and 56,

36 = 2 × 2 × 3 × 3 56 = 2 × 2 × 2 × 7
The common prime factors are 2 × 2
The uncommon prime factors are 3 × 3 for 36 and 2 × 7 for 56.
LCM of 36 and 56 = 2 × 2 × 3 × 3 × 2 × 7 which is 504

To know more about LCM, visit here .

Method of Finding HCF

We know that the greatest number that divides each of the given numbers without leaving any remainder is the highest common factor (HCF) of two or more given numbers. H.C.F can be found using two methods – Prime factorisation and Euclid’s division algorithm.

Given two numbers, we express both of them as products of their respective prime factors. Then, we select the prime factors that are common to both the numbers
Example – To find the H.C.F of 20 and 24 20 = 2 × 2 × 5 and 24 = 2 × 2 × 2 × 3
The factor common to 20 and 24 is 2 × 2 , which is 4, which in turn is the H.C.F of 20 and 24.
It is the repeated use of Euclid’s division lemma to find the H.C.F of two numbers.

The required HCF is 6 .

To know more about HCF, visit here .

For more information on HCF and LCM, watch the below video

To know more about the Properties of HCF and LCM, visit here .

Product of Two Numbers = HCF X LCM of the Two Numbers

For any two positive integers a and b, a × b = H . C . F × L . C . M .
Example – For 36 and 56, the H.C.F is 4 and the L.C.M is 504 36 × 56 = 2016 4 × 504 = 2016 Thus, 36 × 56 = 4 × 504
Let us consider another example: For 5 and 6, the H.C.F is 1 and the L.C.M is 30 5 × 6 = 30 1 × 30 =30 Thus, 5 × 6 = 1 × 30
The above relationship, however, doesn’t hold true for 3 or more numbers

To know the Relationship between LCM and HCF, visit here .

Applications of HCF & LCM in Real-World Problems

L.C.M can be used to find the points of common occurrence. For example,ringing of bells that ring with different frequencies, the time at which two persons running at different speeds meet, and so on.

For more information on Applications Of LCM, watch the below video

Revisiting Irrational Numbers

Irrational numbers.

Any number that cannot be expressed in the form of p/q (where p and q are integers and q ≠ 0 .) is an irrational number. Examples √2 , π , e and so on.

To know more about Irrational Numbers, visit here .

Number theory: Interesting results

If a number p (a prime number) divides a 2 , then p divides a. Example: 3 divides 6 2 i.e 36, which implies that 3 divides 6.
The sum or difference of a rational and an irrational number is irrational
The product and quotient of a non-zero rational and irrational number are irrational.
√p is irrational when ‘p’ is a prime. For example, 7 is a prime number, and √7 is irrational. The above statement can be proved by the method of “Proof by contradiction”.

To know more about Number theory, visit here .

Proof by Contradiction

In the method of contradiction, to check whether a statement is TRUE (i) We assume that the given statement is TRUE. (ii) We arrive at some result which contradicts our assumption, thereby proving the contrary. Eg: Prove that √7 is irrational. Assumption: √7 is rational. Since it is rational √7 can be expressed as √7 = a/b , where a and b are co-prime Integers, b ≠ 0. On squaring, a 2 /b 2 = 7 ⇒ a 2 = 7 b 2 . Hence, 7 divides a. Then, there exists a number c such that a=7c. Then, a 2 = 49 c 2 . Hence, 7 b 2 = 49 c 2 or b 2 = 7 c 2 . Hence 7 divides b. Since 7 is a common factor for both a and b, it contradicts our assumption that a and b are coprime integers. Hence, our initial assumption that √7 is rational is wrong. Therefore, √7 is irrational.

Revisiting Rational Numbers and Their Decimal Expansions

Rational numbers.

Rational numbers are numbers that can be written in the form p/q, where p and q are integers and q ≠ 0 . Examples -1/2 , 4/5, 1 , 0 , − 3 and so on.

To know more about Rational Numbers, visit here .

Terminating and Non-Terminating Decimals

Terminating decimals are decimals that end at a certain point. Example: 0.2, 2.56 and so on. Non-terminating decimals are decimals where the digits after the decimal point don’t terminate. Example: 0.333333….., 0.13135235343… Non-terminating decimals can be : a) Recurring – a part of the decimal repeats indefinitely (0 . 142857 142857 …. ) b) Non-recurring – no part of the decimal repeats indefinitely. Example: π = 3.1415926535…

To know more about terminating and non-terminating decimals, click here .

Check if a given rational number is terminating or not

If a/b is a rational number, then its decimal expansion would terminate if both of the following conditions are satisfied : a) The H.C.F of a and b is 1. b) b can be expressed as a prime factorisation of 2 and 5 i.e b = 2 m × 5 n where either m or n, or both can = 0. If the prime factorisation of b contains any number other than 2 or 5, then the decimal expansion of that number will be recurring

1/40 = 0.025 is a terminating decimal, as the H.C.F of 1 and 40 is 1, and the denominator (40) can be expressed as 2 3 × 5 1 .

3/7 = 0.428571 is a recurring decimal as the H.C.F of 3 and 7 is 1 and the denominator (7) is equal to 7 1

Real Numbers for Class 10 Solved Examples

Find the largest number that divides 70 and 125 leaving the remainder 5 and 8 respectively.

First, subtract the remainder from the number.

(i.e) 70-5 = 65

125-8 = 117.

Thus, we need to find the largest number that divides 65 and 117 and leaves the remainder 0.

To find the largest number, take the HCF of 65 and 117.

Finding HCF of 65 and 117.

65 = 5×13

117 = 3×3×13.

Hence, HCF (65, 117) = 13.

Therefore, the largest number that divides 70 and 125 leaving the remainder 5 and 8 respectively is 13.

Find the LCM of 306 and 657, given that HCF (306, 657) = 9.

Given that, HCF (306, 657) = 9.

We know that HCF × LCM = Product of Numbers

Hence, 9×LCM = 306×657

9×LCM = 201042

LCM = 201042/9

LCM = 22338.

Therefore, LCM of 306 and 657 is 22338.

Prove that 1/√2 is an irrational number.

To prove 1/√2 is an irrational number.

Now, let us take the opposite assumption.

(i.e) Take 1/√2 is a rational number.

We know that rational numbers are the numbers that can be written in the form of p/q, where q is not equal to 0. (p and q are two co-prime numbers)

Hence, 1/√2 = p/q.

Now, simplify the above equation by multiplying √2 on both sides.

1 = (p√2)/q

q = p√2

Hence, we get q/p = √2.

Here, p and q are integers, and hence q/p is a rational number.

But, √2 is an irrational number.

Hence, our assumption is wrong.

Therefore, 1/√2 is an irrational number.

Hence, proved.

Frequently Asked Questions on Class 10 Real Numbers

What is euclid’s division algorithm, what does real numbers for class 10 explains, is 10i a real number, what does the fundamental theory of arithmetic explain.

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CBSE Class 10 Study Material

CBSE Class 10 Maths Case Study Questions for Chapter 2 - Polynomials (Published by CBSE)

Check the case study questions published by cbse for class 10 maths chapter 2 - polynomials. these questions are important for the preparation of cbse class 10 maths exam 2021-22..

CBSE Class 10 Maths paper in Board Exam 2022 will have some questions based on the case study. These questions are entirely new for the class 10 students. Therefore, the board has released a question bank to help the students get familiarised with the case study questions. We have provided here the case study questions for CBSE Class 10 Maths Chapter 2 - Polynomials. All the questions have sub-questions of MCQ type. You can find the answer (correct option) written against each question. Practice all the case study based questions right after you finish with the chapter - Polynomials. This will help you prepare for your Maths exam easily and effectively.

Case Study Questions for Class 10 Maths Chapter 2 - Polynomials

CASE STUDY 1:

The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

1. In the standard form of quadratic polynomial, ax 2 + bx + c, a, b and c are

a) All are Polynomials.

b) All are rational numbers.

c) ‘a’ is a non zero real number and b and c are any Polynomials.

d) All are integers.

Answers: c) ‘a’ is a non zero real number and b and c are any Polynomials.

2. If the roots of the quadratic polynomial are equal, where the discriminant D = b 2 – 4ac, then

a) D > 0

b) D < 0

c) D ≥ 0

Answers: d) D = 0

3. If α and 1/α are the zeroes of the quadratic polynomial 2x2 – x + 8k, then k is

c) –1/4

Answers: b) 1/4

4. The graph of x 2 +1 = 0

a) Intersects x‐axis at two distinct points.

b)Touches x‐axis at a point.

c) Neither touches nor intersects x‐axis.

d)Either touches or intersects x‐ axis.

Answers: c) Neither touches nor intersects x‐axis.

5. If the sum of the roots is –p and product of the roots is –1/p, then the quadratic polynomial is

a) k(–px 2 + x/p + 1)

b) k(px 2 – x/p – 1)

c) k(x 2 + px – 1/p)

d) k(x 2 – px + 1/p)

Answers: c) k(x 2 + px – 1/p)

CASE STUDY 2:

An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

1. The shape of the poses shown is

d) Parabola

Answer: d) Parabola

2. The graph of parabola opens downwards, if _______

a) a ≥ 0

c) a < 0

d) a > 0

Answer: c) a < 0

3. In the graph, how many zeroes are there for the polynomial?

Answer: c) 2

4. The two zeroes in the above shown graph are

Answer: b) -2, 4

CASE STUDY 3:

Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.

1. The shape of the path traced shown is

2. The graph of parabola opens upwards, if _______

b) a < 0

c) a > 0

d) a ≥ 0

Answer: c) a > 0

3. Observe the following graph and answer

In the above graph, how many zeroes are there for the polynomial?

Answer: d) 3

4. The three zeroes in the above shown graph are

b) -2, 3, 1

c) -3, -1, 2

d) -2, -3, -1

Answer: c) -3, -1, 2

5. What will be the expression of the polynomial?

a) x 3 + 2x 2 – 5x – 6

b) x 3 + 2x 2 – 5x + 6

c) x 3 + 2x 2 + 5x – 6

d) x 3 + 2x 2 + 5x + 6

Answer: a) x 3 + 2x 2 – 5x – 6

Also Check:

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CBSE Class 10 Maths Case Study Questions for Class 10 Maths Chapter 1
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Class 10 Maths Chapter 1 MCQ

Case Study – 1

What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?

If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32, 36) is

36 can be expressed as a product of its primes as

7 х 11 х 13 х 15 + 15 is a

If p and q are positive integers such that p = ab² and q = a²b, where a, b are prime numbers, then the LCM (p, q) is

Case Study – 2

In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are

What is the minimum number of rooms required during the event?

The LCM of 60, 84, and 108 is

The product of HCF and LCM of 60, 84, and 108 is

108 can be expressed as a product of its primes as

Case Study – 3

What is the maximum capacity of a container which can measure the petrol of either tanker in exact number of time?

If the product of two positive integers is equal to the product of their HCF and LCM is true then, the LCM (850, 680) is

680 can be expressed as a product of its primes as

2 х 3 х 5 х 11 х 17 + 11 is a

If p and q are positive integers such that p = a³b² and q = a²b³, where a, b are prime numbers, then the LCM (p, q) is