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case study questions real numbers

case study questions real numbers

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CBSE Class 10 Maths Case Study Questions for Class 10 Maths Chapter 1 - Real Numbers (Published by CBSE)

CBSE Class 10 Maths Cased Study Question Bank for Chapter 1 - Real Numbers is available here. This question bank is very useful to prepare for the Class 10 Maths Exam 2021-2022.

case study questions real numbers

The Central Board of Secondary Education has introduced the case study questions in class 10 exam pattern 2021-2022. The CBSE Class 10 questions papers of Board Exam 2022 will have questions based on case study. Therefore, students should get familiarised with these questions to do well in their board exam.

We have provided here case study questions for Class 10 Maths Chapter 1 - Real Numbers. These questions have been published by the CBSE board itself. Students must solve all these questions at the same time they finish with the chapter - Real numbers. 

Case Study Questions for Class 10 Maths Chapter 1 - Real Numbers

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.

case study questions real numbers

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?

Answer: c) 288

2. 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

Answer: b) 4

3. 36 can be expressed as a product of its primes as

a) 2 2 × 3 2

b) 2 1 × 3 3

c) 2 3 × 3 1

d) 2 0 × 3 0

Answer: a) 2 2 × 3 2

4. 7 × 11 × 13 × 15 + 15 is a

a) Prime number

b) Composite number

c) Neither prime nor composite

d) None of the above

Answer: b) Composite number

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

Answer: b) a 2 b 2

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.

case study questions real numbers

1. 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

Answer: b) 12

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

Answer: d) 21

3. The LCM of 60, 84 and 108 is

Answer: a) 3780

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

Answer: d) 45360

5. 108 can be expressed as a product of its primes as

a) 2 3 × 3 2

b) 2 3 × 3 3

c) 2 2 × 3 2

d) 2 2 × 3 3

Answer: d) 2 2 × 3 3

CASE STUDY 3:

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.

case study questions real numbers

Observe the following factor tree and answer the following:

1. What will be the value of x?

Answer: b) 13915

2. What will be the value of y?

Answer: c) 11

3. What will be the value of z?

Answer: b) 23

4. According to Fundamental Theorem of Arithmetic 13915 is a

a) Composite number

b) Prime number

d) Even number

Answer: a) Composite number

5. The prime factorisation of 13915 is

a) 5 × 11 3 × 13 2

b) 5 × 11 3 × 23 2

c) 5 × 11 2 × 23

d) 5 × 11 2 × 13 2

Answer: c) 5 × 11 2 × 23

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

Tips to Solve Case Study Based Questions Accurately

CBSE Class 10 Maths Best & Complete Study Material for 2021-2022

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Case Study Questions Chapter 1: Real Numbers

Case Study Questions/ Passage Based Questions

Question no. 1. 

In a classroom activity on real numbers, the students have to pick a number card from a pile and frame a 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}` ?

(a) It is a natural number (b) It is an irrational number (c) It is a rational number (d) None of these

(ii) Shreya picked up ‘BONUS’ and her question was: Which of the following is not irrational?

(a) `3-4\sqrt{5}` (b) `\sqrt{7}-6` (c) `2+2\sqrt{9}` (d) `4\sqrt{11}-6`

(iii) Ananya picked up `\sqrt{15}-\sqrt{10}` and her question was: `\sqrt{15}-\sqrt{10}` is ____ number.

(a) a natural (b) an irrational (c) a whole (d) a rational

(iv) Suman picked up `\frac{1}{\sqrt{5}}` and her question was: `\frac{1}{\sqrt{5}}` is _______ number.

(a) a whole (b) a rational (c) an irrational (d) a natural

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

(a) `15+3\sqrt{6}` (b) `\sqrt{24}-9` (c) `5\sqrt{150}` (d) None of these

Case Study Question

Question no. 2.

Decimal form of rational numbers can be classified into two types. Let x be a rational number whose decimal expansion terminates. Then x can be expressed in the form `\frac{p}{q}`, where p and q are co-prime and the prime factorisation of q is of the form `2^{n}\cdot5^{m}`, where n, m are non-negative integers and vice-versa. Let x = `\frac{p}{q}` be a rational number, such that the prime factorisation of q is not of the form `2^{n}\cdot5^{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?

(a) `\frac{125}{441}` (b) `\frac{77}{210}` (c) `\frac{15}{1600}` (d) `\frac{129}{2^{2}\times5^{2}\times7^{2}}`

(ii) `\frac{23}{2^{3}\times5^{2}}` =

(a) 0.575 (b) 0.115 (c) 0.92 (d) 1.15

(iii) `\frac{441}{2^{2}\times5^{7}\times7^{2}}` is a ______ decimal.

(a) terminating (b) recurring (c) non-terminating and non-recurring (d) None of these

(iv) For which of the following value(s) of p, `\frac{251}{2^{3}\timesp^{2}}` is a non-terminating recurring decimal?

(a) 3 (b) 7 (c) 15 (d) All of these

(v) `\frac{241}{2^{5}\times5^{3}}` is a decimal.

Question no. 3.

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}\times` LCM (b) LCM = `pq^{2}\times` HCF (c) LCM = `p^{2}q\times` HCF (d) HCF = `p^{2}q\times` LCM

(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 no. 4. 

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. Answer them.

(i) For what value of n, `4^{n}` ends in 0?

(a) 10 (b) when n is even (c) when n is odd (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?

(a) when n is any even integer (b) when n is any odd integer (c) for all n > 1 (d) only when n=0

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

(a) `x^{2}+y^{2}` is even (b) `x^{2}+y^{2}` is not divisible by 4 (c) `x^{2}+y^{2}` is odd (d) both (a) and (b)

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

(a) always true (b) always false (c) sometimes true (d) None of these

(v) If n is any odd integer, then `n^{2}-1` is divisible by

(a) 22 (b) 55 (c) 88 (d) 8

Answer 4. (i)    d

Question no.5.

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?

(a) 6120 cm (b) 12240 cm (c) 4080 cm (d) None of these

(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?

(a) 9 (b) 6 (c) 27 (d) 29

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

(a) 1 litres (b) 7 litres (c) 12 litres (d) 18 litres

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

(a) 1 m 25 cm (b) 75 cm (c) 90 cm (d) 1 m 35 cm

(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.

(a) 3 and 2 (b) 2 and 5 (c) 3 and 4 (d) 4 and 5

(i)    b   

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Self Studies

CBSE Class 10 Mathematics Chapter 1 Real Numbers Case Study

Cbse class 10 mathematics chapter 1 real numbers case study questions pdfs.

If you are looking for the CBSE Class 10 Mathematics Chapter 1 Real Numbers Case Study Questions in PDF, then you are in the right place. CBSE 10th Class Case Study for the Mathematics Chapter 1 Real Numbers Subject is available here on this website. These Case studies can help the students to solve the different types of questions that are based on the case study.

CBSE Board will be asking case study questions based on Mathematics Chapter 1 Real Numbers subjects in the upcoming board exams. Thus, it becomes an essential resource to study. 

The Mathematics Chapter 1 Real Numbers Subject case study for class 10th covers a wide range of chapters from the Mathematics Chapter 1 Real Numbers. Students willing to score good marks in their board exams can use it. The questions are highly interactive and it allows students to use their thoughts and skills to solve such kinds of questions.

Download CBSE Board Class 10 Mathematics Chapter 1 Real Numbers Case Study (Passage Based)

Download links of class 10 Mathematics Chapter 1 Real Numbers case study questions pdf is given on this website. Students can download them for free of cost because it is going to help them to practice questions.

Case Study Questions Class 10 from Mathematics Chapter 1 Real Numbers subjects includes all chapters wise questions. A few passages are given in the case study PDF of Mathematics Chapter 1 Real Numbers. Students can download them to read and solve the relevant questions that are given below the passage.

CBSE Class 10 Case Study Questions of Mathematics Chapter 1 Real Numbers are quite easy to solve if you have a good basic knowledge of Mathematics Chapter 1 Real Numbers Subjects. For gaining the basic knowledge students can refer to the NCERT Class 10th Textbooks . After gaining the basic information students can easily solve the case study questions.

Case Study Type Questions in Mathematics Chapter 1 Real Numbers Class 10

Case Study Type Questions in Mathematics Chapter 1 Real Numbers Class 10 includes the information or data. Students willing to solve them are required to read the passage carefully and then solve them. While solving the paragraph the ideal way is to highlight the key information or given data.

Because, later it will ease them to write the final answers. Mathematics Chapter 1 Real Numbers Case study type questions consist of 4 to 5 questions that should be answered in MCQ manner. 

While reading the paragraph students will get the clue in between about the possible answer of the question. They should definitely highlight those questions. This is the best way to solve such kind of Case study Type Questions.

Also, before solving the Case study type questions it is ideal to use the Revision Notes to brush up the previous learnings.

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Case Study Questions for Class 9 Maths Chapter 1 Real Numbers

Case Study Questions:

Question 1:

Himanshu 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. Answer them.

(i) For what value of n, 4 n  ends in 0?

(a) 10 (b) when n is even (c) when n is odd (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 is a rational number?

(a) when n is any even integer (b) when n is any odd integer (c) for all n > 1 (d) only when n=0

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

(a) x 2 +y 2  is even (b) x 2 +y 2  is not divisible by 4 (c) x 2 +y 2  is odd (d) both (a) and (b)

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

(a) always true (b) always false (c) sometimes true (d) None of these

(v) If n is any odd integer, then n 2  – 1 is divisible by

(a) 22 (b) 55 (c) 88 (d) 8

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COMMENTS

  1. real numbers- case study

    How many questions did he guess? 3. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got?

  2. CBSE Class 10 Maths Case Study Questions for Chapter 1

    We have provided here case study questions for Class 10 Maths Chapter 1 - Real Numbers. These questions have been published by the CBSE

  3. Case Study Questions Chapter 1: Real Numbers -

    Case Study Questions/ Passage Based Questions Question no. 1. In a classroom activity on real numbers, the students have to pick a number card from a pile

  4. CBSE Class 10 Mathematics Chapter 1 Real Numbers Case Study

    Case Study Questions Class 10 from Mathematics Chapter 1 Real Numbers subjects includes all chapters wise questions. A few passages are given in the case study

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  9. Case Study Questions for Class 10 Maths Chapter 1 Real Numbers

    (i) If two positive integers x and y are expressible in terms of primes as x =p2q3 and y=p3q, then which of the following is true?

  10. Case Study Questions for Class 9 Maths Chapter 1 Real Numbers

    Case Study Questions: Question 1: Himanshu has made a project on real numbers, where he finely explained the applicability of exponential laws