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

By QB365 on 22 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

An agency has decided to install customised playground equipments at various colony parks. For that they decided to study the age-group of children playing in a park of the particular colony. The classification of children according to their ages, playing in a park is shown in the following table

Based on the above information, answer the following questions. (i) The maximum number of children are of the age-group

(ii) The lower limit of the modal class is

(iii) Frequency of the class succeeding the modal class is

(iv) The mode of the ages of children playing in the park is

(v) If mean and mode of the ages of children playing in the park are same, then median will be equal to

Based on the above information, answer the following questions. (i) If A is taken as assumed mean, then the possible value of A is

(ii) If x i 's denotes the class marks and f i 's denotes the deviation of assumed mean (A) from x i 's, then the minimum value of |d i | is

(iii) The mean of toll tax received. by NHAI by assumed mean method is

(iv) The mean of toll tax received by NHAI by direct method is

(v) The average toll tax received by NHAI in a day, from that particular toll plaza, is

Based on the above information, answer the following questions. (i) The upper limit of a class and lower limit of its succeeding class is differ by

(ii) The median class is

(iii) The cumulative frequency of the class preceding the median class is

(iv) The median of the distance travelled is

(v) If the mode of the distance travelled is 223.78 km, then mean of the distance travelled by the bus is

An electric scooter manufacturing company wants to declare the mileage of their electric scooters. For this, they recorded the mileage (km/ charge) of 50 scooters of the same model. Details of which are given in the following table.

(ii) The modal value of the given data is

(ill) The median value of the given data is

(iv) Assumed mean method is useful in determining the

(v) The manufacturer can claim that the mileage for his scooter is

Household income in India was drastically impacted due to the COVID-19 loekdown. Most of the companies decided to bring down the salaries of the employees by 50%. The following table shows the salaries (in percent) received by 25 employees during loekdown.

(ii) Total number of persons whose salary is reduced by atmost 40%, is

(iii) The modal class is

(iv) The median class of the given data is

(v) The empirical relationship between mean, median and mode is

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

(i) (b) : Since, the highest frequency is 70, therefore the maximum number of children are of the age-group 10-12. (ii) (a): Since, the modal class is 10-12 \(\therefore\) Lower limit of modal class = 10 (iii) (c) : Here,f 0  = 58,f 1 = 70 and f 2 = 42 Thus, the frequency of the class succeeding the modal class is 42. (iv) (d) : Mode  \(=l+\left[\frac{f_{1}-f_{0}}{2 f_{1}-f_{0}-f_{2}}\right] \times h\) \(=10+\left[\frac{70-58}{140-58-42}\right] \times 2\) \(=10+\frac{12}{40} \times 2=10+\frac{24}{40}=10.6 \text { years }\) (v) (c): Given that, Mean = Mode \(\therefore\) By Empirical relation, we have Mode = 3 Median - 2 Mean \(\Rightarrow\) Mode = 3 Median - 2 Mode \(\Rightarrow\) 3 Mode = 3 Median \(\Rightarrow\) Median = Mode = Mean

Let us consider the following table:

(i) (d): Clearly, the possible values of assumed mean (A) are 35, 45, 55, 65, 75. (ii) (c) : The values of |d i | are 0, 10,20 Thus, the minimum value of |d i | is 0. (iii) (b): Required Mean  \(=A+\frac{\sum f_{i} d_{i}}{\sum f_{i}}=55-\frac{1200}{420}\) = Rs 52.14. (iv) (a): Mean by direct and assumed mean method are always equal. (v) (d): Average toll tax received by a vehicle = Rs 52.14 Total number of vehicles = 420 \(\therefore\) Average toll tax received in a day = Rs (52.14 x 420) = Rs 21898.80

(i) (b): The upper limit of a class and the lower class of its succeeding class differ by 1. (ii) (d) : Here, class intervals are in inclusive form. So, we first convert them in exclusive form. The frequency distribution table in exclusive form is as follows:

\(\text { Here, } \Sigma f_{i} \text { i.e., } N=60 \) \(\Rightarrow \frac{N}{2}=30\)

Now, the class interval whose cumulative frequency is just greater than 30 is 219.5 - 229.5. \(\therefore\) Median class is 219.5 - 229.5. (iii) (b): Clearly, the cumulative frequency of the class preceding the median class is 18 (iv) (d) : Median  \(=l+\left[\frac{\frac{N}{2}-c . f .}{f}\right] \times h\) \(=219.5+\left(\frac{30-18}{26}\right) \times 10 \) \(=219.5+\frac{12 \times 10}{26}=219.5+4.62=224.12\) \(\therefore\) Median of the distance travelled is 224.12 km (v) (d) : We know, Mode = 3 Median - 2 Mean \(\therefore \quad \text { Mean }=\frac{1}{2}(3 \text { Median }-\text { Mode }) \) \(=\frac{1}{2}(672.36-223.78)=224.29 \mathrm{~km}\)

Given frequency distribution table can be drawn as:

(i) (d): Clearly, average mileage \(=\frac{7240}{50}=144.8 \mathrm{~km} / \text { charge }\) (ii) (b) : Since, highest frequency is IS, therefore, modal class is 140-160. Here, l = 140,f 1 = 18,f 0  = 12,f 2 = 13, h = 20 \(\therefore \quad \text { Mode }=140+\frac{18-12}{36-12-13} \times 20=140+\frac{6}{11} \times 20 \) \(=140+\frac{120}{11}=140+10.91=150.91\) (iii) (b) : Here  \(\frac{N}{2}=\frac{50}{2}=25\)  and the corresponding class whose cumulative frequency is just greater than 25 is 140-160. Here, l = 140, c.f = 19, h = 20 and f= 18 \(\therefore \quad \text { Median }=l+\left(\frac{\frac{N}{2}-c . f .}{f}\right) \times h\) \(=140+\frac{25-19}{18} \times 20=140+\frac{60}{9}=146.67\) (iv) (a) : Assumed mean method is useful in determining the mean. (v) (a): Since, Mean = 144.S, Mode = 150.91 and Median = 146.67 and minimum of which is 144 approx, therefore manufacturer can claim the mileage for his scooter 144 km/charge.

(i) (d): Required number of persons = 9 + 6 = 15 (ii) (c) : Required number of persons = 6 + 8 + 2 = 16 (iii) (a) : 50-60 is the modal class as the maximum frequency is 9. (iv) (b) : The cumulative frequency distribution table for the given data can be drawn as :

\(\text { Here, } \frac{N}{2}=\frac{25}{2}=12.5\) The cumulative frequency just greater than 12.5 lies in the interval 60-70. Hence, the median class is 60-70. (v) (a): We know, Mode = 3 Median - 2 Mean \(\therefore\)   3 Median = Mode + 2 Mean.

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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.

Since you are already on this page, you can scroll to the top section of this page to get access to the Case Study on Real Numbers. To help others reach this page let them know these steps:

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• Once the website gets loaded, click on the navigation button

• Find CBSE from the given menu

• Click on Case Study

• Choose Class 10 
• Search Maths and then navigate to the Real Numbers Class 10 Maths Case Study

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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

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

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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