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Case Study Class 10 Maths Questions

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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

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

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

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

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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Case Study Questions Class 10 Maths with Solutions PDF Download

 case study questions class 10 maths pdf, case study questions class 10 maths with solutions, case study questions class 10 maths cbse chapter wise pdf download, how to solve case-based question in maths.

• First of all, a student needs to read the complete passage thoroughly. Then start solving the question
• After reading the question try to understand from which topics the question is asked. and try to remember all the concepts of that topic.
• Sometimes the question is very tricky and you will find it very difficult to understand. In that case, Read the question and passage again and again.
• After solving the answer check your answer with the options given.
• Remember, write only answering your answer book

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CBSE Case Study Questions for Class 6 – 10, 12 for Maths, Science, SST

Cbse case study questions for maths, science, social science.

CBSE Case Study Questions:   Case Study Questions for all Class 1, 2, 4, 5, 6, 7, 8, 9,10, 11 and 12 by Experienced Teachers. We Net Ex. Arranged here Important Case Based Questions for CBSE Board – Maths, Science, Social Science, English.

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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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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

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?

(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

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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 for Class 10 Maths Chapter 7 Coordinate Geometry

• Last modified on: 1 year ago
• Reading Time: 3 Minutes

Case Study Questions:

Question 1:

The top of a table is shown in the figure given below:

(i) The coordinates of the points H and G are respectively (a) (1, 5), (5, 1) (b) (0, 5), (5, 0) (c) (1, 5), (5, 0) (d) (5, 1), (1, 5)

(ii) The distance between the points A and B is (a) 4 units (b) 4 2 units (c) 16 units (d) 32 units

(iii) The coordinates of the mid point of line segment joining points M and Q are (a) (9, 3) (b) (5, 11) (c) (14, 14) (d) (7, 7)

(iv) Which among the following have same ordinate? (a) H and A (b) T and O (c) R and M (d) N and R

(v) If G is taken as the origin, and x, y axis put along GF and GB, then the point denoted by coordinate (4, 2) is (a) H (b) F (c) Q (d) R

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Chapter 1 Real Numbers Chapter 2 Polynomials Chapter 3 Pair of Linear Equations in Two Variables C hapter 4 Quadratic Equations Chapter 5 Arithmetic Progressions Chapter 6 Triangles Chapter 7 Coordinate Geometry Chapter 8 Introduction to Trigonometry Chapter 9 Some Applications of Trigonometry Chapter 10 Circles Chapter 11 Constructions Chapter 12 Areas Related to Circles Chapter 13 Surface Areas and Volumes Chapter 14 Statistics Chapter 15 Probability

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• Direct and Inverse Proportions Class 8 Case Study Questions Maths Chapter 11

Last Updated on September 17, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 8 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 8 maths. In this article, you will find case study questions for CBSE Class 8 Maths Chapter 11 Direct and Inverse Proportions. It is a part of Case Study Questions for CBSE Class 8 Maths Series.

Table of Contents

Case Study Questions on Direct and Inverse Proportions

A hotel has 320 rooms and 32 cleaners to maintain them. With full capacity of staff, it took 2 hours to clean all the rooms.

Q. 1. On Monday 20% of the cleaners were not available. Will the cleaning of all rooms take more than 2 hours? How can you say so?

Difficulty Level: Easy

Sol. Yes. As, Number of man required to complete work is inversely proportional to time taken by them.

Q. 2. Ishan says, “The number cleaners available in the hotel is directly proportional to the time taken by them to clean the rooms.” Mira says, “The number of cleaners available in the hotel is inversely proportional to the time taken by them to clean the rooms.” Who is correct? Give reason.

Difficulty Level: Medium

Sol. Mira is correct, As Number of cleaners are inversely proportional to time taken

Q. 3. Equal number of rooms are allocated for each staff member for cleaning. How many rooms each cleaner had to maintain?

Sol. Number of rooms = 320 Number of cleaners = 32 Number of rooms cleaned by each cleaner = 320 / 32 = 10

Q. 4. The hotel administration hired 8 more cleaners. What is the change in number of rooms maintained by each cleaner?

Ans. Option (b) is correct. Explanation: Number of cleaners = 40 (32 + 8) Number of rooms cleaned by each cleaner = 320 / 40 = 8 So, Number of rooms decreased by (10 – 8) = 2

Q. 5. How many rooms has to be cleaned in an hour by each cleaner after the increase in the number of staff? ( (a) 1 (b) 4 (c) 8 (d) 10

Ans. Option (b) is correct. Explanation: Number of rooms to be cleaned in 2 hours = 8 Number of rooms to be cleaned in 1 hour = 8/2 = 4

• Exponents and Powers Class 8 Case Study Questions Maths Chapter 10
• Mensuration Class 8 Case Study Questions Maths Chapter 9
• Algebraic Expressions and Identities Class 8 Case Study Questions Maths Chapter 8
• Comparing Quantities Class 8 Case Study Questions Maths Chapter 7
• Cube and Cube Roots Class 8 Case Study Questions Maths Chapter 6
• Square and Square Roots Class 8 Case Study Questions Maths Chapter 5
• Data Handling Class 8 Case Study Questions Maths Chapter 4
• Understanding Quadrilaterals Class 8 Case Study Questions Maths Chapter 3

Linear Equations in One Variable Class 8 Case Study Questions Maths Chapter 2

Rational numbers class 8 case study questions maths chapter 1, download ebooks for cbse class 8 maths.

• Rational Numbers Topicwise Worksheet for CBSE Class 8 Maths
• Linear Equations in One Variable Worksheet for CBSE Class 8 Maths
• Understanding Quadrilaterals Worksheet for CBSE Class 8 Maths
• Data Handling Worksheet for CBSE Class 8 Maths
• Squares and Square Roots Worksheet for CBSE Class 8 Maths
• Cube and Cube Roots Worksheet for CBSE Class 8 Maths
• Comparing Quantities Worksheet for CBSE Class 8 Maths
• Algebraic Expressions and Identities Worksheet for CBSE Class 8 Maths

Topics from which case study questions may be asked

• Direct Proportions
• Inverse Proportion

Whenever two quantities have a relation with each other such that if one changes, the other also changes then these quantities are said to be inter related with each other. This is called variation.

Example: (a) If number of something purchased increases then cost also increases. (b) If speed of vehicle increases, time taken decreases.

Quantities increasing or decreasing together need not be in direct proportion or indirect proportion.

Case study questions from the above given topic may be asked.

Frequently Asked Questions (FAQs) on Direct and Inverse Proportions Case Study

Q1: what is direct proportion.

A1: Direct proportion refers to a relationship between two quantities where an increase in one quantity leads to a proportional increase in the other, and a decrease in one result in a proportional decrease in the other. Mathematically, two quantities x and y are in direct proportion if x/y=k, where k is a constant.

Q2: What is inverse proportion?

A2: Inverse proportion describes a relationship between two quantities where an increase in one quantity leads to a proportional decrease in the other and vice versa. In this case, the product of the two quantities remains constant. Mathematically, two quantities x and y are in inverse proportion if x × y = k, where k is a constant.

Q3: How can I identify if two quantities are in direct proportion?

A3: – To identify if two quantities are in direct proportion, check if their ratio remains constant when they change. If the ratio of the two quantities stays the same, they are in direct proportion. For example, if 4 pencils cost ₹20, and 8 pencils cost ₹40, the ratio of pencils to price remains constant, indicating direct proportion.

Q4: How can I identify if two quantities are in inverse proportion?

A4: To determine if two quantities are in inverse proportion, check if the product of the two quantities remains constant when they change. If multiplying the two quantities always gives the same result, they are in inverse proportion. For example, if 4 workers take 6 days to complete a task, and 8 workers take 3 days, the product of workers and days (4 × 6 = 24 and 8 × 3 = 24) remains constant, indicating inverse proportion.

Q5: Can you give a real-life example of direct proportion?

A5: A common real-life example of direct proportion is the relationship between distance and time when speed is constant. If a car travels at a constant speed, doubling the time will double the distance covered, maintaining a constant ratio between distance and time.

Q6: Can you provide an example of inverse proportion in daily life?

A6: A typical example of inverse proportion is the relationship between the number of workers and the time taken to complete a task. If more workers are assigned to a job, the time required to finish the work decreases proportionally, assuming the work is equally distributed among the workers.

Q7: Why is learning about direct and inverse proportions important?

A7: Understanding direct and inverse proportions is crucial as these concepts are frequently used in real-life situations, such as calculating speed, cost, work efficiency, and more. Mastery of these concepts helps students develop problem-solving skills and apply mathematical relationships to practical problems.

Q8: Are there any online resources or tools available for practicing Direct and Inverse Proportions case study questions?

A8: We provide case study questions for CBSE Class 8 Maths on our  website . Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit  Physics Gurukul  website. they are having a large collection of case study questions for all classes.

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CBSE Class 12 Maths Case Study Questions With Solutions

CBSE Class 12 Mathematics Case Study Questions are introduced this year in the updated CBSE Board Exam Pattern. According to that this year the candidates need to prepare for the case study problems along with the questions that are legacy of CBSE Board.

In Class XIIth Mathematics Case Study Questions there are problems based on Objective types of questions, Assertions and Reason, and cae based problems. These problems have the intention to examine the students' overall understanding of the subject. If you are preparing for the Maths board exam then this is the right place for you. 

Here, we have provided the complete set of CBSE class 12 maths case study questions With Solutions. These are developed by the subject matter expert. If you want to score good marks in the board papers then you should practice these Case based problems. It is absolutely free of cost. 

Download PDF CBSE Class 12 Maths Case Study From the Given links. It is in chapter wise format.

Class 12th Mathematics Important Formulas, MCQ, Case-Based, Assertion and Reason

Class 12th Maths Case Study

In class 12th Maths Case Study the questions are based on the real world scenarios. A passage filled with information or data is provided to the students. On the basis of that paragraph upto 5 questions are developed which should be answered by the students. To answer them they need to read the passage carefully and then pay attention to the given data to solve such questions.

These types of problems are generally known as case based questions which can be only solved by referring to the given paragraph.

Class 12 Maths Important Formulas

Knowing about the Maths Important Formulas is a crucial part of solving the Maths questions. Formulas help in solving the problems more efficiently and faster. Therefore the PDF file that we have provided here consists of all the basics and Important formulas of maths. It will help in revisions and solving the questions more accurately and easily.

Every chapter has its own topics and formulas so the PDF has been divided into chapter wise format. And if you access them from this place then you will be able to get all the formulas and other questions separately.

Class 12 Maths Assertion and Reason MCQs

Class 12th Maths Assertion and Reason MCQs PDF with Solutions are also given here. It is the most important part of Case Study Questions because scoring good marks in this section is not that much hard. If your basic concepts are clear. Because most of the time such types of questions are directly prepared by referring to the concepts.

Furthermore, the assertion and reason MCQs are solved by applying the distinct approaches. For instance, to answer these questions first candidates need to verify the Assertion (Statement) and then the reason if both are correct, then learners need to verify whether both statement and reason support each other or not.

There are a total of 5 sections in CBSE Class 12 Maths Questions Term 1. Section A contains 1 mark, Section B contains 2 marks, Section C contains 3 marks, Section D contains 4 marks and the last Section E contains 5 marks. A total of 5 questions are given in these sections.

No, In Term 1 exam there will be a total of 5 questions in each case study of class 12 maths, out of which 4 are compulsory to solve.

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• CBSE Class 10 Study Material

CBSE Class 10 Maths Case Study Questions for Chapter 4 Quadratic Equations (Published by CBSE)

Cbse class 10 maths case study questions for chapter 4 - quadratic equations are released by the board. solve all these questions to perform well in your cbse class 10 maths exam 2021-22..

Check here the case study questions for CBSE Class 10 Maths Chapter 4 - Quadratic Equations. The board has published these questions to help class 10 students to understand the new format of questions. All the questions are provided with answers. Students must practice all the case study questions to prepare well for their Maths exam 2021-2022.

Case Study Questions for Class 10 Maths Chapter 4 - Quadratic Equations

CASE STUDY 1:

Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h while Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete the journey of 400 km.

1. What will be the distance covered by Ajay’s car in two hours?

 a) 2(x + 5)km

b) (x – 5)km

c) 2(x + 10)km

d) (2x + 5)km

Answer: a) 2(x + 5)km

2. Which of the following quadratic equation describe the speed of Raj’s car?

a) x 2 – 5x – 500 = 0

b) x 2 + 4x – 400 = 0

c) x 2 + 5x – 500 = 0

d) x 2 – 4x + 400 = 0

Answer: c) x 2 + 5x – 500 = 0

3. What is the speed of Raj’s car?

a) 20 km/hour

b) 15 km/hour

c) 25 km/hour

d) 10 km/hour

Answer: a) 20 km/hour

4. How much time took Ajay to travel 400 km?

Answer: d) 16 hour

CASE STUDY 2:

The speed of a motor boat is 20 km/hr. For covering the distance of 15 km the boat took 1 hour more for upstream than downstream.

1. Let speed of the stream be x km/hr. then speed of the motorboat in upstream will be

a) 20 km/hr

b) (20 + x) km/hr

c) (20 – x) km/hr

Answer: c) (20 – x)km/hr

2. What is the relation between speed ,distance and time?

a) speed = (distance )/time

b) distance = (speed )/time

c) time = speed x distance

d) speed = distance x time

Answer: b) distance = (speed )/time

3. Which is the correct quadratic equation for the speed of the current?

a) x 2 + 30x − 200 = 0

b) x 2 + 20x − 400 = 0

c) x 2 + 30x − 400 = 0

d) x 2 − 20x − 400 = 0

Answer: c) x 2 + 30x − 400 = 0

4. What is the speed of current ?

b) 10 km/hour

c) 15 km/hour

d) 25 km/hour

Answer: b) 10 km/hour

5. How much time boat took in downstream?

a) 90 minute

b) 15 minute

c) 30 minute

d) 45 minute

Answer: d) 45 minute

Also Check:

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Tips to Solve Case Study Based Questions Accurately

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Home » 7th Class » Class 7 Maths Notes for Integers (PDF) – Study Material

Class 7 Maths Notes for Integers (PDF) – Study Material

Class 7 Maths Integers – Get here the Notes, Question & Practice Paper of Class 7 Maths for topic Integers Notes. Integers Notes for Class 7 Maths are here. You can download the Integers Notes PDF to study all the topics in this chapter. Moreover the Class 7 Maths notes include chapter summary, definitions, examples, and key pointers for Integers . Thus if you are studying class Maths (गणित), then the  Integers notes  will help you easily understand the topic and ace it.

Class 7 Maths Notes for Integers

Integers is a critical part in the study of Maths . In India, it is taught in class. Therefore the Class 7 Notes for Maths topic Integers have been compiled by teachers and field experts. They explain the complete chapter of Integers in one-shot .

Integers Notes Download Link – Click Here to Download PDF

Integers Notes for Class 7 Maths

Integers Class 7 notes is as follows. You can view the document here and also download it use it anytime for future reference whenever you want to brush up your concepts of Maths.

Chapter 1 – Integers

Previous Knowledge:

Integers – Integers are bigger collection of numbers which is formed by whole numbers and their negatives or we can say that all positive and negative numbers including zero are integers. Example: -3, -2, -1, 0, 1, 2, 3…

Integers on Number Line – On a number line, when we:

• add a positive integer, we move to the right.
• add a negative integer, we move to the left.
• subtract a positive integer, we move to the left.
• subtract a negative integer, we move to the right.

Properties of Addition and Subtraction of Integers

(a) Closure Property: Integers are closed for addition and subtraction both, i.e. a + b and a – b are again integers, where a and b are any integers. Example: For any two integers 2 and 3, we have 2+ 3 = 5 an integer and 2 – 3 = -1 is also an integer.

(b) Commutative Property: Addition is commutative for integers, i.e. a + b = b + a for all integers a and b. Example: For any two integers say 5 and 4, we have 5+ 4 = 4 + 5 = 9, but the same does not holds for subtraction as 5– 4 =1 and 4 – 5 = -1.

(c) Associative Property: Addition is associative for integers, i.e., (a + b) + c = a + (b + c) for all integers a, b and c. Example: For any three integers say 6, 3 & 7 we have (6 + 3) +7= 6 + (3 + 7) Again it does not hold under subtraction.

(d) Additive Identity: Integer 0 is the identity under addition i.e. a + 0 = 0 + a = a for every integer a. Example: 3 + 0 = 0 + 3 = 3

Multiplication of Integers

The product of a positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer and the product of two positive integers is always a positive integer. Example: – 2 × 7 = – 14 and – 3 × – 8 = 24 and 5 × 6 = 30.

Also we can see that the product of even number of negative integers is positive. whereas the product of odd number of negative integers is negative.

Example: (-1) × (-1) × (-1) × (-1) = 1 but (-1) × (-1) × (-1) = -1.

Properties of Multiplication of Integers

(a) Closure Property: Integers are closed under multiplication, i.e., a × b is an integer for any two integers a and b, Example: 2 x 3 =6, 6 is also an integer.

(b) Commutative Property: Multiplication is commutative for integers, i.e., a × b = b × a for any integers a and b Example: 4 x 3 = 3 x 4 = 12.

(c) Associative Property: Multiplication is associative for integers, i.e., (a × b) × c = a × (b × c) for any three integers a, b & c. Example: (2 × 3) × 4 = 2 × (3 × 4) = 24

(d) Multiplicative Identity: The integer 1 is the identity under multiplication, i.e., 1 × a = a × 1 = a for any integer a. Example: 1 × 9 = 9 × 1 = 9

(e) Distributive Property: Under addition and multiplication, integers show a property called distributive property i.e., a × (b + c) = (a × b) + (a × c) for any three integers a, b and c. Examples: i) 16 x12 = 16 x (10 +2) = (16 x 10) + (16 x 2) = 160 + 32 =192 ii) -23 x 48 = -23 x (50 – 2) = (-23 x 50) + (-23 x 2) = -1150 + (-46) = -1150 – 46 = -1196 iii) 52 x (-8) + (-52) x 2 = [52 x (-8)] + [ 52 x (-2)] = 52 x [(-8 -2)] =52 x (-10) = -520.

Properties of Division of Integers

(a) When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa. Example: 2/−3 = – 2/3 (b) Division of a negative integer by another negative integer gives a positive integer as quotient. Example: −5 / −6 = 5 / 6

Other Properties of Integer: For any integer a, we have (i) a ÷ 0 is not defined and (ii) a ÷ 1 = a. Example: 4÷0 is not defined and 6 ÷1 = 6

Candidates who are ambitious to qualify the Class 7 with good score can check this article for Notes, Study Material, Practice Paper. Above we provided the link to access the Notes , Important Question and Practice Paper of Class 7 Maths for topic Integers.

All Topics Class 7 Maths Notes

Chapter wise notes for Maths (गणित) are given below.

• Fractions and Decimals
• Data Handling
• Simple Equations
• Lines & Angles
• Triangles & Its Properties
• Comparing Quantities
• Rational Numbers
• Perimeter and Area
• Algebraic Expressions
• Exponents and Powers
• Visualing Solid Shapes

Class 7 Notes for All Subjects

• Class 7 Maths Notes
• Class 7 Science Notes

NCERT Solutions for Class 7 Maths Integers

The Integers notes here help you solve the questions and answers . Also, you can complete the Class 7 Integers worksheet using the same. In addition you will also tackle CBSE Class 7 Maths Important Questions with these Class 7 notes .

However if you still need help, then you can use the NCERT Solutions for Class 7 Maths Integers to get all the answers. Integers solutions contain questions, answers, and steps to solve all questions.

Notes for All Classes

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• Class 10 Notes
• Class 11 Notes
• Class 12 Notes

Integers Notes for Class 7 Maths – An Overview

Class 7 Integers Notes for All Boards

You can use the Class 7 Maths notes of Integers for all boards.

The education boards in India for which Integers notes are relevant are – CBSE, CISCE, AHSEC, CHSE Odisha, CGBSE, HBSE, HPBOSE, PUE Karnataka, MSBSHSE, PSEB, RBSE, TBSE, UPMSP, UBSE, BIEAP, BSEB, GBSHSE, GSEB, JAC, JKBOSE, KBPE, MBOSE, MBSE, MPBSE, NBSE, DGE TN, TSBIE, COHSEM, WBCHSE .

Therefore you can refer to these notes as CBSE, CISCE, AHSEC, CHSE Odisha, CGBSE, HBSE, HPBOSE, PUE Karnataka, MSBSHSE, PSEB, RBSE, TBSE, UPMSP, UBSE, BIEAP, BSEB, GBSHSE, GSEB, JAC, JKBOSE, KBPE, MBOSE, MBSE, MPBSE, NBSE, DGE TN, TSBIE, COHSEM, WBCHSE notes for class Class 7 / Class / Maths for the topic Integers.

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Class 7 Maths Notes for (PDF) – Study Material

Class 7 maths notes for fractions and decimals (pdf) – study material, related posts.

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CBSE Case Study Questions Class 9 Maths Chapter 6 Lines and Angles PDF Download

Case Study Questions Class 9 Maths Chapter 6  are very important to solve for your exam. Class 9 Maths Chapter 6 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  case study-based   questions for Class 9 Maths Chapter 6  Lines and Angles

CBSE Case Study Questions for Class 9 Maths Lines and Angles PDF

Case study questions class 9 maths chapter 6 lines and angles.

Case Study 1. A group of students is studying the concepts of lines and angles. They encountered the following scenario during their class:

A classroom has two parallel boards, Board A and Board B, on opposite walls. Two students, Rahul and Riya, are standing in the classroom, facing the boards. Rahul is standing between the two boards and looking at Board A, while Riya is standing near Board B and looking at Board A. They observed the following:

• Rahul and Riya are facing each other.
• Rahul’s left hand is pointing towards the ceiling.
• Riya’s right hand is pointing towards the floor.

Based on this information, the students were asked to analyze the angles formed by the hands of Rahul and Riya. Let’s see if you can answer the questions correctly:

Q1. The angle formed between Rahul’s left hand and his line of sight is a: (a) Right angle (b) Obtuse angle (c) Acute angle (d) Straight angle

Answer: (a) Right angle

Q2. The angle formed between Riya’s right hand and her line of sight is a: (a) Right angle (b) Obtuse angle (c) Acute angle (d) Straight angle

Q3. The angle between the hands of Rahul and Riya is a: (a) Complementary angle (b) Supplementary angle (c) Vertical angle (d) Adjacent angle

Answer: (c) Vertical angle

Q4. The angle formed between Rahul’s left hand and Riya’s right hand is a: (a) Complementary angle (b) Supplementary angle (c) Vertical angle (d) Adjacent angle

Answer: (b) Supplementary angle

Q5. The sum of all the angles formed by the hands of Rahul and Riya is: (a) 180 degrees (b) 360 degrees (c) 90 degrees (d) 270 degrees

Answer: (b) 360 degrees

Case Study 2. A group of students is learning about the properties of angles and the concepts of lines. During their study session, they encountered the following scenario:

In their classroom, there is a wall with a vertical line drawn on it. The line is intersected by a horizontal line, forming four angles. The students observed the following:

• The angle formed at the top-left corner is acute.
• The angle formed at the top-right corner is obtuse.
• The angle formed at the bottom-left corner is a right angle.
• The angle formed at the bottom-right corner is a straight angle.

Based on this information, the students were asked to analyze the angles formed by the intersecting lines. Let’s see if you can answer the questions correctly

Q1. The acute angle formed at the top-left corner measures: (a) 90 degrees (b) Less than 90 degrees (c) More than 90 degrees (d) It cannot be determined

Answer: (b) Less than 90 degrees

Q2. The obtuse angle formed at the top-right corner measures: (a) 90 degrees (b) Less than 90 degrees (c) More than 90 degrees (d) It cannot be determined

Answer: (c) More than 90 degrees

Q3. The right angle formed at the bottom-left corner measures: (a) 90 degrees (b) Less than 90 degrees (c) More than 90 degrees (d) It cannot be determined

Answer: (a) 90 degrees

Q4. The straight angle formed at the bottom-right corner measures: (a) 90 degrees (b) Less than 90 degrees (c) More than 90 degrees (d) It cannot be determined

Answer: (d) It cannot be determined

Q5. The sum of all the angles formed by the intersecting lines is: (a) 90 degrees (b) 180 degrees (c) 270 degrees (d) 360 degrees

Answer: (b) 180 degrees

Hope the information shed above regarding Case Study and Passage Based Questions for Case Study Questions Class 9 Maths Chapter 6 Lines and Angles with Answers Pdf free download has been useful to an extent. If you have any other queries about Case Study Questions Class 9 Maths Chapter 6 Lines and Angles and Passage-Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible.

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