case study questions for class 10th maths

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CBSE Class 10 Maths Case Study Questions PDF

Download Case Study Questions for Class 10 Mathematics to prepare for the upcoming CBSE Class 10 Final Exam. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 10 so that they can score 100% on Boards.

CBSE Class 10 Mathematics Exam 2024  will have a set of questions based on case studies in the form of MCQs. The CBSE Class 10 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

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Chapterwise Case Study Questions for Class 10 Mathematics

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

The above  Case studies for Class 10 Maths will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

• Class 10th Science Case Study Questions
• Assertion and Reason Questions of Class 10th Science
• Assertion and Reason Questions of Class 10th Social Science

Class 10 Maths Syllabus 2024

Chapter-1  real numbers.

Starting with an introduction to real numbers, properties of real numbers, Euclid’s division lemma, fundamentals of arithmetic, Euclid’s division algorithm, revisiting irrational numbers, revisiting rational numbers and their decimal expansions followed by a bunch of problems for a thorough and better understanding.

Chapter-2  Polynomials

This chapter is quite important and marks securing topics in the syllabus. As this chapter is repeated almost every year, students find this a very easy and simple subject to understand. Topics like the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of a polynomial, division algorithm for polynomials followed with exercises and solved examples for thorough understanding.

Chapter-3  Pair of Linear Equations in Two Variables

This chapter is very intriguing and the topics covered here are explained very clearly and perfectly using examples and exercises for each topic. Starting with the introduction, pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solving a pair of linear equations, substitution method, elimination method, cross-multiplication method, equations reducible to a pair of linear equations in two variables, etc are a few topics that are discussed in this chapter.

Chapter-4  Quadratic Equations

The Quadratic Equations chapter is a very important and high priority subject in terms of examination, and securing as well as the problems are very simple and easy. Problems like finding the value of X from a given equation, comparing and solving two equations to find X, Y values, proving the given equation is quadratic or not by knowing the highest power, from the given statement deriving the required quadratic equation, etc are few topics covered in this chapter and also an ample set of problems are provided for better practice purposes.

Chapter-5  Arithmetic Progressions

This chapter is another interesting and simpler topic where the problems here are mostly based on a single formula and the rest are derivations of the original one. Beginning with a basic brief introduction, definitions of arithmetic progressions, nth term of an AP, the sum of first n terms of an AP are a few important and priority topics covered under this chapter. Apart from that, there are many problems and exercises followed with each topic for good understanding.

Chapter-6  Triangles

This chapter Triangle is an interesting and easy chapter and students often like this very much and a securing unit as well. Here beginning with the introduction to triangles followed by other topics like similar figures, the similarity of triangles, criteria for similarity of triangles, areas of similar triangles, Pythagoras theorem, along with a page summary for revision purposes are discussed in this chapter with examples and exercises for practice purposes.

Chapter-7  Coordinate Geometry

Here starting with a general introduction, distance formula, section formula, area of the triangle are a few topics covered in this chapter followed with examples and exercises for better and thorough practice purposes.

Chapter-8  Introduction to Trigonometry

As trigonometry is a very important and vast subject, this topic is divided into two parts where one chapter is Introduction to Trigonometry and another part is Applications of Trigonometry. This Introduction to Trigonometry chapter is started with a general introduction, trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles, trigonometric identities, etc are a few important topics covered in this chapter.

Chapter-9  Applications of Trigonometry

This chapter is the continuation of the previous chapter, where the various modeled applications are discussed here with examples and exercises for better understanding. Topics like heights and distances are covered here and at the end, a summary is provided with all the important and frequently used formulas used in this chapter for solving the problems.

Chapter-10  Circle

Beginning with the introduction to circles, tangent to a circle, several tangents from a point on a circle are some of the important topics covered in this chapter. This chapter being practical, there are an ample number of problems and solved examples for better understanding and practice purposes.

Chapter-11  Constructions

This chapter has more practical problems than theory-based definitions. Beginning with a general introduction to constructions, tools used, etc, the topics like division of a line segment, construction of tangents to a circle, and followed with few solved examples that help in solving the exercises provided after each topic.

Chapter-12  Areas related to Circles

This chapter problem is exclusively formula based wherein topics like perimeter and area of a circle- A Review, areas of sector and segment of a circle, areas of combinations of plane figures, and a page summary is provided just as a revision of the topics and formulas covered in the entire chapter and also there are many exercises and solved examples for practice purposes.

Chapter-13  Surface Areas and Volumes

Starting with the introduction, the surface area of a combination of solids, the volume of a combination of solids, conversion of solid from one shape to another, frustum of a cone, etc are to name a few topics explained in detail provided with a set of examples for a better comprehension of the concepts.

Chapter-14  Statistics

In this chapter starting with an introduction, topics like mean of grouped data, mode of grouped data, a median of grouped, graphical representation of cumulative frequency distribution are explained in detail with exercises for practice purposes. This chapter being a simple and easy subject, securing the marks is not difficult for students.

Chapter-15  Probability

Probability is another simple and important chapter in examination point of view and as seeking knowledge purposes as well. Beginning with an introduction to probability, an important topic called A theoretical approach is explained here. Since this chapter is one of the smallest in the syllabus and problems are also quite easy, students often like this chapter

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Case Study Class 10 Maths Questions and Answers (Download PDF)

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Case Study Class 10 Maths

If you are looking for the CBSE Case Study class 10 Maths in PDF, then you are in the right place. CBSE 10th Class Case Study for the Maths 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 or passage.

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

The Case Study Class 10 Maths Questions cover a wide range of chapters from the subject. Students willing to score good marks in their board exams can use it to practice questions during the exam preparation. The questions are highly interactive and it allows students to use their thoughts and skills to solve the given Case study questions.

Download Class 10 Maths Case Study Questions and Answers PDF (Passage Based)

Download links of class 10 Maths Case Study questions and answers pdf is given on this website. Students can download them for free of cost because it is going to help them to practice a variety of questions from the exam perspective.

Case Study questions class 10 Maths include all chapters wise questions. A few passages are given in the case study PDF of Maths. Students can download them to read and solve the relevant questions that are given in the passage.

Students are advised to access Case Study questions class 10 Maths CBSE chapter wise PDF and learn how to easily solve questions. 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 class 10 Maths questions.

Case Study Questions Class 10 Maths Chapter 1 Real Numbers

Case Study Questions Class 10 Maths Chapter 2 Polynomials

Case Study Questions Class 10 Maths Chapter 3 Pair of Equations in Two Variables

Case Study Questions Class 10 Maths Chapter 4 Quadratic Equations

Case Study Questions Class 10 Maths Chapter 5 Arithmetic Progressions

Case Study Questions Class 10 Maths Chapter 6 Triangles

Case Study Questions Class 10 Maths Chapter 7 Coordinate Geometry

Case Study Questions Class 10 Maths Chapter 8. Introduction to Trigonometry

Case Study Questions Class 10 Maths Chapter 9 Some Applications of Trigonometry

Case Study Questions Class 10 Maths Chapter 10 Circles

Case Study Questions Class 10 Maths Chapter 12 Areas Related to Circles

Case Study Questions Class 10 Maths Chapter 13 Surface Areas & Volumes

Case Study Questions Class 10 Maths Chapter 14 Statistics

Case Study Questions Class 10 Maths Chapter 15 Probability

How to Solve Case Study Based Questions Class 10 Maths?

In order to solve the Case Study Based Questions Class 10 Maths students are needed to observe or analyse the given information or data. Students willing to solve Case Study Based Questions are required to read the passage carefully and then solve them. 

While solving the class 10 Maths Case Study questions, the ideal way is to highlight the key information or given data. Because, later it will ease them to write the final answers. 

Case Study class 10 Maths consists of 4 to 5 questions that should be answered in MCQ manner. While answering the MCQs of Case Study, students are required to read the paragraph as they can get some clue in between related to the topics discussed.

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

Features Of Class 10 Maths Case Study Questions And Answers Pdf

Students referring to the Class 10 Maths Case Study Questions And Answers Pdf from Selfstudys will find these features:-

• Accurate answers of all the Case-based questions given in the PDF.
• Case Study class 10 Maths solutions are prepared by subject experts referring to the CBSE Syllabus of class 10.
• Free to download in Portable Document Format (PDF) so that students can study without having access to the internet.

Benefits of Using CBSE Class 10 Maths Case Study Questions and Answers

Since, CBSE Class 10 Maths Case Study Questions and Answers are prepared by our maths experts referring to the CBSE Class 10 Syllabus, it provided benefits in various way:-

• Case study class 10 maths helps in exam preparation since, CBSE Class 10 Question Papers contain case-based questions.
• It allows students to utilise their learning to solve real life problems.
• Solving case study questions class 10 maths helps students in developing their observation skills.
• Those students who solve Case Study Class 10 Maths on a regular basis become extremely good at answering normal formula based maths questions.
• By using class 10 Maths Case Study questions and answers pdf, students focus more on Selfstudys instead of wasting their valuable time.
• With the help of given solutions students learn to solve all Case Study questions class 10 Maths CBSE chapter wise pdf regardless of its difficulty level.

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Case Study Class 10 Maths Questions

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Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

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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• CBSE Practice Papers 2023
• Class 10 Maths Sample Papers 2024
• Competency Based Learning in CBSE Schools

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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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Top Case-Based Questions: Last Minute Prep for CBSE Class 10 Maths Exam

Cracking case studies: conquer your cbse class 10 maths exam (2023-24 session).

With the CBSE Class 10 board exams just around the corner ( March 11th, 2024 !), many students feel a surge of anxiety, especially when it comes to case-based questions in Maths. The lengthy descriptions can be daunting, making them seem complex. But fear not! Case-based questions are actually a great opportunity to showcase your problem-solving skills, provided your foundational concepts are strong.

This blog post is your one-stop guide to mastering case studies in your upcoming Maths exam. The CBSE board format incorporates 3 case study questions , each worth a total of 4 marks (broken down as 1+1+2). To help you ace these questions, I've compiled a list of practice problems directly from the official CBSE sample papers. By familiarizing yourself with these case studies before the big day, you'll be well-equipped to tackle them with confidence. So, let's dive in and conquer those case studies!

Also See: 🎯  Class 10 Maths (Standard) Topper's Answer Sheet (2023)  ✨

Q. No. 1) Manpreet Kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86m at the Asian Grand Prix in 2017 is the maximum distance for an Indian female athlete. Keeping her as a role model, Sanjitha is determined to earn gold in the Olympics one day.

Initially, her throw reached 7.56m only. Being an athlete in school, she regularly practiced both in the mornings and in the evenings and was able to improve the distance by 9cm every week.

During the special camp for 15 days, she started with 40 throws and every day kept increasing the number of throws by 12 to achieve this remarkable progress.

(i) How many throws Sanjitha practiced on 11th day of the camp?

(ii) What would be Sanjitha’s throw distance at the end of 6 weeks?

When will she be able to achieve a throw of 11.16 m?

(iii) How many throws did she do during the entire camp of 15 days?

Ans. (i) Number of throws during camp. a = 40; d = 12 𝑡 11 = 𝑎 + 10𝑑 = 40 + 10 × 12 = 160 𝑡ℎ𝑟𝑜𝑤𝑠

(ii) a = 7.56 m; d = 9cm = 0.09 m n = 6 weeks t n = a + (n-1)d = 7.56 + 6(0.09) = 7.56 + 0.54 Sanjitha’s throw distance at the end of 6 weeks = 8.1 m

a = 7.56 m; d = 9cm = 0.09 m t n =11.16 m t n = a + (n-1) d 11.16 = 7.56 + (n-1) (0.09) 3.6 = (n-1) (0.09) n-1 = 3.6/0.09 = 40 n = 41 Sanjitha’s will be able to throw 11.16 m in 41 weeks.

(iii) a = 40; d = 12; n = 15 S n = n / 2 [2a + (n-1) d] Sn = 15 / 2 [2(40) + (15-1) (12)] = 15 / 2 [80 + 168] = 15 / 2 [248] =1860 throws

Q. No. 2) Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane.

(i) At an instance, the midfielders and forward formed a parallelogram. Find the position of the central midfielder (D) if the position of other players who formed the parallelogram are:- A(1,2), B(4,3) and C(6,6)

(ii) Check if the Goal keeper G(-3,5), Sweeper H(3,1) and Wing-back K(0,3) fall on a same straight line.

Check if the Full-back J(5,-3) and centre-back I(-4,6) are equidistant from forward C(0,1) and if C is the mid-point of IJ.

(iii) If Defensive midfielder A(1,4), Attacking midfielder B(2,-3) and Striker E(a,b) lie on the same straight line and B is equidistant from A and E, find the position of E.

Ans. (i) Let D be (a,b), then

Mid point of AC = Midpoint of BD

4 + a = 7 and 3+ b = 8

a = 3 and b = 5

Central midfielder is at (3,5)

iii. A, B and E lie on the same straight line and B is equidistant from A and E

⇒ B is the mid-point of AE

1 + 𝑎 = 4 ; a = 3.

4+b = -6; b = -10

E is (3,-10)

Q. No. 3) One evening, Kaushik was in a park. Children were playing cricket. Birds were singing on a nearby tree of height 80m. He observed a bird on the tree at an angle of elevation of 45°.

When a sixer was hit, a ball flew through the tree frightening the bird to fly away. In 2 seconds, he observed the bird flying at the same height at an angle of elevation of 30° and the ball flying towards him at the same height at an angle of elevation of 60°.

(i) At what distance from the foot of the tree was he observing the bird sitting on the tree?

(ii) How far did the bird fly in the mentioned time?

After hitting the tree, how far did the ball travel in the sky when Kaushik saw the ball?

(iii) What is the speed of the bird in m/min if it had flown 20(√3 + 1) m?

Ans. i. tan 45° = 80/CE

⇒ 1/√3 = 80/CE

⇒ CE = 80√3

Distance the bird flew = AD = BE = CE-CB = 80√3 – 80 = 80(√3 -1) m

tan 60° = 80/CG

⇒ √3 = 80/CG

⇒ CG = 80/√3

Distance the ball travelled after hitting the tree =FA=GB = CB -CG

GB = 80 - 80 / √3 = 80 (1- 1 / √3 ) m

iii. Speed of the bird = distance/time = 20(√3 + 1)/2 m/sec = 10(√3 + 1)m/sec = 10(√3 + 1) x 60 m/min = 600(√3 + 1) m/min

Q. No. 4) An interior designer, Sana, hired two painters, Manan and Bhima to make paintings for her buildings. Both painters were asked to make 50 different paintings each.

The prices quoted by both the painters are given below:

• Manan asked for Rs 6000 for the first painting, and an increment of Rs 200 for each following painting.
• Bhima asked for Rs 4000 for the first painting, and an increment of Rs 400 for each following painting.

(i) How much money did Manan get for his 25th painting? Show your work.

(ii) How much money did Bhima get in all? Show your work.

(iii) If both Manan and Bhima make paintings at the same pace, find the first painting for which Bhima will get more money than Manan. Show your steps.

(iii) Sana's friend, Aarti hired Manan and Bhima to make paintings for her at the same rates as for Sana. Aarti had both painters make the same number of paintings, and paid them the exact same amount in total.

How many paintings did Aarti get each painter to make? Show your work.

Ans. i. Notes that the amounts Manan is paid for each painting forms an AP.

Takes a = 6000, d = 200 and n = 25 to find the amount as

6000 + (25 - 1)200 = Rs 10800.

ii. Finds the total amount earned by Bhima as follows:

S 50 = 50/2 [2(4000) + (50 - 1)(400)]

Solves the above expression to find the total amount as Rs 6,90,000.

iii. Frames equation as follows:

6000 + ( n - 1)200 = 4000 + ( n - 1)400

Solves the above equation to find the value of n as 11 .

Writes that, since they both earn the same amount for the 11th painting, as Bhima's increment is more, Bhima gets more money than Manan for the 12th painting.

Assumes that the number of paintings required is n .

Frames equation as follows:

S n (Manan) = S n (Bhima)

=> 𝑛/2 [2(6000) + ( n -1)200] = 𝑛/2 [2(4000) + ( n -1)400]

Solves the equation from step 1 to find n as 21.

Q. No. 5) In the game of archery, a bow is used to shoot arrows at a target board. The player stands far away from the board and aims the arrow so that it hits the board.

One such board, which is divided into 4 concentric circular sections, is drawn on a coordinate grid as shown. Each section carries different points as shown in the figure. If an arrow lands on the boundary, the inner section points are awarded.

(i) After shooting two arrows, Rohan scored 25 points.

Write one set of coordinates for each arrow that landed on the target.

(ii) If one player's arrow lands on (2, 2.5), how many points will be awarded to the player? Show your work.

(iii) One of Rohan’s arrow landed on (1.2, 1.6). He wants his second arrow to land on the line joining the origin and first arrow such that he gets 10 points for it.

Find one possible pair of coordinates of the second arrow's landing mark. Show your work.

(iii) An arrow landed on the boundary and is worth 20 points. The coordinates of the landing mark were of the form ( m , - m ).

Find all such coordinates. Show your steps.

Ans. i. Writes two pairs of possible coordinates such that Rohan scored 20 and 5 points for them. For examples, (1.5, 0) and (3.5, 0).

ii. Finds the distance of (2, 2.5) from (0, 0) as:

√(4 + 6.25) = √10.25 units

Hence, concludes that 5 points will be awarded.

iii. Finds the distance of (1.2, 1.6) from the origin as:

√{(1.2) 2 + (1.6) 2 } = 2 units

Assumes that the second arrow lands on the boundary mark and writes that the ratio in which the first arrow divides the origin and the second arrow's landing mark is the ratio of their radii = 2:1.

Assumes the coordinates of the second arrow's landing mark as ( x , y ) and uses section formula to write:

(2𝑥+0/3 , 2𝑦+0/3) = (1.2, 1.6)

Solves the above equation to find the values of the coordinates of the second arrow's landing mark as (1.8, 2.4).

Identifies the distance between the origin and the coordinate ( m , -m ) as 2 units and uses the distance formula to write the equation as:

m 2 + (- m ) 2 = 22

Simplifies the above equation as 2 m 2 = 4.

Solves the above equation to get y as √2 and (-√2).

Finds the coordinates as (√2, -√2) and (-√2, √2)

Q. No. 6) A drone, is an aircraft without any human pilot and is controlled by a remote-control device. Its various applications include policing, surveillance, photography, precision agriculture, forest fire monitoring, river monitoring and so on.

David used an advanced drone with high resolution camera during an expedition in a forest region which could fly upto 100 m height above the ground level. David rode on an open jeep to go deeper into the forest. The initial position of drone with respect to the open jeep on which David was riding is shown below.

David’s jeep started moving to enter the forest at an average speed of 10 m/s. He Simultaneously started flying the drone in the same direction as that of the jeep.

(i) David reached near one of the tallest trees in the forest. He stopped the drone at a horizontal distance of 5√3 m from the top of the tree and at a vertical distance of 65 m below its maximum vertical range.

If the angle of elevation of the drone from the top of the tree was 30°, find the height of the tree. Show your work.

(ii) The drone was flying at a height of 30√3 metres at a constant speed in the horizontal direction when it spotted a zebra near a pond, right below the drone.

The drone travelled for 30 metres from there and it could see the zebra, at the same place, at an angle of depression of θ from it.

Draw a diagram to represent this situation and find θ . Show you work.

(iii) After 2 minutes of starting the expedition both the drone and the jeep stopped at the same moment so that the drone can capture some images. The position of the drone and the jeep when they stopped is as shown below.

Find the average speed of the drone in m/s rounded off upto 2 decimal places. Show your work.

(iii) At some point during the expedition, David kept the drone stationary for some time to capture the images of a tiger. The angle of depression from the drone to the tiger changed from 30° to 45° in 3 seconds as shown below.

What was the average speed of the tiger during that time? Show your work.

(Note: Take √3 as 1.73.)

Ans. Assumes the vertical distance between the top of the tree and the drone to be h and finds h as:

h = 5√3 × tan 30° = 5√3 × 1/√3 = 5 m

Finds the height of the tree as 100 - 65 - 5 = 30 m

Finds the value of θ as:

tan θ = 30√3/30 = √3

Thus finds the value of θ as 60°

iii. Assumes the horizontal distance between the remote and the drone as x and finds its value as:

x = 50√3/tan60° = 50 m

Finds the distance covered by the jeep in 2 mins as:

10 × 120 = 1200 m

Finds the horizontal distance covered by the drone before it stopped as:

1200 + 50 = 1250 m

Finds the speed of the drone as:

1250/120 = 10.42 m/s

Assumes the horizontal distance between the drone and the tiger to be x when the angle of depression was 30° and finds the value of x as:

x = 54√3 × tan 30° = 54√3 × 1/√3 = 54 m

Assumes the horizontal distance between the drone and the tiger after 3 seconds as y and finds the value of y as:

y = 54√3 × tan 45° = 54√3 m

Finds the distance covered by the tiger in 3 seconds as:

54√3 - 54 = 39.42 m

Finds the average speed of the tiger during that time as:

39.42/3 = 13.14 m/s

Q. No. 7) Shown below is the trophy shield Akshi received on winning an international Table tennis tournament. The trophy is made of a glass sector DOC supported by identical wooden right triangles ∆ DAO and ∆ COB. Also, AO = 7 cm and AO : DA = 1 ∶ √3 (Use √3 = 1.73)

Based on the given information, answer the following questions:

(i) Find ∠𝐷𝑂𝐶

(ii) Find the area of the wooden triangles

(iii) Find the area of the shape formed by the glass portion

If Akshi wants to decorate the boundary of the glass portion with glitter tape, then find the length of the tape she needs.

Ans. (i) Let ∠𝐷𝑂𝐴 = 𝜃, then tan 𝜃 =𝐴𝐷/𝐴𝑂 = √3/1 ⟹ 𝜃 = 60° ∠𝐷𝑂𝐴 = ∠𝐶𝑂𝐵 = 60° ∠𝐷𝑂𝐶 = 180° − (60° + 60°) = 60°

(ii) Area of two wooden triangles = 2 × 1/2 × 7 × 7√3 = 84.77 𝑐𝑚 2 (iii) 𝐴𝑂/𝐷𝑂 = cos 60° ⟹ 7/𝐷𝑂 = 1/2 ⟹ 𝐷𝑂 = 14 𝑐𝑚 Area of sector 𝐷𝑂𝐶 = 60/360 × 𝜋 × 14 2 = 102.67 𝑐𝑚 2

𝐴𝑂/𝐷𝑂 = cos 60° ⟹ 7/𝐷𝑂 = 1/2 ⟹ 𝐷𝑂 = 14 𝑐𝑚 Length of tape required = 2 × 14 + 60/360 × 2 × 𝜋 × 14 = 42.67 cm

Q. No. 8) A school auditorium has to be constructed with a capacity of 2000 people. The chairs in the auditorium are arranged in a concave shape facing towards the stage in such a way that each succeeding row has 5 seats more than the previous one.

(i) If the first row has 15 seats, then how many seats will be there in 12 th row?

(ii) If there are 15 rows in the auditorium, then how many seats will be there in the middle row?

(iii) If total 1875 guests were there in the auditorium for a particular event, then how many rows will be needed to make all of them sit?

If total 1250 guests were there in the auditorium for a particular event, then how many rows will be left blank out of total 30 rows?

Ans. (i) 𝑎 = 15, 𝑑 = 5

𝑎 12 = 15 + 11×5 = 70

(ii) 𝑛 = 15

Middle row = 8th row

𝑎8 = 15 + 7 × 5 = 50

(iii) 1875 = 𝑛/2 [2 × 15 + (𝑛 − 1) × 5]

⟹ 𝑛 2 + 5𝑛 − 750 = 0

⟹ (𝑛 + 30)(𝑛 − 25) = 0 ⟹ 𝑛 = 25

∴ Total number of rows required = 25

1250 = 𝑛/2 [2×15 +(𝑛 − 1) × 5]

⟹ 𝑛 2 + 5𝑛 − 500 = 0

(𝑛 + 25)(𝑛 − 20) = 0 ⟹ 𝑛 = 20

∴ Number of rows left = 30 − 20 = 10

Q. No. 9) The students of Class X of a secondary school have been allotted a rectangular plot of land for their gardening activity. Saplings are being planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to row seeds of the flowering plant on the remaining area of the plot.

(i) If a tree is to be planted exactly in the middle of the triangle PQR ie. at the centroid of ∆PQR to give shed to the people sitting in the lawn, then find the coordinates of the point where the tree should be planted.

(ii) What type of triangle is formed by the grassy lawn?

(iii) Find the area of the plot in which the students have to row the seeds.

If a special flowering plant has to be planted at a point which divides the line joining the points C and Q in the ratio 2:3, then find the coordinates of the point where this plant will be planted

Ans. (i) 𝑃(3,3), 𝑄(8,2), 𝑅(6,5)

Coordinates of required point are ( 3+8+6/3, 3+2+5/3) = ( 17/3 , 10/3 )

(ii) 𝑃𝑅 = 𝑄𝑅 = √13

𝑃𝑄 2 = 𝑃𝑅 2 + 𝑄𝑅 2

∴ ∆ 𝑃𝑄𝑅 is an isosceles right triangle

(iii) Area of the plot to row seeds = 13 × 9 − 1/2 × √13 × √13 = 110.5 𝑚

Coordinates of required point are ( 2×8 + 3 ×13 / 2+3 , 2×2+3×9 / 2+3 ) = (11, 31/5 )

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CBSE Class 10 Maths Case Study Questions for Chapter 9 - Some Applications of Trigonometry (Published By CBSE)

Check case study questions for cbse class 10 maths chapter 9 - some applications of trigonometry. these questions are published by the cbse itself for class 10 students..

Case study based questions are new for class 10 students. Therefore, it is quite essential that students practice with more of such questions so that they do not have problem in solving them in their Maths board exam. We have provided here the case study questions for CBSE Class 10 Maths Chapter 9 - Some Applications of Trigonometry. All these questions have been published by the Central Board of Secondary Education (CBSE) for the class 10 students. Therefore, students must solve all the questions seriously so that they may score the desired marks in their Maths exam.

Check Case Study Questions for Class 10 Maths Chapter 9:

CASE STUDY 1:

A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919. The teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42 metres) in height.

1. What is the angle of elevation if they are standing at a distance of 42m away from the monument?

Answer: b) 45 o

2. They want to see the tower at an angle of 60 o . So, they want to know the distance where they should stand and hence find the distance.

Answer: a) 25.24 m

3. If the altitude of the Sun is at 60 o , then the height of the vertical tower that will cast a shadow of length 20 m is

a) 20√3 m

b) 20/ √3 m

c) 15/ √3 m

d) 15√3 m

Answer: a) 20√3 m

4. The ratio of the length of a rod and its shadow is 1:1. The angle of elevation of the Sun is

5. The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level is

a) corresponding angle

b) angle of elevation

c) angle of depression

d) complete angle

Answer: a) corresponding angle

CASE STUDY 2:

A Satellite flying at height h is watching the top of the two tallest mountains in Uttarakhand and Karnataka, them being Nanda Devi(height 7,816m) and Mullayanagiri (height 1,930 m). The angles of depression from the satellite, to the top of Nanda Devi and Mullayanagiri are 30° and 60° respectively. If the distance between the peaks of the two mountains is 1937 km, and the satellite is vertically above the midpoint of the distance between the two mountains.

1. The distance of the satellite from the top of Nanda Devi is

a) 1139.4 km

b) 577.52 km

d) 1025.36 km

Answer: a) 1139.4 km

2. The distance of the satellite from the top of Mullayanagiri is

Answer: c) 1937 km

3. The distance of the satellite from the ground is

Answer: b) 577.52 km

4. What is the angle of elevation if a man is standing at a distance of 7816m from Nanda Devi?

5.If a mile stone very far away from, makes 45 o to the top of Mullanyangiri mountain. So, find the distance of this mile stone from the mountain.

a) 1118.327 km

b) 566.976 km

Also Check:

Case Study Questions for All Chapters of CBSE Class 10 Maths

Tips to Solve Case Study Based Questions Accurately

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Class 10 Maths Case Study Questions Chapter 2 Polynomials

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Case study Questions in the Class 10 Mathematics Chapter 2  are very important to solve for your exam. Class 10 Maths Chapter 2 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 2  Polynomials

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.

Polynomials Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 2 Polynomials

Case Study/Passage-Based Questions

Question 1:

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 indoors on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of a parabola representing quadratic polynomial.

1. The shape of the path traced shown is

d) Parabola

Answer: d) Parabola

2. The graph of parabola opens upwards, if _______

b) a < 0

c) 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) x3 + 2×2 – 5x – 6

Answer: (b) parabolic

(ii) The expression of the polynomial represented by the graph is

Answer: (c) x2-36

(iii) Find the value of the polynomial represented by the graph when x = 6.

Answer: (c) 0

(iv) The sum of zeroes of the polynomial x 2  + 2x – 3 is

Answer: (b) -2

(v) If the sum of zeroes of polynomial at 2  + 5t + 3a is equal to their product, then find the value of a.

Answer:  (d) −53

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 2 Polynomials with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Polynomials 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 Coordinate Geometry Case Study Questions 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

(ii) How far is the library from Shaguns house?

(iii) How far is the library from Alia's house?

(iv) Which of the following is true?

(v) How far is the school from Alia's house than Shaguns house?

(ii) The value of x is equal to

(iii) If M is any point exactly in between city A and city B, then coordinates of M are

(iv) The ratio in which A divides the line segment joining the points O and M is

(v) If the person analyse the petrol at the point M(the mid point of AB), then what should be his decision?

(ii) The distance of the bus stand from the house is

(iii) If the grocery store and electrician's shop lie on a line, the ratio of distance of house from grocery store to that from electrician's shop, is

(iv) The ratio of distances of house from bus stand to food cart is

(v) The coordinates of positions of bus stand, grocery store, food cart and electrician's shop form a

(ii) The centre of circle is the

(iii) The radius of the circle is

(iv) The area of the circle is

(v) If  \(\left(1, \frac{\sqrt{7}}{3}\right)\)   is one of the ends of a diameter, then its other end is

(ii) If S be the mid-point of line joining P and Q, then coordinates of S are

(iii) If T be the mid-point of line joining Rand Q, then coordinates of T are

(iv) If Ube the mid-point of line joining Rand P, then coordinates of U are

(v) The coordinates of centroid of \(\Delta\) STU are

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

Cbse 10th standard maths subject coordinate geometry case study questions 2021 answer keys.

(i) (d): Since the coordinates of A and Bare (2, 3) and (2, 1) respectively. \(\therefore\) Required distance = AB \(=\sqrt{(2-2)^{2}+(1-3)^{2}}=\sqrt{2^{2}}=2 \text { units }\) (ii) (b): Since, library is situated at C(4, 1) \(\therefore\) Required distance = BC \(=\sqrt{(4-2)^{2}+(1-1)^{2}}=\sqrt{2^{2}+0^{2}}=2 \text { units }\) (iii) (d): Required distance = AC \(=\sqrt{(4-2)^{2}+(1-3)^{2}}=\sqrt{2^{2}+2^{2}}=2 \sqrt{2} \text { units }\) (iv) (b): Since AB = BC \(\neq\) AC, therefore \(\Delta\) ABC is an isosceles triangle. (v) (d): Distance between O and A \(=\sqrt{2^{2}+3^{2}}=\sqrt{4+9}=\sqrt{13} \text { units }\) and distance between O and B = \(\sqrt{2^{2}+1^{2}}=\sqrt{4+1}=\sqrt{5} \text { units }\) Thus, required distance =  \((\sqrt{13}-\sqrt{5}) \text { units }\)

(i) (a): We have, OA = 2 \(\sqrt{2}\) km \(\Rightarrow \sqrt{2^{2}+y^{2}}=2 \sqrt{2} \) \(\Rightarrow 4+y^{2}=8 \Rightarrow y^{2}=4 \) \(\Rightarrow y=2 \quad(\because y=-2 \text { is not possible })\) (ii) (c): We have OB = 8 \(\sqrt{2}\) \(\Rightarrow \sqrt{x^{2}+8^{2}}=8 \sqrt{2} \) \(\Rightarrow x^{2}+64=128 \Rightarrow x^{2}=64 \) \(\Rightarrow x=8 \quad(\because x=-8 \text { is not possible })\) (iii) (c) : Coordinates of A and Bare (2, 2) and (8, 8) respectively, therefore coordinates of point M are \(\left(\frac{2+8}{2}, \frac{2+8}{2}\right)\) i.e .,(5.5) (iv) (d): Let A divides OM in the ratio k: 1.Then \(2=\frac{5 k+0}{k+1} \Rightarrow 2 \mathrm{k}+2=5 k \Rightarrow 3 k=2 \Rightarrow k=\frac{2}{3}\) \(\therefore\) Required ratio = 2 : 3 (v) (b): Since M is the mid-point of A and B therefore AM = MB. Hence, he should try his luck moving towards B.

(i) (c): Required coordinates are  \(\left(0, \frac{4}{3}\right)\) (ii) (c) (iii) (a): Radius = Distance between (0,0) and  \(\left(\frac{4}{3}, 0\right)\) \(=\sqrt{\left(\frac{4}{3}\right)^{2}+0^{2}}=\frac{4}{3} \text { units }\) (iv) (b): Area of circle = \(\pi\) (radius) 2 \(=\pi\left(\frac{4}{3}\right)^{2}=\frac{16}{9} \pi \text { sq. units }\) (v) (d): Let the coordinates of the other end be (x,y). Then (0,0) will bethe mid-point of  \(\left(1, \frac{\sqrt{7}}{3}\right)\)  and (x, y). \(\therefore\left(\frac{1+x}{2}, \frac{\frac{\sqrt{7}}{3}+y}{2}\right)=(0,0) \) \(\Rightarrow \frac{1+x}{2}=0 \text { and } \frac{\frac{\sqrt{7}}{3}+y}{2}=0 \) \(\Rightarrow x=-1 \text { and } y=-\frac{\sqrt{7}}{3}\) Thus, the coordinates of other end be  \(\left(-1, \frac{-\sqrt{7}}{3}\right)\)

(i) (c): We have, P( -3,4), Q(3, 4) and R( -2, -1). \(\therefore\) Coordinates of centroid of \(\Delta\) PQR \(=\left(\frac{-3+3-2}{3}, \frac{4+4-1}{3}\right)=\left(\frac{-2}{3}, \frac{7}{3}\right)\) (ii) (d): Coordinates of S=  \(\left(\frac{-3+3}{2}, \frac{4+4}{2}\right)=(0,4)\) (iii) (c): Coordinates of T=  \(\left(\frac{-2+3}{2}, \frac{-1+4}{2}\right)=\left(\frac{1}{2}, \frac{3}{2}\right)\) (iv) (a): Coordinates of U =  \(\left(\frac{-2-3}{2}, \frac{-1+4}{2}\right)=\left(\frac{-5}{2}, \frac{3}{2}\right)\) (v) (c): The centroid of triangle formed by joining the mid-points of sides of given triangle is same as that of the given trangle. So, centroid of  \(\Delta S T U=\left(\frac{-2}{3}, \frac{7}{3}\right)\)

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