case studies class 10 maths

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CBSE Class 10 Maths Case Study

CBSE Board has introduced the case study questions for the ongoing academic session 2021-22. The board will ask the paper on the basis of a different exam pattern which has been introduced this year where 50% syllabus is occupied for MCQ for Term 1 exam. Selfstudys has provided below the chapter-wise questions for CBSE Class 10 Maths. Students must solve these case study based problems as soon as they are done with their syllabus. 

These case studies are in the form of Multiple Choice Questions where students need to answer them as asked in the exam. The MCQs are not that difficult but having a deep and thorough understanding of NCERT Maths textbooks are required to answer these. Furthermore, we have provided the PDF File of CBSE Class 10 maths case study 2021-2022.

Class 10 Maths (Formula, Case Based, MCQ, Assertion Reason Question with Solutions)

In order to score good marks in the term 1 exam students must be aware of the Important formulas, Case Based Questions, MCQ and Assertion Reasons with solutions. Solving these types of questions is important because the board will ask them in the Term 1 exam as per the changed exam pattern of CBSE Class 10th.

Important formulas should be necessarily learned by the students because the case studies are solved with the help of important formulas. Apart from that there are assertion reason based questions that are important too. 

Assertion Reasoning is a kind of question in which one statement (Assertion) is given and its reason is given (Explanation of statement). Students need to decide whether both the statement and reason are correct or not. If both are correct then they have to decide whether the given reason supports the statement or not. In such ways, assertion reasoning questions are being solved. However, for doing so and getting rid of confusions while solving. Students are advised to practice these as much as possible.

For doing so we have given the PDF that has a bunch of MCQs questions based on case based, assertion, important formulas, etc. All the Multiple Choice problems are given with detailed explanations.

CBSE Class 10th Case study Questions

Recently CBSE Board has the exam pattern and included case study questions to make the final paper a little easier. However, Many students are nervous after hearing about the case based questions. They should not be nervous because case study are easy and given in the board papers to ease the Class 10th board exam papers. However to answer them a thorough understanding of the basic concepts are important. For which students can refer to the NCERT textbook.

Basically, case study are the types of questions which are developed from the given data. In these types of problems, a paragraph or passage is given followed by the 5 questions that are given to answer . These types of problems are generally easy to answer because the data are given in the passage and students have to just analyse and find those data to answer the questions.

CBSE Class 10th Assertion Reasoning Questions

These types of questions are solved by reading the statement, and given reason. Sometimes these types of problems can make students confused. To understand the assertion and reason, students need to know that there will be one statement that is known as assertion and another one will be the reason, which is supposed to be the reason for the given statement. However, it is students duty to determine whether the statement and reason are correct or not. If both are correct then it becomes important to check, does reason support the statement? 

Moreover, to solve the problem they need to look at the given options and then answer them.

CBSE Class 10 Maths Case Based MCQ

CBSE Class 10 Maths Case Based MCQ are either Multiple Choice Questions or assertion reasons. To solve such types of problems it is ideal to use elimination methods. Doing so will save time and answering the questions will be much easier. Students preparing for the board exams should definitely solve these types of problems on a daily basis.

Also, the CBSE Class 10 Maths MCQ Based Questions are provided to us to download in PDF file format. All are developed as per the latest syllabus of CBSE Class Xth.

Class 10th Mathematics Multiple Choice Questions

Class 10 Mathematics Multiple Choice Questions for all the chapters helps students to quickly revise their learnings, and complete their syllabus multiple times. MCQs are in the form of objective types of questions whose 4 different options are given and one of them is a true answer to that problem. Such types of problems also aid in self assessment.

Case Study Based Questions of class 10th Maths are in the form of passage. In these types of questions the paragraphs are given and students need to find out the given data from the paragraph to answer the questions. The problems are generally in Multiple Choice Questions.

The Best Class 10 Maths Case Study Questions are available on Selfstudys.com. Click here to download for free.

To solve Class 10 Maths Case Studies Questions you need to read the passage and questions very carefully. Once you are done with reading you can begin to solve the questions one by one. While solving the problems you have to look at the data and clues mentioned in the passage.

In Class 10 Mathematics the assertion and reasoning questions are a kind of Multiple Choice Questions where a statement is given and a reason is given for that individual statement. Now, to answer the questions you need to verify the statement (assertion) and reason too. If both are true then the last step is to see whether the given reason support=rts the statement or not.

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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

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myCBSEguide App

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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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 Case Study Questions for Class 10 Maths Real Numbers Free PDF

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

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

CBSE Case Study Questions for Class 10 Maths Real Numbers PDF

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Class 10 Maths Case Study Questions of Chapter 1 Real Numbers

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

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

Real Numbers Case Study Questions With Answers

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

Case Study/Passage-Based Questions

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

Answer: (d) no value of n

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

Answer: (c) for all n > 1 

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

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

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

Answer: (a) always true

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

Answer: (d) 8

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

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

Answer: (b) LCM = pq2 x HCF

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

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

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

Answer: (d) 17

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

Answer: (b) 12599

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

Answer: (a) 3

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

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

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

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

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

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

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

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CBSE Class 10 Maths Case Study Questions for Chapter 7 - Coordinate Geometry (Released By CBSE)

Cbse's question bank on case study for class 10 maths chapter 7 is available here. practice this new type of questions to score good marks in your board exam..

Case study based questions for CBSE Class 10 Maths Chapter 7 - Coordinate Geometry are provided here for students to practice this new format of questions for their Maths Board Exam 2022. All these questions are published by the Central Board of Secondary Education (CBSE) for Class 10 Maths. Students must solve these questions to familiarise themselves with the concepts and logic used in the case study. You can also check the right answer at the end of each question.

Check Case Study Questions for Class 10 Maths Chapter 7 - Coordinate Geometry

CASE STUDY 1:

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th distance AD on the eighth line and posts a red flag.

1. Find the position of green flag

b) (2,0.25)

d) (0, -25)

Answer:  a) (2,25)

2. Find the position of red flag

Answer: c) (8,20)

3. What is the distance between both the flags?

a) √41

b) √11

c) √61

d) √51

Answer: c) √61

4. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

a) (5, 22.5)

d) (2.5,20)

Answer: a) (5, 22.5)

5. If Joy has to post a flag at one-fourth distance from green flag , in the line segment joining the green and red flags, then where should he post his flag?

a) (3.5,24)

b) (0.5,12.5)

c) (2.25,8.5)

Answer: a) (3.5,24)

CASE STUDY 2:

The class X students school in krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer: a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer: c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer: d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer: a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer: d) 4.5

Also Check:

Tips to Solve Case Study Based Questions Accurately

CBSE Class 10 Maths Best Study Material for 2021-2022

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CBSE Class 10 Mathematics Question Papers 2024

The CBSE Class 10 Mathematics exam was conducted on 11th March 2024. The duration of the CBSE Class 10 Mathematics Question Paper 2024 was 3 hours with 80 marks. Students who appeared for the exam found that the Mathematics question paper was moderately complex.

The question paper was framed in a way to test the student’s understanding of mathematical concepts and their applications. The length of the question paper was appropriate. The students who had concept clarity and practised enough before the exam could finish well before time and got enough time to review the solutions before submission.

Class 10 Mathematics Answer Key 2024

Practising the Class 10 Mathematics Question Paper 2024 is one of the most effective ways to prepare for an examination. Practising a good set of previous years’ question papers is no less than a treasure chest for a student preparing for board exams.

Students can download different sets of CBSE Class 10 Mathematics Question Paper 2024 in PDF format from the links given below:

CBSE Class 10 Mathematics Question Paper 2024 – All Sets

The download link lets students access the CBSE Class 10 Mathematics Question Paper 2024.

Note: CBSE Class 10 Mathematics 2024 Question Paper and Solutions PDFs will be updated soon.

Access Other Sets of CBSE Class 10 Mathematics Question Paper 2024

The other sets of CBSE Class 10 Mathematics Previous Years Question Paper 2024 are given here for free download. Click on the download link to access and download the papers in PDF formats.

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CBSE 10th Standard Maths Subject Arithmetic Progressions Case Study Questions With Solution 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) Find the sum of common difference of the two progressions.

(iii) Find the 19 th term of the progression written by Geeta.

(iv) Find the sum of first 10 terms of the progression written by Geeta.

(v) Which term of the two progressions will have the same value?

(ii) What is the total amount saved by Anuj in 8 days?

(iii) What is the amount saved by Anuj on 30 th day?

(iv) What is the total amount saved by him in the month of June, if he starts savings from 1 st June?

(v) On which day, he save tens times as much as he saved on day-I?

(ii) The number on first card is

(iii) What is the number on the 19 th card?

(iv) What is the number on the 23 rd card?

(v) The sum of numbers on the first 15 cards is 

A sequence is an ordered list of numbers. A sequence of numbers such that the difference between the consecutive terms is constant is said to be an arithmetic progression (A.P.). On the basis of above information, answer the following questions. (i) Which of the following sequence is an A.P.?

(ii) If x, y and z are in A.P., then

(iii) If a 1  a 2 , a 3  ..... , a n are in A.P., then which of the following is true?

(iv) If the n th term (n > 1) of an A.P. is smaller than the first term, then nature of its common difference (d) is

(v) Which of the following is incorrect about A.P.?

(ii) What is the first term?

(iii) Which term of the A.P. is -160?

(iv) Which of the following is not a term of the given A.P.?

(v) What is the 75 th term of the A.P.?

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