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Case Study Class 10 Maths Questions

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Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

• Real Numbers Case Study Question
• Polynomials Case Study Question
• Pair of Linear Equations in Two Variables Case Study Question
• Quadratic Equations Case Study Question
• Arithmetic Progressions Case Study Question
• Triangles Case Study Question
• Coordinate Geometry Case Study Question
• Introduction to Trigonometry Case Study Question
• Some Applications of Trigonometry Case Study Question
• Circles Case Study Question
• Area Related to Circles Case Study Question
• Surface Areas and Volumes Case Study Question
• Statistics Case Study Question
• Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

• Find the production in the 1 st year.
• Find the production in the 12 th year.
• Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

• Find the distance between Lucknow (L) to Bhuj(B).
• If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
• Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

• Find the distance PA.
• Find the distance PB
• Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

• What is the length of the line segment joining points B and F?
• The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
• What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

• If the first circular row has 30 seats, how many seats will be there in the 10th row?
• For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
• If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

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

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

More Case Study Questions

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

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

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

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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• CBSE Class 10 Maths Sample Paper 2020-21
• Class 12 Maths Case Study Questions
• CBSE Reduced Syllabus Class 10 (2020-21)
• Class 10 Maths Basic Sample Paper 2024
• How to Revise CBSE Class 10 Maths in 3 Days
• CBSE Practice Papers 2023
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• Competency Based Learning in CBSE Schools

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CBSE 10th Standard Maths Subject Case Study Questions With Solution 2021 Part - II

By QB365 on 21 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) Proportional expense for each person is

(iii) The fixed (or constant) expense for the party is

(iv) If there would be 15 guests at the lunch party, then what amount Mr Jindal has to pay?

(v) The system of linear equations representing both the situations will have

(ii) Represent the situation faced by Suman, algebraically

(iii) The price of one Physics book is

(iv) The price of one Mathematics book is

(v) The system of linear equations represented by above situation, has

(ii) Represent algebraically the situation of day- II.

(iii) The linear equation represented by day-I, intersect the x axis at

(iv) The linear equation represented by day-II, intersect the y-axis at

(v) Linear equations represented by day-I and day -II situations, are

Amit is preparing for his upcoming semester exam. For this, he has to practice the chapter of Quadratic Equations. So he started with factorization method. Let two linear factors of  \(a x^{2}+b x+c \text { be }(p x+q) \text { and }(r x+s)\) \(\therefore a x^{2}+b x+c=(p x+q)(r x+s)=p r x^{2}+(p s+q r) x+q s .\) Now, factorize each of the following quadratic equations and find the roots. (i) 6x 2 + x - 2 = 0

(ii) 2x 2 -+ x - 300 = 0

(iii) x 2 -  8x + 16 = 0

(iv) 6x 2 -  13x + 5 = 0

(v) 100x 2 - 20x + 1 = 0

(ii) Difference of pairs of shoes in 17 th  row and 10 th row is

(iii) On next day, she arranges x pairs of shoes in 15 rows, then x =

(iv) Find the pairs of shoes in 30 th row.

(v) The total number of pairs of shoes in 5 th and 8 th row is

(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) Find the radius of the core.

(iii) S 2 =

(iv) What is the diameter of roll when one tissue sheet is rolled over it?

(v) Find the thickness of each tissue sheet

(ii) Distance travelled by aeroplane towards west after   \(1 \frac{1}{2}\)   hr is

(iii) In the given figure, \(\angle\) POQ is 

(iv) Distance between aeroplanes after  \(1 \frac{1}{2}\)   hr is

(v) Area of \(\Delta\) POQ is

(ii) The value of x is

(iii) The value of PR is 

(iv) The value of RQ is 

(v) How much distance will be saved in reaching city Q after the construction of highway? 

(ii) Length of BC =

(iii) Length of AD =

(iv) Length of ED = 

(v) Length of AE = 

(ii) The value of x + y is 

(iii) Which of the following is true?

(iv) The ratio in which B divides AC is

(v) Which of the following equations is satisfied by the given points?

(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 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) The distance between A and Cis

(iii) If it is assumed that both buses have same speed, then by which bus do you want to travel from A to B?

(iv) If the fare for first bus is Rs10/km, then what will be the fare for total journey by that bus?

(v) If the fare for second bus is Rs 15/km, then what will be the fare to reach to the destination by this bus?

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

Cbse 10th standard maths subject case study questions with solution 2021 part - ii answer keys.

(i) (a): 1 st situation can be represented as x + 7y = 650 ...(i) and 2 nd situation can be represented as x + 11y = 970 ...(ii) (ii) (b): Subtracting equations (i) from (ii), we get  \(4 y=320 \Rightarrow y=80\) \(\therefore\)  Proportional expense for each person is Rs 80. (iii) (c): Puttingy = 80 in equation (i), we get x + 7 x 80 = 650 \(\Rightarrow\) x = 650 - 560 = 90 \(\therefore\)  Fixed expense for the party is Rs 90 (iv) (d): If there will be 15 guests, then amount that Mr Jindal has to pay = Rs (90 + 15 x 80) = Rs 1290 (v) (a): We have a 1  = 1, b 1  = 7, c 1  = -650 and  \(a_{2}=1, b_{2}=11, c_{2}=-970 \) \(\therefore \frac{a_{1}}{a_{2}}=1, \frac{b_{1}}{b_{2}}=\frac{7}{11}, \frac{c_{1}}{c_{2}}=\frac{-650}{-970}=\frac{65}{97}\) \(\text { Here, } \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}\) Thus, system of linear equations has unique solution.

(i) (a): Situation faced by Sudhir can be represented algebraically as 2x + 3y = 850 (ii) (b): Situation faced by Suman can be represented algebraically as 3x + 2y = 900 (iii) (c) : We have 2x + 3y = 850 .........(i) and 3x + 2y = 900 .........(ii) Multiplying (i) by 3 and (ii) by 2 and subtracting, we get 5y = 750 \(\Rightarrow\)   Y = 150 Thus, price of one Physics book is Rs 150. (iv) (d): From equation (i) we have, 2x + 3 x 150 = 850 \(\Rightarrow\) 2x = 850 - 450 = 400 \(\Rightarrow\) x = 200 Hence, cost of one Mathematics book = Rs 200 (v) (a): From above, we have \(a_{1} =2, b_{1}=3, c_{1}=-850 \) \(\text { and } a_{2} =3, b_{2}=2, c_{2}=-900\) \(\therefore \quad \frac{a_{1}}{a_{2}}=\frac{2}{3}, \frac{b_{1}}{b_{2}}=\frac{3}{2}, \frac{c_{1}}{c_{2}}=\frac{-850}{-900}=\frac{17}{18} \Rightarrow \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}\) Thus system of linear equations has unique solution.

(i) (b): Algebraic representation of situation of day-I is 2x + y = 1600. (ii) (a): Algebraic representation of situation of day- II is 4x + 2y = 3000 \(\Rightarrow\) 2x + y = 1500. (iii) (c) : At x-axis, y = 0 \(\therefore\)   At y = 0, 2x + y = 1600 becomes 2x = 1600 \(\Rightarrow\) x = 800 \(\therefore\) Linear equation represented by day- I intersect the x-axis at (800, 0). (iv) (d) : At y-axis, x = 0 \(\therefore\) 2x + Y = 1500 \(\Rightarrow\)  y = 1500 \(\therefore\) Linear equation represented by day-II intersect the y-axis at (0, 1500). (v) (b): We have, 2x + y = 1600 and 2x + y = 1500 Since  \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} \text { i.e., } \frac{1}{1}=\frac{1}{1} \neq \frac{16}{15}\) \(\therefore\) System of equations have no solution. \(\therefore\) Lines are parallel.

(i) (b): We have  \(6 x^{2}+x-2=0\) \(\Rightarrow \quad 6 x^{2}-3 x+4 x-2=0 \) \(\Rightarrow \quad(3 x+2)(2 x-1)=0 \) \(\Rightarrow \quad x=\frac{1}{2}, \frac{-2}{3}\) (ii) (c):  \(2 x^{2}+x-300=0\) \(\Rightarrow \quad 2 x^{2}-24 x+25 x-300=0 \) \(\Rightarrow \quad(x-12)(2 x+25)=0 \) \(\Rightarrow \quad x=12, \frac{-25}{2}\) (iii) (d):   \(x^{2}-8 x+16=0\) \(\Rightarrow(x-4)^{2}=0 \Rightarrow(x-4)(x-4)=0 \Rightarrow x=4,4\) (iv) (d):   \(6 x^{2}-13 x+5=0\) \(\Rightarrow \quad 6 x^{2}-3 x-10 x+5=0 \) \(\Rightarrow \quad(2 x-1)(3 x-5)=0 \) \(\Rightarrow \quad x=\frac{1}{2}, \frac{5}{3}\) (v) (a):  \(100 x^{2}-20 x+1=0\) \(\Rightarrow(10 x-1)^{2}=0 \Rightarrow x=\frac{1}{10}, \frac{1}{10}\)  

Number of pairs of shoes in 1 st , 2 nd , 3 rd row, ... are 3,5,7, ... So, it forms an A.P. with first term a = 3, d = 5 - 3 = 2 (i) (d): Let n be the number of rows required. \(\therefore S_{n}=120 \) \(\Rightarrow \quad \frac{n}{2}[2(3)+(n-1) 2]=120 \) \(\Rightarrow \quad n^{2}+2 n-120=0 \Rightarrow n^{2}+12 n-10 n-120=0\) \(\Rightarrow \quad(n+12)(n-10)=0 \Rightarrow n=10\) So, 10 rows required to put 120 pairs. (ii) (b): No. of pairs in 1ih row = t 17 = 3 + 16(2) = 35 No. of pairs in 10th row = t 10  = 3 + 9(2) = 21 \(\therefore\) Required difference = 35 - 21 = 14 (iii) (c) : Here n = 15 \(\therefore\) t 15  = 3 + 14(2) = 3 + 28 = 31 (iv) (a): No. of pairs in 30 th row = t 30 = 3 +29(2) = 61 (v) (c): No. of pairs in 5 th row = t 5  = 3 + 4(2) = 11 No. of pairs in 8 th row = t 8  = 3 + 7(2) = 17 \(\therefore\) Required sum = 11 + 17 = 28

Let the numbers on the cards be a, a + d, a + Zd, ... According to question, We have (a + 5d) + (a + 13d) = -76 \(\Rightarrow\) 2a+18d = -76 \(\Rightarrow\) a + 9d= -38 ... (1) And (a + 7d) + (a + 15d) = -96 \(\Rightarrow\) 2a + 22d = -96 \(\Rightarrow\) a + 11d = -48 ...(2) From (1) and (2), we get 2d= -10 \(\Rightarrow\) d= -5 From (1), a + 9(-5) = -38 \(\Rightarrow\) a = 7 (i) (b): The difference between the numbers on any two consecutive cards = common difference of the A.P.=-5 (ii) (d): Number on first card = a = 7 (iii) (b): Number on 19th card = a + 18d = 7 + 18(-5) = -83 (iv) (a): Number on 23rd card = a + 22d = 7 + 22( -5) = -103 (v) (d):  \(S_{15}=\frac{15}{2}[2(7)+14(-5)]=-420\)

(i) (c) (ii) (c) (iii) (d) (iv) (b) (v) (c)

Here S n = 0.1n 2 + 7.9n (i) (c): S n -1 = 0.1(n - 1) 2 + 7.9(n - 1) = 0.1n 2 + 7.7n - 7.8 (ii) (b): S 1 = t 1  = a = 0.1(1) 2 + 7.9(1) = 8 cm = Diameter of core So, radius of the core = 4 cm (iii) (a): S 2 = 0.1(2) 2 + 7.9(2) = 16.2 (iv) (d): Required diameter = t 2 = S 2 - S 1 = 16.2 - 8 = 8.2 cm (v) (c): As d = t 2 - t 1  = 8.2 - 8 = 0.2 cm So, thickness of tissue = 0.2 \(\div\)   2 = 0.1 cm = 1 mm

(i) (a): Speed = 1200 km/hr \(\text { Time }=1 \frac{1}{2} \mathrm{hr}=\frac{3}{2} \mathrm{hr}\) \(\therefore\)  Required distance = Speed x Time \(=1200 \times \frac{3}{2}=1800 \mathrm{~km}\) (ii) (c): Speed = 1500 km/hr Time =  \(\frac{3}{2}\)  hr. \(\therefore\)  Required distance = Speed x Time \(=1500 \times \frac{3}{2}=2250 \mathrm{~km}\) (iii) (b): Clearly, directions are always perpendicular to each other. \(\therefore \quad \angle P O Q=90^{\circ}\) (iv) (a): Distance between aeroplanes after  \(1\frac{1}{2}\)   hour  \(\begin{array}{l} =\sqrt{(1800)^{2}+(2250)^{2}}=\sqrt{3240000+5062500} \\ =\sqrt{8302500}=450 \sqrt{41} \mathrm{~km} \end{array}\) (v) (d): Area of  \(\Delta\) POQ= \(\frac{1}{2}\) x base x height \(=\frac{1}{2} \times 2250 \times 1800=2250 \times 900=2025000 \mathrm{~km}^{2}\)

(i) (b) (ii) (c): Using Pythagoras theorem, we have PQ 2 = PR 2 + RQ 2 \(\Rightarrow(26)^{2}=(2 x)^{2}+(2(x+7))^{2} \Rightarrow 676=4 x^{2}+4(x+7)^{2} \) \(\Rightarrow 169=x^{2}+x^{2}+49+14 x \Rightarrow x^{2}+7 x-60=0\) \(\Rightarrow x^{2}+12 x-5 x-60=0 \) \(\Rightarrow x(x+12)-5(x+12)=0 \Rightarrow(x-5)(x+12)=0 \) \(\Rightarrow x=5, x=-12\) \(\therefore \quad x=5\)   [Since length can't be negative] (iii) (a) : PR = 2x = 2 x 5 = 10 km (iv) (b): RQ= 2(x + 7) = 2(5 + 7) = 24 km (v) (d): Since, PR + RQ = 10 + 24 = 34 km Saved distance = 34 - 26 = 8 km

(i) (b): If \(\Delta\) AED and \(\Delta\) BEC, are similar by SAS similarity rule, then their corresponding proportional sides are  \(\frac{B E}{A E}=\frac{C E}{D E}\) (ii) (c): By Pythagoras theorem, we have \(\begin{array}{l} B C=\sqrt{C E^{2}+E B^{2}}=\sqrt{4^{2}+3^{2}}=\sqrt{16+9} \\ =\sqrt{25}=5 \mathrm{~cm} \end{array}\) (iii) (a): Since \(\Delta\) ADE and \(\Delta\) BCE are similar. \(\therefore \quad \frac{\text { Perimeter of } \triangle A D E}{\text { Perimeter of } \Delta B C E}=\frac{A D}{B C} \) \(\Rightarrow \frac{2}{3}=\frac{A D}{5} \Rightarrow A D=\frac{5 \times 2}{3}=\frac{10}{3} \mathrm{~cm}\) (iv) (b): \(\frac{\text { Perimeter of } \triangle A D E}{\text { Perimeter of } \Delta B C E}=\frac{E D}{C E} \) \(\Rightarrow \frac{2}{3}=\frac{E D}{4} \Rightarrow E D=\frac{4 \times 2}{3}=\frac{8}{3} \mathrm{~cm}\) (v) (d) :   \(\frac{\text { Perimeter of } \Delta A D E}{\text { Perimeter of } \Delta B C E}=\frac{A E}{B E} \Rightarrow \frac{2}{3} B E=A E\) \(\Rightarrow A E=\frac{2}{3} \sqrt{B C^{2}-C E^{2}} \) \(\text { Also, in } \triangle A E D, A E=\sqrt{A D^{2}-D E^{2}}\)

(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  \(\left(-1, \frac{-\sqrt{7}}{3}\right)\)

Coordinates of A, Band Care (-2, -3), (2, 3) and (3,2). (i) (d): Required distance  \(=\sqrt{(2+2)^{2}+(3+3)^{2}}\) \(=\sqrt{4^{2}+6^{2}}=\sqrt{16+36}=2 \sqrt{13} \mathrm{~km} \approx 7.2 \mathrm{~km}\) (ii) (d): Required distance  \(=\sqrt{(3+2)^{2}+(2+3)^{2}}\) \(=\sqrt{5^{2}+5^{2}}=5 \sqrt{2} \mathrm{~km}\) (iii) (b): Distance between Band C \(=\sqrt{(3-2)^{2}+(2-3)^{2}}=\sqrt{1+1}=\sqrt{2} \mathrm{~km}\) Thus, distance travelled by first bus to reach to B \(=A C+C B=5 \sqrt{2}+\sqrt{2}=6 \sqrt{2} \mathrm{~km} \approx 8.48 \mathrm{~km}\) and distance travelled by second bus to reach to B \(=A B=2 \sqrt{13} \mathrm{~km} \approx 7.2 \mathrm{~km}\) \(\therefore\)  Distance of first bus is greater than distance of the second bus, therefore second bus should be chosen. (iv) (d): Distance travelled by first bus = 8.48 km \(\therefore\) Total fare = 8.48 x 10 = Rs 84.80 (v) (b): Distance travelled by second bus = 7. 2 km \(\therefore\) Total fare = 7.2 x 15 = Rs 108  

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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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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.

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• Remember, write only answering your answer book

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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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Class 10 Maths Case Study Questions Chapter 8 Introduction to Trigonometry

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Case study Questions in the Class 10 Mathematics Chapter 8  are very important to solve for your exam. Class 10 Maths Chapter 8 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 8  Introduction to Trigonometry

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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.

Introduction to Trigonometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 8 Introduction to Trigonometry

Case Study/Passage-Based Questions

Question 1:

Answer: (d) 6m

(ii) Measure of ∠A =

Answer: (c) 45°

(iii) Measure of ∠C =

(iv) Find the value of sinA + cosC.

Answer: (d) 2√2

(v) Find the value of tan 2 C + tan 2  A.

Answer: (c) 2

Question 2:

Answer: (a) 30°

(ii) The measure of  ∠C is

Answer: (c) 60°

(iii) The length of AC is 

Answer: (d)6√3m

(iv) cos2A =

Answer: (b)1/2

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Introduction to Trigonometry 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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Case Study Questions Class 10 Maths Arithmetic Progressions

Case study questions class 10 maths chapter 5 arithmetic progressions.

CBSE Class 10 Case Study Questions Maths Arithmetic Progressions. Term 2 Important Case Study Questions for Class 10 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Arithmetic Progressions.

CBSE Case Study Questions Class 10 Maths Arithmetic Progressions

Case Study – 1

[ KVS Raipur 2021 – 22 ]

(ii) Find the difference in number of candies placed in 7th and 3rd rows.

(ii) 7th row=3+(7-1)X2 = 3 + 12 = 15 and 3rd row = 3+(3-1) X 2 = 7 their diff.= 8

4.) Find the production during first 3 years.

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Case Study Questions for Class 10 Maths

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This article covers case study questions for Class 10 Maths. Students are suggested to go through all the questions to score better in the exams.

Why Students Fear Case Study Questions for Class 10 Maths?

Students may fear Case Study questions for Class 10 Maths for the following reasons:

• Application of Concepts: Case Study questions require the application of mathematical concepts to real-world situations. Students may find it difficult to apply the concepts they have learned to solve the given scenario.
• Limited Practice: Unlike other types of questions, students may have limited practice with Case Study questions. This lack of familiarity may cause anxiety and fear among students.
• Lengthy and Complex Scenarios: Case Study questions often present lengthy and complex scenarios, which can be overwhelming for students. They may struggle to identify the relevant information and apply the appropriate mathematical concepts.
• Time Pressure: Case Study questions may require more time to solve compared to other types of questions. This can add to the stress and anxiety of students, especially during an exam.
• Fear of Making Mistakes: Since Case Study questions involve applying concepts to real-world situations, students may fear making mistakes or getting the wrong answer. This fear may cause them to avoid attempting the question altogether.

In conclusion, students may fear Case Study questions for Class 10 Maths due to the application of concepts, limited practice, lengthy and complex scenarios, time pressure, and fear of making mistakes. Teachers can help alleviate these fears by providing ample practice opportunities, breaking down the scenarios into smaller parts, and encouraging students to attempt the questions.

Best Way to Approach Case Study Questions for Class 10 Maths

Here are some tips on how to approach Case Study questions for Class 10 Maths:

• Read the scenario carefully: The first step is to read the scenario carefully and identify the key information. Pay attention to the given values, units, and any other important details.
• Identify the mathematical concepts involved: Once you have read the scenario, identify the mathematical concepts that are involved. This will help you determine which formulas or equations to apply.
• Break down the scenario into smaller parts: Some Case Study questions may have lengthy and complex scenarios. To make it easier, try to break down the scenario into smaller parts and identify the specific information that is needed to solve each part.
• Solve the problem step by step: Once you have identified the key information and the mathematical concepts involved, start solving the problem step by step. Show all the calculations and equations used.
• Check your answers: After you have solved the problem, check your answers to ensure that they are accurate and relevant to the scenario given. If possible, try to cross-check your answer using a different approach or formula.
• Practice, Practice, Practice: The more you practice Case Study questions, the more familiar you will become with the format and the types of scenarios presented. This will help you develop confidence and improve your performance.

In conclusion, approaching Case Study questions for Class 10 Maths involves careful reading of the scenario, identifying the mathematical concepts involved, breaking down the problem into smaller parts, solving the problem step by step, checking the answers, and practicing regularly.

Topics Covered in CBSE Class 10 Maths

Here are the topics covered in CBSE Class 10 Maths:

• Real Numbers: Euclid’s division lemma, HCF and LCM, irrational numbers, decimal representation of rational numbers, and the relationship between roots and coefficients of a quadratic equation.
• Polynomials: Zeros of a polynomial, relationship between zeros and coefficients of a polynomial, division algorithm for polynomials, and factorization of polynomials.
• Pair of Linear Equations in Two Variables: Graphical method of solution, algebraic methods of solution, and word problems based on linear equations.
• Quadratic Equations: Standard form of a quadratic equation, solutions of a quadratic equation by factorization and by using the quadratic formula, relationship between roots and coefficients, and nature of roots.
• Arithmetic Progressions: nth term of an AP, sum of first n terms of an AP, and word problems based on arithmetic progressions.
• Triangles: Properties of triangles, congruence of triangles, criteria for similarity of triangles, and Pythagoras theorem.
• Coordinate Geometry: Distance formula, section formula, area of a triangle, and equation of a line in different forms.
• Introduction to Trigonometry: Trigonometric ratios, trigonometric ratios of complementary angles, and word problems based on trigonometry.
• Some Applications of Trigonometry: Heights and distances.
• Circles: Tangent to a circle, number of tangents from a point on a circle, and chord properties.
• Constructions: Construction of bisectors of line segments and angles, construction of a triangle similar to a given triangle, and construction of a triangle of given perimeter and base angles.
• Areas Related to Circles: Areas of sectors and segments of a circle.
• Surface Areas and Volumes: Surface areas and volumes of spheres, cones, cylinders, and cuboids.

In conclusion, CBSE Class 10 Maths covers a wide range of topics including real numbers, polynomials, linear equations, quadratic equations, arithmetic progressions, triangles, coordinate geometry, trigonometry, circles, constructions, areas related to circles, and surface areas and volumes.

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Class 10 Maths: Case Study Questions of Chapter 4 Quadratic Equations PDF

Case study Questions on the Class 10 Mathematics Chapter 4  are very important to solve for your exam. Class 10 Maths Chapter 4 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 10 Maths Chapter 4 Quadratic Equations

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.

Quadratic Equations Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 4 Quadratic Equations

Case Study/Passage Based Questions

1)Formation of Quadratic Equation

Quadratic equations started around 3000 B.C. with the Babylonians. They were one of the world’s first civilizations and came up with some great ideas like agriculture, irrigation, and writing. There were many reasons why Babylonians needed to solve quadratic equations. For example to know what amount of crop you can grow on the square field. Now represent the following situations in the form of a quadratic equation.

The sum of squares of two consecutive integers is 650. (a) x 2 + 2x – 650 = 0 (b) 2x 2 +2x – 649 = 0 (c) x 2 – 2x – 650 = 0 (d) 2x 2 + 6x – 550 = 0

Answer: (b) 2×2 +2x – 649 = 0

The sum of two numbers is 15 and the sum of their reciprocals is 3/10. (a) x 2 + 10x – 150 = 0 (b) 15x 2 – x + 150 = 0 (c) x 2 – 15x + 50 = 0 (d) 3x 2 – 10x + 15 = 0

Answer: (c) x2 – 15x + 50 = 0

Two numbers differ by 3 and their product is 504. (a) 3x 2 – 504 = 0 (b) x 2 – 504x + 3 = 0 (c) 504x 2 +3 = x (d) x 2 + 3x – 504 = 0

Answer: (d) x2 + 3x – 504 = 0

A natural number whose square diminished by 84 is thrice of 8 more of a given number. (a) x 2 + 8x – 84 = 0 (b) 3x 2 – 84x + 3 = 0 (c) x 2 – 3x – 108 = 0 (d) x 2 –11x + 60 = 0

Answer: (c) x2 – 3x – 108 = 0

A natural number when increased by 12, equals 160 times its reciprocal. (a) x 2 – 12x + 160 = 0 (b) x 2 – 160x + 12 = 0 (c) 12x 2 – x – 160 = 0 (d) x 2 + 12x – 160 = 0

Answer: (d) x2 + 12x – 160 = 0

2)Nature of Roots A quadratic equation can be defined as an equation of degree 2. This means that the highest exponent of the polynomial in it is 2. The standard form of a quadratic equation is ax 2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Every quadratic equation has two roots depending on the nature of its discriminant, D = b 2 – 4ac

Which of the following quadratic equation have no real roots? (a) –4x 2 + 7x – 4 = 0 (b) –4x 2 + 7x – 2 = 0 (c) –2x 2 +5x – 2 = 0 (d) 3x 2 + 6x + 2 = 0

Answer: (a) –4×2 + 7x – 4 = 0

Which of the following quadratic equation have rational roots? (a) x 2 + x – 1 = 0 (b) x 2 – 5x + 6 = 0 (c) 4x 2 – 3x – 2 = 0 (d) 6x 2 – x + 11 = 0

Answer: (b) x2 – 5x + 6 = 0

Which of the following quadratic equation have irrational roots? (a) 3x 2 +2x + 2 = 0 (b) 4x 2 – 7x + 3 = 0 (c) 6x 2 – 3x – 5 = 0 (d) 2x 2 +3x – 2 = 0

Answer: (c) 6×2 – 3x – 5 = 0

Which of the following quadratic equations have equal roots? (a) x 2 – 3x + 4 = 0 (b) 2x 2 – 2x + 1 = 0 (c) 5x 2 – 10x + 1 = 0 (d) 9x 2 + 6x + 1 = 0

Answer: (d) 9×2 + 6x + 1 = 0

Which of the following quadratic equations has two distinct real roots? (a) x 2 + 3x + 1 = 0 (b) –x 2 + 3x – 3 = 0 (c) 4x 2 + 8x + 4 = 0 (d) 3x 2 + 6x + 4 = 0

Answer: (a) x2 + 3x + 1 = 0

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 4 Quadratic Equations with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 10 Maths Quadratic Equations 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 Maths Chapter 6 (Published by CBSE)

Check case study questions released by cbse for class 10 maths chapter 6 - triangles. solve these questions to prepare the case study questions for the cbse class 10 maths exam 2021-22..

CBSE Class 10 Maths Case Study Questions for Chapter 6 - Triangles are available here. Students must practice with these questions to perform well in their Maths exam. All these case study questions have been published by the Central Board of Secondary Education (CBSE). For the convenience of students, all the questions are provided with answers.

Case Study Questions for Class 10 Maths Chapter 6 - Triangles

CASE STUDY 1:

Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles.The height of Vijay’s house if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground.

1. What is the height of the tower?

Answer: c) 100m

2. What will be the length of the shadow of the tower when Vijay’s house casts a shadow of 12m?

Answer: d) 60m

3. What is the height of Ajay’s house?

Answer: b) 40m

4. When the tower casts a shadow of 40m, same time what will be the length of the shadow of Ajay’s house?

Answer: a) 16m

5. When the tower casts a shadow of 40m, same time what will be the length of the shadow of Vijay’s house?

Answer: d) 8m

CASE STUDY 2:

Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure below. To find the distance between the points, he makes a right-angled triangle using rope connecting B with another point C are a distance of 12m, connecting C to point D at a distance of 40m from point C and the connecting D to the point A which is are a distance of 30m from D such the ∠ ADC=90 0 .

1. Which property of geometry will be used to find the distance AC?

a) Similarity of triangles

b) Thales Theorem

c) Pythagoras Theorem

d) Area of similar triangles

Answer: c)Pythagoras Theorem

2. What is the distance AC?

Answer: a) 50m

3. Which is the following does not form a Pythagoras triplet?

a) (7, 24, 25)

b) (15, 8, 17)

c) (5, 12, 13)

d) (21, 20, 28)

Answer: d) (21, 20, 28)

4. Find the length AB?

Answer: b) 38m

5. Find the length of the rope used.

Answer: c)82m

SCALE FACTOR

Case study:

A scale drawing of an object is the same shape at the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. The ratio of two corresponding sides in similar figures is called the scale factor

Scale factor= length in image / corresponding length in object

If one shape can become another using revising, then the shapes are similar. Hence, two shapes are similar when one can become the other after a resize, flip, slide or turn. In the photograph below showing the side view of a train engine. Scale factor is 1:200

This means that a length of 1 cm on the photograph above corresponds to a length of 200cm or 2 m, of the actual engine. The scale can also be written as the ratio of two lengths.

1. If the length of the model is 11cm, then the overall length of the engine in the photograph above, including the couplings (mechanism used to connect) is:

Answer: a)22m

2. What will affect the similarity of any two polygons?

a) They are flipped horizontally

b) They are dilated by a scale factor

c) They are translated down

d) They are not the mirror image of one another.

Answer: d)They are not the mirror image of one another

3. What is the actual width of the door if the width of the door in photograph is 0.35cm?

Answer: a)0.7m

4. If two similar triangles have a scale factor 5:3 which statement regarding the two triangles is true?

a) The ratio of their perimeters is 15:1

b) Their altitudes have a ratio 25:15

c) Their medians have a ratio 10:4

d) Their angle bisectors have a ratio 11:5

Answer: b)Their altitudes have a ratio 25:15

5. The length of AB in the given figure:

Answer: c)4cm

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• Lines and Angles Class 9 Case Study Questions Maths Chapter 6

Last Updated on August 26, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 9 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 9 maths. In this article, you will find case study questions for CBSE Class 9 Maths Chapter 6 Lines and Angles. It is a part of Case Study Questions for CBSE Class 9 Maths Series.

Table of Contents

Case Study Questions on Lines and Angles

A math’s teacher was teaching students about intersecting lines.

Suppose AB and CD are two intersecting lines, which meets at point O. In this point O, she draw a line OE and all these lines were making different angles with each other.

After explaining the description of the figure, she asked the following questions from the students.

On the basis of the above information, solve the following questions.

Q 1. Find the measure of ∠BOD.

Q 2. Check whether pair of angles ∠AOC and ∠BOC makes a linear pair.

Q 3. Which of the following angles form a non collinear lines? (i) A, O, B (ii) C, O, E

Q 4. Find the measure of ∠AOE.

1. From figure,

$$ \angle B O D=\angle A O C=35^{\circ} $$

[Vertically opposite angles]

2. From figure, it is clear that

$$ \angle A O C+\angle B O C=180^{\circ} $$

$[\because A B$ is a straight line $]$ Hence, $\angle A O C$ and $\angle B O C$ makes a linear pair.

3. (i) It is clear from the figure that points $A, O$ and $B$ form a collinear points. (ii) It is clear from the figure that points $\mathrm{C}, \mathrm{O}, \mathrm{E}$ forms a non-collinear points.

Hence, points C, O, E form a non-collinear line.

4. From the given figure, $C D$ is a line segment.

Therefore, the sum of all angles of the same side of a line is $180^{\circ}$.

$$ \begin{aligned} & \therefore \angle \mathrm{COA}+\angle \mathrm{AOE}+\angle \mathrm{EOD}=180^{\circ} \\ & \Rightarrow 35^{\circ}+\angle A O E+75^{\circ}=180^{\circ} \\ & \Rightarrow \angle \mathrm{AOE}=180^{\circ}-110^{\circ} \\ & =70^{\circ} \end{aligned} $$

Understanding Lines and Angles

Line: A geometrical object that is straight and extends indefinitely in both directions. Line Segment: A part of a line with two end points. Ray: A part of line with one end point. Collinear Points: Three or more points lying on the same line are known as collinear points. Otherwise, they are non-collinear points. Angle: It is formed when two rays originate from the same end point. The rays are called arms and the end point is called vertex.

Types of Angles:

• Acute Angle: An angle with measure more than 0° but less than 90°. In figure, ∠AOB is acute angle.
• Obtuse Angle: An angle with measure more than 90° but less than 180°. In figure, ∠AOD is obtuse angle.
• Right Angle: An angle with measure exactly 90°. In figure, ∠AOC is right angle.
• Straight Angle: An angle with measure 180°. In figure, ∠AOE is straight angle.
• Reflex Angle: An angle with measure more than 180° but less than 360°. In figure, ∠AOF is reflex angle, when measured anticlockwise.
• Complete Angle: An angle with measure 360°. In figure, ∠AOA is complete angle.

Pair of Angles:

• Complementary Angles: Two angles with the sum of 90°. In above figure, ∠AOB + ∠BOC = 90°, so ∠AOB and ∠BOC are complementary angles.
• Supplementary Angles: Two angles with the sum of 180°. In above figure, ∠AOB + ∠BOE = 180°, so ∠AOB and ∠BOE are supplementary angles
• Adjacent Angles: Two angles having a common vertex and a common arm with uncommon arms on either side of the common arm. In figure, ∠AOC and ∠BOC are adjacent angles. OR When two angles are adjacent, then their sum is always equal to the angle formed by the two non-common arms. In figure, ∠AOB = ∠AOC + ∠BOC
• Linear Pair of Angles: Two adjacent angles with the sum of 180°. In figure, ∠AOC and ∠BOC are linear pair of angles.

Vertically Opposite Angles: The pair of angles lying on the opposite sides of the point of intersection. In figure, (∠AOC and ∠BOD) and (∠AOD and ∠BOC) are pairs of vertically opposite angles.

Bisector of an Angle: A ray which divides an angle into two equal parts.

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Number systems class 9 case study questions maths chapter 1, topics from which case study questions may be asked.

• Basic Terms and Definitions
• Types of Angles
• Intersecting Lines and Non-Intersecting Lines
• Pairs of Angles
• Parallel Lines and a Transversal
• Angle Sum Property of a Triangle

The length of perpendiculars at different points on the parallel lines is same.

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

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Frequently Asked Questions (FAQs) on Lines and Angles Case Study

Q1: what are the different types of angles.

A1: Angles are classified based on their measures: Acute Angle : Measures less than 90°. Right Angle : Measures exactly 90°. Obtuse Angle : Measures more than 90° but less than 180°. Straight Angle : Measures exactly 180°. Reflex Angle : Measures more than 180° but less than 360°.

Q2: What are complementary and supplementary angles?

A2: Complementary Angles : Two angles are complementary if their sum is 90°. Supplementary Angles : Two angles are supplementary if their sum is 180°.

Q3: What is a linear pair of angles?

A3: A linear pair of angles is formed when two adjacent angles add up to 180°. The angles in a linear pair are always supplementary.

Q4: What is the Angle Sum Property of a Triangle?

A4: The Angle Sum Property states that the sum of the interior angles of a triangle is always 180°.

Q5: What are parallel lines and a transversal?

A5: Parallel Lines : Two lines that are equidistant from each other and never intersect. Transversal : A line that intersects two or more lines at distinct points. When a transversal cuts through parallel lines, it forms angles with specific relationships, like corresponding, alternate interior, and alternate exterior angles.

Q6: What is the significance of corresponding angles when a transversal intersects parallel lines?

A6: When a transversal intersects two parallel lines, the corresponding angles formed are equal. This property helps in proving that the lines are parallel and in solving various geometrical problems.

Q7: Are there any online resources or tools available for practicing Lines and Angles case study questions?

A8: We provide case study questions for CBSE Class 9 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.

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