case study questions class 12 maths

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Class 12 Maths Case...

Class 12 Maths Case Study Questions

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Class 12 Maths question paper will have 1-2 Case Study Questions. These questions will carry 5 MCQs and students will attempt any four of them. As all of these are only MCQs, it is easy to score good marks with a little practice. Class 12 Maths Case Study Questions are available on the myCBSEguide App and Student Dashboard .

Why Case Studies in CBSE Syllabus?

CBSE has introduced case study questions in the CBSE curriculum recently. The purpose was to make students ready to face real-life challenges with the knowledge acquired in their classrooms. It means, there was a need to connect theories with practicals. Whatsoever the students are learning, they must know how to apply it in their day-to-day life. That’s why CBSE is emphasizing case studies and competency-based education .

Case Study Questions in Maths

Let’s have a look over the class 12 Mathematics sample question paper issued by CBSE, New Delhi. Question numbers 17 and 18 are case study questions.

Focus on concepts

If you go through each MCQ there, you will find that the theme/case study is common but the questions are based on different concepts related to the theme. It means, that if you have done ample practice on the various concepts, you can solve all these MCQs in minutes.

Easy Questions with a Practical Approach

The difficulty level of the questions is average or say easy in some cases. On the other hand, you get four options to choose from. So, you get two levels of support to get full marks with very little effort.

Practice Questions Regularly

Most of the time we feel that it’s easy and neglect it. But in the end, we have to pay for this negligence. This may happen here too. Although it’s easy to score good marks on the case study questions if you don’t practice such questions, you may lose your marks. So, we suggest students should practice at least 30-40 such questions before writing the board exam.

12 Maths Case-Based Questions

We are giving you some examples of case study questions here. We have arranged hundreds of such questions chapter-wise on the myCBSEguide App. It is the complete guide for CBSE students. You can download the myCBSEguide App and get more case study questions there.

Case Study Question – 1

A is a diagonal matrix
A is a scalar matrix
A is a zero matrix
A is a square matrix
If A and B are two matrices such that AB = B and BA = A, then B 2 is equal to

Case Study Question – 2

4(x 3 – 24x 2 + 144x)
4(x 3 – 34x 2 + 244x)
x 3 – 24x 2 + 144x
4x 3 – 24x 2 + 144x
Local maxima at x = c 1
Local minima at x = c 1
Neither maxima nor minima at x = c 1
None of these

Case Study Questions Matrices -1

Answer Key:

Case Study Questions Matrices – 2

Read the case study carefully and answer any four out of the following questions: Once a mathematics teacher drew a triangle ABC on the blackboard. Now he asked Jose,” If I increase AB by 11 cm and decrease the side BC by 11 cm, then what type of triangle it would be?” Jose said, “It will become an equilateral triangle.”

Again teacher asked Suraj,” If I multiply the side AB by 4 then what will be the relation of this with side AC?” Suraj said it will be 10 cm more than the three times AC.

Find the sides of the triangle using the matrix method and answer the following questions:

(a) 3 × 3

Case Study Questions Determinants – 01

DETERMINANTS: A determinant is a square array of numbers (written within a pair of vertical lines) that represents a certain sum of products. We can solve a system of equations using determinants, but it becomes very tedious for large systems. We will only do 2 × 2 and 3 × 3 systems using determinants. Using the properties of determinants solve the problem given below and answer the questions that follow:

Three shopkeepers Ram Lal, Shyam Lal, and Ghansham are using polythene bags, handmade bags (prepared by prisoners), and newspaper envelopes as carrying bags. It is found that the shopkeepers Ram Lal, Shyam Lal, and Ghansham are using (20,30,40), (30,40,20), and (40,20,30) polythene bags, handmade bags, and newspapers envelopes respectively. The shopkeeper’s Ram Lal, Shyam Lal, and Ghansham spent ₹250, ₹270, and ₹200 on these carry bags respectively.

(b) Shyam Lal
(a) Ram Lal

Case Study Questions Determinants – 02

Case study questions application of derivatives.

R(x) = -x 2 + 200x + 150000
R(x) = x 2 – 200x – 140000
R(x) = 200x 2 + x + 150000
R(x) = -x 2 + 100 x + 100000
R'(x) > 0
R'(x) < 0
R”(x) = 0
(a) -x 2 + 200x + 150000
(a) R'(x) = 0
(c) 257, -63

Case Study Questions Vector Algebra

tan−1⁡(5/12)
tan−1⁡(12/3)
(b) 130 m/s
(a) tan−1⁡(5/12)
(b) 170 m/s

12 Maths Exam pattern

Question Paper Design of CBSE class 12 maths is as below. It clearly shows that 20% weightage will be given to HOTS questions. Whereas 55% of questions will be easy to solve.


1.	Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas	44	55
2.	Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.	20	25
3.	Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations	16	20
	Present and defend opinions by making judgments about information, the validity of ideas, or quality of work based on a set of criteria.
	Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions
		80	100

No. chapter-wise weightage. Care to be taken to cover all the chapters
Suitable internal variations may be made for generating various templates keeping the overall weightage to different forms of questions and typology of questions the same.

Choice(s): There will be no overall choice in the question paper. However, 33% of internal choices will be given in all the sections


Periodic Tests ( Best 2 out of 3 tests conducted)	10 Marks
Mathematics Activities	10 Marks

12 Maths Prescribed Books

Mathematics Part I – Textbook for Class XII, NCERT Publication
Mathematics Part II – Textbook for Class XII, NCERT Publication
Mathematics Exemplar Problem for Class XII, Published by NCERT
Mathematics Lab Manual class XII, published by NCERT

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Case Study Questions for Class 12 Maths PDF Download

We have provided here Case Study questions for the Class 12 Maths for board exams. You can read these chapter-wise Case Study questions. These questions are prepared by subject experts and experienced teachers. The answer key is also provided so that you can check the correct answer for each question. Practice these questions to score well in your final exams.

CBSE 12th Standard CBSE Maths question papers, important notes, study materials, Previous Year questions, Syllabus, and exam patterns. Free 12th Standard CBSE Maths books and syllabus online. Important keywords, Case Study Questions, and Solutions.

Class 12 Maths Case Study Questions

CBSE Class 12 Maths question paper will have case study questions too. These case-based questions will be objective type in nature. So, Class 12 Maths students must prepare themselves for such questions. First of all, you should study NCERT Textbooks line by line, and then you should practice as many questions as possible.

Chapter-wise Solved Case Study Questions for Class 12 Maths

Class 12 students should go through important Case Study problems for Maths before the exams. This will help them to understand the type of Case Study questions that can be asked in Grade 12 Maths examinations. Our expert faculty for standard 12 Maths have designed these questions based on the trend of questions that have been asked in last year’s exams. The solutions have been designed in a manner to help the grade 12 students understand the concepts and also easy to learn solutions.

Books for Class 12 Maths

Strictly as per the new term-wise syllabus for Board Examinations to be held in the academic session 2022-23 for class 12 Multiple Choice Questions based on new typologies introduced by the board- Stand-Alone MCQs, MCQs based on Assertion-Reason Case-based MCQs. Include Questions from CBSE official Question Bank released in April 2022 Answer key with Explanations What are the updates in the book: Strictly as per the Term wise syllabus for Board Examinations to be held in the academic session 2022-23. Chapter-wise -Topic-wise Multiple choice questions based on the special scheme of assessment for Board Examination for Class 12th.

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CBSE Class 12

CBSE Class 12 Maths Exam 2024 Important Case Study Based Questions

Case study questions for class 12 maths: check here the important case study based questions of section e in the cbse class 12 maths exam 2024 for last minute preparation..

CBSE Class 12 Maths Exam 2024 Important Questions: The Central Board of Secondary Education is the largest and one of the most famed school boards in India, and lakhs of students are currently enrolled in it. The CBSE conducts the Class 12 board exams annually. The next paper is arguably the most important for science and commerce stream students: Maths on 9 March. Maths is essential for non-medical science and commerce aspirants and is also required in subjects like physics, statistics and accounts. CBSE Class 12 Maths requires extensive practice, especially important topics like Calculus and Algebra. There will be five sections in the 2024 CBSE Class 12 Maths exam, and the last section E will comprise two case study-based questions of 4 marks. These questions are quite important from the exam point of view, and you can check and practice the solved versions here.

CBSE Class 12 Maths Unit Wise Marks Distribution 2024

CBSE Maths Previous Year Question Paper Class 12

CBSE Class 12 Maths Case Study Questions 2023

Q uestion 1: Ramesh is elder brother of Suresh. Ramesh wants to help his younger brother Suresh to solve the following problems of integrals. Write the suitable substitution by which Ramesh can help him.

Question 2: Mr Shashi, who is an architect, designs a building for a small company. The design of window on the ground floor is proposed to be different than other floors. The window is in the shape of a rectangle which is surmounted by a semi-circular opening. This window is having a perimeter of 10 m as shown below :

Based on the above information answer the following :

(i) If 2x and 2y represents the length and breadth of the rectangular portion of the windows, then the relation between the variables is:

(ii) The combined area (A) of the rectangular region and semi-circular region of the window expressed as a function of x is:

(iii) The maximum value of area A, of the whole window is

The owner of this small company is interested in maximizing the area of the whole window so that maximum light input is possible.

For this to happen, the length of rectangular portion of the window should be

(i) 4y = 10 - (2 + π)x

(ii) A = 10x - (2 + 12π)x 2

(iii) 50/4 + π

20/4 + π

Question 3: Read the following and answer the questions given below

The front gate of a building is in the shape of a trapezium as shown below. Its three sides other than base are of 10 m each. The height of the gate is h meter. On the basis of below figure, answer the following questions:

(i) Write the Area (A) of the gate in terms of .

(ii) Write the value of when Area (A) is maximum.

(iii) Write the value of h when Area (A) is maximum .

Write the Maximum value of Area (A) .

(i) (10 + x)√100 - x 2

(iii) 5√3m OR 75√3/m.m2

Question 4 : Read the following and answer the questions given below

Given three identical boxes 1 st, 2 nd and 3 rd each containing two coins. In 1 st box both coins are gold coins, in 2 nd box both are silver coins and in 3 rd box there is one gold and one silver coin. A person chooses a box at random and takes out a coin.

On the basis of above information, answer the following questions:

(i) What is the probability of choosing 1 st box ?

(ii) What is the probability of getting gold coin from 3 rd box ?

(iii) What is the total probability of drawing gold coin ?

If drawn coin is of gold the probability that other coin in the box is also of gold?

(iii) 1/2 Or 2/3

Question 5: Read the following and answer the questions given below

Sand is pouring from a pipe at the rate of 12 cm 3 / second the falling sand forms a cone on the ground in such a way that the height of the cone is always 1/6 th of the radius of the base. Based on above information answer the following:

(i) Write the expression for volume in terms of height only.

(ii) What is the rate of Change of height, when height is 4 cm?

i) 12πh 3

(ii) 1/48 cm/s

Question 6: There are two antiaircraft guns, named as A and B. The probabilities that the shell fired from them hits an airplane are 0.3 and 0.2 respectively. Both of them fired one shell at an airplane at the same time.

(i) What is the probability that the shell fired from exactly one of them hit the plane?

(ii) If it is known that the shell fired from exactly one of them hit the plane, then what is the probability that it was fired from B?

CBSE Class 12 Maths Deleted Syllabus 2023-24
NCERT Solutions 12th Maths PDF

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CBSE Class 12 Maths Case Study Problems

In Coming Exams, CBSE will ask two Case Study Questions in the CBSE class 12 maths questions paper. Each theme will have five questions and students will have a choice to attempt any four of them.

Here are some example questions Based On Case Study Problems:

Question-1 Read the case study carefully and answer any four out of the following questions:

Three friends Ganesh, Dinesh, and Ramesh went for playing a Tug of war game. Team A, B, and C belong to Ganesh, Dinesh, and Ramesh respectively. Teams A, B, C have attached a rope to a metal ring and are trying to pull the ring into their own area (team areas shown below). Team A pulls with F1 = 4i + 0j KN Team B → F2 = -2i+ 4j KN Team C → F3 = -3i – 3j KN

1. Which team will win the game? (a). Team B (b). Team A (c). Team C (d). No one

2. What is the magnitude of the team’s combine Force? (a). 7 KN (b). 1.4 KN (c). 1.5 KN (d). 2 KN

3. In with direction approx the ring getting pulls: (a). 2.0 radian (b). 2.5 radian (c). 2.4 radian (d). 3 radian

4. What is the magnitude of the force of Team B? (a). 25–√25 KN (b). 6 KN (c). 2 KN (d). 6–√6 KN

5. How many KN Force is applied by Team A? (a). 5 KN (b). 4 KN (c). 2 KN (d). 16 KN

Question-2 Read the case study carefully and answer any four out of the following questions:

Three shopkeepers Ram Lal, Shyam Lal, and Ghansham are using polythene bags, handmade bags (prepared by prisoners), and newspaper’s envelope as carry bags. It is found that the shopkeepers Ram Lal, Shyam Lal, and Ghansham are using (20,30,40), (30,40,20), and (40,20,30) polythene bags, handmade bags, and newspapers envelopes respectively. The shopkeeper’s Ram Lal, Shyam Lal, and Ghansham spent ₹250, ₹270, and ₹200 on these carry bags respectively.

1. What is the cost of one polythene bag? (a). ₹ 1 (b). ₹ 2 (c). ₹ 3 (d). ₹ 5

2. What is the cost of one handmade bag? (a). ₹ 1 (b). ₹ 2 (c). ₹ 3 (d). ₹ 5

3. What is the cost of one newspaper bag? (a). ₹ 1 (b). ₹ 2 (c). ₹ 3 (d). ₹ 5

4. Keeping in mind the social conditions, which shopkeeper is better? (a). Ram Lal (b). Shyam Lal (c). Ghansham (d). None of these

5. Keeping in mind the environmental conditions, which shopkeeper is better? (a). Ram Lal (b). Shyam Lal (c). Ghansham (d). None of these

Question-3 Read the case study carefully and answer any four out of the following questions:

Three friends Ravi, Raju, and Rohit were doing buying and selling stationery items in a market. The price per dozen of Pen, Notebook, and toys are Rupees x, y, and z respectively. Ravi purchases 4 dozens of notebooks and sells 2 dozens of pens and 5 dozens of toys. Raju purchases 2 dozens of toys and sells 3 dozens of pens and 1 dozen of notebooks. Rohit purchases one dozen of pens and sells 3 dozens of notebooks and one dozen toys. In the process, Ravi, Raju, and Rohit earn ₹ 1500, ₹ 100, and ₹400 respectively.

Answer the following questions using the matrix method:

1. What is the price of one dozen of pens? (a). ₹ 100 (b). ₹ 200 (c). ₹ 300 (d). ₹ 400

2. What is the total price of one dozen of pens and one dozen of notebooks? (a). ₹ 100 (b). ₹ 200 (c). ₹ 300 (d). ₹ 400

3. What is the sale amount of Ravi? (a). ₹ 1000 (b). ₹ 1100 (c). ₹ 1300 (d). ₹ 1200

4. What is the amount of purchases made by all three friends? (a). ₹ 1200 (b). ₹ 1500 (c). ₹ 1300 (d). ₹ 1400

5. What is the price of sales made by all three friends? (a). ₹ 3000 (b). ₹ 2500 (c). ₹ 2700 (d). ₹ 2400

Question-4 Read the case study carefully and answer any four out of the following questions:

Dinesh is having a jewelry shop at Green Park, Normally he does not sit in the shop as he remains busy in political meetings. The manager Lisa takes care of jewelry shop where she sells earrings and necklaces. She sells earrings for ₹ 30 and necklaces for 40. It takes 30 minutes to make a pair of earrings and 1 hour to make a necklace, and there are 10 hours a week to make jewelry. In addition, there are only enough materials to make 15 total jewelry items per week. The profit of 15 and 20 is made on each pair of earrings and a necklace respectively. The graph of the equations formed is shown here:

Answer the following questions:

1. What is the first inequality formed? (a). 0.5x + y ≤ 10 (b). x +0.5 y ≤ 10 (c). 0.5x + y ≤ 15 (d). x + 0.5 y ≤ 20

2. What is the second inequality formed? (a). 0.5x + y ≤ 10 (b). x + y ≤ 10 (c). x + y ≤ 15 (d). x + 0.5 y ≤ 10

3. In order to maximize the profits, per week how many pair of earrings and necklaces should be made? (a). 10 and 5 (b). 5 and 10 (c). 15 and 5 (d). 5 and 15

4. What would be the profit if 5 pairs of earrings and 5 necklaces are made? (a). 150 (b). 300 (c). 175 (d). 250

5. What would be the maximum possible profit? (a). 150 (b). 300 (c). 175 (d). 250

Question-5 Read the case study carefully and answer any four out of the following questions:

A telephone company in a town has 500 subscribers on its list and collects fixed charges of 300 per subscriber per year. The company proposes to increases the annual subscription and it is believed that for every increase of 1 one subscriber will discontinue the service.

1. If x be the annual subscription then the total revenue of the company after increment will be: (a). R(x) = -x2 + 200x + 150000 (b). R(x) = x2 – 200x – 140000 (c). R(x) = 200×2 + x + 150000 (d). R(x) = -x2 + 100 x + 100000

2. To find maximum profit we put (a). R'(x) = 0 (b). R'(x) > 0 (c). R'(x) < 0 (d). R”(x) = 0

3. How much fee the company should increase to have maximum profit? (a). Rs. 150 (b). Rs. 100 (c). Rs. 200 (d). Rs. 250

4. Find the maximum profit that the company can make if the profit function is given by P(x) = 41 + 24x – 18×2. (a). 25 (b). 44 (c). 45 (d). 49

5. Find both the maximum and minimum value respectively of 3×4 – 8×3 + 48x + 1 on the interval [1, 4]. (a). -63, 257 (b). 258, -63 (c). 257, -63 (d). -63, -257

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CBSE 12th Standard Maths Subject Matrices Case Study Questions With Solution 2021

By QB365 on 21 May, 2021

QB365 Provides the updated CASE Study Questions for Class 12 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

12th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) The cost incurred by the organisation on village Y is

(iii) The cost incurred by the organisation on village Z is

(iv) The total number of toilets that can be expected after the promotion in village X, is

(v) The total number of toilets that can be expected after the promotion in village Z, is

(ii) The combined sales of Urad in September and October, for farmer Shyam is

(iii) Find the decrease in sales of Mung from September to October, for the farmer Shyam.

If $A=\left[a_{i j}\right]_{m \times n} \text { and } B=\left[b_{i j}\right]_{m \times n}$ are two matrices, then $A \pm B$ is of order m x n and is defined as $(A \pm B)_{i j}=a_{i j} \pm b_{i j}$ , where i = 1,2, , m and j = 1,2, ..., n If $A=\left[a_{i j}\right]_{m \times n} \text { and } B=\left[b_{j k}\right]_{n \times p}$ are two matrices, then AB is of order m x p and is defined as $(A B)_{i k}=\sum_{r=1}^{n} a_{i r} b_{r k}=a_{i 1} b_{1 k}+a_{i 2} b_{2 k}+\ldots . .+a_{i n} b_{n k}$ Consider $A=\left[\begin{array}{cc} 2 & -1 \\ 3 & 4 \end{array}\right], B=\left[\begin{array}{ll} 5 & 2 \\ 7 & 4 \end{array}\right], C=\left[\begin{array}{ll} 2 & 5 \\ 3 & 8 \end{array}\right] \text { and } D=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]$ Using the concept of matrices answer the following questions. (i) Find the product AB.

(ii) If A and B are any other two matrices such that AB exists, then

(iii) Find the values of a and c in the matrix D such than CD - AB = 0.

(iv) Find the values of band d in the matrix D such that CD - AB = 0.

(

(v) Find B + D.

(iii) If the trust fund obtains an annual total interest of Rs.3200, then the investment in two bonds is

(iv) The total amount of interest received on both bonds is given by

(v) If the amount of interest given to old age home is Rs.500, then the amount of investment in bond Y is

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

Cbse 12th standard maths subject matrices case study questions with solution 2021 answer keys.

(i) (c) : Let Rs. A, Rs. B and Rs.C be the cost incurred by the organisation for villages X, Y and Z respectively. Then A, B, C will be given by the following matrix equation. $\left[\begin{array}{ccc} 400 & 300 & 100 \\ 300 & 250 & 75 \\ 500 & 400 & 150 \end{array}\right]\left[\begin{array}{l} 50 \\ 20 \\ 40 \end{array}\right]=\left[\begin{array}{c} A \\ B \\ C \end{array}\right]$ $\Rightarrow\left[\begin{array}{l} A \\ B \\ C \end{array}\right]=\left[\begin{array}{c} 400 \times 50+300 \times 20+100 \times 40 \\ 300 \times 50+250 \times 20+75 \times 40 \\ 500 \times 50+400 \times 20+150 \times 40 \end{array}\right]$ (ii) (c) (iii) (b) (iv) (c) : Total number of toilets that can be expected in each village is given by the following matrix. $\begin{array}{l} X \\ Y \\ Z \end{array}\left[\begin{array}{ccc} 400 & 300 & 100 \\ 300 & 250 & 75 \\ 500 & 400 & 150 \end{array}\right]$ $\left[\begin{array}{c} 2 / 100 \\ 4 / 100 \\ 20 / 100 \end{array}\right]$ $\begin{array}{l} X \\ Y \\ Z \end{array}$ $\left[\begin{array}{c} 8+12+20 \\ 6+10+15 \\ 10+16+30 \end{array}\right]$ = $\begin{array}{l} X \\ Y \\ Z \end{array}$ $\left[\begin{array}{c} 40 \\ 31 \\ 56 \end{array}\right]$ (v) (d)

(i) (a) : $A B=\left[\begin{array}{cc} 2 & -1 \\ 3 & 4 \end{array}\right]\left[\begin{array}{ll} 5 & 2 \\ 7 & 4 \end{array}\right]$ $=\left[\begin{array}{cc} 10-7 & 4-4 \\ 15+28 & 6+16 \end{array}\right]=\left[\begin{array}{cc} 3 & 0 \\ 43 & 22 \end{array}\right]$ (ii) (c) (iii) (b) : We have, CD - AB = 0 $\Rightarrow\left[\begin{array}{ll} 2 & 5 \\ 3 & 8 \end{array}\right]\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]-\left[\begin{array}{cc} 3 & 0 \\ 43 & 22 \end{array}\right]=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right]$ $\Rightarrow\left[\begin{array}{ll} 2 a+5 c & 2 b+5 d \\ 3 a+8 c & 3 b+8 d \end{array}\right]-\left[\begin{array}{cc} 3 & 0 \\ 43 & 22 \end{array}\right]=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right]$ $\Rightarrow\left[\begin{array}{cc} 2 a+5 c-3 & 2 b+5 d \\ 3 a+8 c-43 & 3 b+8 d-22 \end{array}\right]=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right]$ By equality of matrices, we get 2a + 5c - 3 = 0 ...(i) 3a + 8c - 43 = 0 ...(ii) 2b + 5d = 0 ...(iii) 3b + 8d - 22 = 0 ...(iv) Solving (i) and (ii), we get a = -191, e = 77 (iv) (c) : Solving (iii) and (iv), we get b = -110, d = 44 (v) (d) : Wehave, $B+D=\left[\begin{array}{ll} 5 & 2 \\ 7 & 4 \end{array}\right]+\left[\begin{array}{cc} -191 & -110 \\ 77 & 44 \end{array}\right]$ $=\left[\begin{array}{cc} -186 & -108 \\ 84 & 48 \end{array}\right]$

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Class 12 Maths: Case Study of Chapter 6 Applications of Derivatives PDF Download

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In Class 12 Boards there will be Case studies and Passage Based Questions will be asked, So practice these types of questions. Study Rate is always there to help you. Free PDF Download of CBSE Class 12 Mathematics Chapter 6 Applications of Derivatives Case Study and Passage Based Questions with Answers were Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Applications of Derivatives to know their preparation level.

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In CBSE Class 12 Maths Paper, 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.

Applications of Derivatives Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 12 Mathematics Chapter 6 Applications of Derivatives

Case Study/Passage-Based Questions

(i) To construct a garden using 200 ft of fencing, we need to maximize its

(a) volume

(b) area

(d) length of the side

Answer: (b) area

(ii) If x denote the length of side of garden perpendicular to brick wall and y denote the length, of side parallel to brick wall, then find the relation representing total amount of fencing wire.

(a) x+2y=150

(b) x+2y=50

(d) y+2x=100

Answer: (c) y+2x=200

(iii) Area of the garden as a function of x, say A(x), can be represented as

(a) 200 + 2x

(b) x – 2x

(d) 200-x

Answer: (c) 200x – 2×2

(iv) Maximum value of A(x) occurs at x equals

(a) 50 ft

(b) 30 ft

(d) 31 ft

Answer: (a) 50 ft

(v) Maximum area of garden will be

(a) 2500sq.ft

(b) 4000sq.ft

(d) 6000 sq. ft

Answer: (c) 5000sq.ft

Hope the information shed above regarding Case Study and Passage Based Questions for Class 12 Maths Chapter 6 Applications of Derivatives with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 12 Mathematics Applications of Derivatives 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 Case Study Questions for Class 12 Maths Relations and Functions Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 12 Maths Relations and Functions 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 12 Maths Relations and Functions PDF

Mcq set 1 -, mcq set 2 -, checkout our case study questions for other chapters.

Chapter 2 Inverse Trigonometric Functions Case Study Questions
Chapter 3 Matrices Case Study Questions
Chapter 4 Determinants Case Study Questions
Chapter 5 Continuity and Differentiability Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

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CBSE Case Study Class 12

While preparing for the board exams, students are being judged on different levels of skills, such as writing, reading, etc. CBSE Case Study Class 12 questions are one of them that helps in assessing critical thinking.

The Central Board of Secondary Education will be asking the case study questions in the Class 12 board examination. Therefore, here on this page, we have provided the CBSE Case Study Class 12 for Maths, Physics, Chemistry, Biology and other subjects. Our subject matter experts have prepared Case Study questions so that Apart from the basic standard questions, students can have a variety of problems to solve.

Just like MCQs, and other written types questions CBSE Case Study Class 12 questions will impact the overall performance of a student. Therefore for the convenience of the students we have provided the download links here, so that they can easily access the Class 12 Case Study.

Download Subject Wise CBSE Case Study Class 12 Question and Answers PDF

There are three different streams in class 12th: Science, Arts & Commerce. And all these streams have a variety of subjects therefore, here our subject experts have crafted the Subject Wise Case Study For Class 12. Download Subject Wise CBSE Case Study Class 12 Question and Answers PDF from the below given links.

CBSE Case Study Questions Class 12 for Maths

To learn how to answer CBSE Case Study Class 12 maths questions, it would be a good choice to refer to the separate set of questions in PDF. CBSE Case Study Questions for Class 12 Maths can be quite useful and helpful in understanding how the board will prepare the case based questions for maths.

The Maths Case studies are distributed into different chapters as per the prescribed syllabus of maths. Each and every chapter contains several number of case studies problems which enable the learners to gain in-depth knowledge in the subject.

The maths case study questions of class 12 are usually based on the formula. If any student wants to get a good score in maths case studies then they have to be well versed with a set of formulas as per the chapters and topics. Case Study Class 12 Maths can be downloaded here on this website for free of cost.

Case Study Questions Class 12 Chapter 1 Relations And Functions

Case Study Questions Class 12 Chapter 3 Matrices

Case Study Questions Class 12 Chapter 4 Determinants

Case Study Questions Class 12 Chapter 5 Continuity And Differentiability

Case Study Questions Class 12 Chapter 6 Application Of Derivatives

Case Study Questions Class 12 Chapter 8 Application Of Integrals

Case Study Questions Class 12 Chapter 9 Differential Equations

Case Study Questions Class 12 Chapter 10 Vector Algebra

Case Study Questions Class 12 Chapter 11 Three Dimensional Geometry

Case Study Questions Class 12 Chapter 12 Linear Programming

Case Study Questions Class 12 Chapter 13 Probability

CBSE Case Study Questions Class 12 for Physics

CBSE Class 12 Physics Case Study for different chapters can be interesting to solve. Class 12th physics case studies generally contain descriptive paragraphs and 4 to 5 different questions are given based on the paragraph. Students are required to read the paragraph thoroughly and understand them as well as observe the given data and information to answer the Class 12 Case Study Questions for Physics.

In order to solve those questions students are required to have a better understanding of the basic level of physics concepts too, so make sure to use Class 12 Revision Notes of Physics.

Case Study Questions Class 12 Chapter 1 Electric Charges and Fields

Case Study Questions Class 12 Chapter 2 Electrostatic Potential And Capacitance

Case Study Questions Class 12 Chapter 3 Current Electricity

Case Study Questions Class 12 Chapter 4 Moving Charges And Magnetism

Case Study Questions Class 12 Chapter 5 Magnetism And Matter

Case Study Questions Class 12 Chapter 6 Electromagnetic Induction

Case Study Questions Class 12 Chapter 7 Alternating Current

Case Study Questions Class 12 Chapter 8 Electromagnetic Waves

Case Study Questions Class 12 Chapter 9 Ray Optics & Optical Instruments

Case Study Questions Class 12 Chapter 10 Wave Optics

Case Study Questions Class 12 Chapter 11 Dual Nature Radiation & Matter

Case Study Questions Class 12 Chapter 12 Atoms

Case Study Questions Class 12 Chapter 13 Nuclei

Case Study Questions Class 12 Chapter 14 Semiconductor Electronics - Materials, Devices & Simple Circuits

CBSE Case Study Questions Class 12 for Chemistry

Students opted for Science stream will have to study CBSE Case Study Class 12 Chemistry. The given PDF of CBSE Class 12 Case Study Questions for Chemistry will enable the students to practice tons of questions on a regular basis. It will help them to revise the chemistry questions and its syllabus frequently. The Case study questions allow students to think more creative and find the answers in the quickest way possible. Links to download the PDF file of Class 12 Chemistry Case Study are given here.

Case Study Questions Class 12 Chapter 1 The Solid State

Case Study Questions Class 12 Chapter 2 Solutions

Case Study Questions Class 12 Chapter 3 Electrochemistry

Case Study Questions Class 12 Chapter 4 Chemical Kinetics

Case Study Questions Class 12 Chapter 5 Surface Chemistry

Case Study Questions Class 12 Chapter 7 The p-Block Elements

Case Study Questions Class 12 Chapter 8 The d- and f-Block Elements

Case Study Questions Class 12 Chapter 9 Coordination Compounds

Case Study Questions Class 12 Chapter 10 Haloalkanes And Haloarenes

Case Study Questions Class 12 Chapter 11 Alcohols, Phenols And Ethers

Case Study Questions Class 12 Chapter 12 Aldehydes. Ketones & Carboxylic Acids

Case Study Questions Class 12 Chapter 13 Amines

Case Study Questions Class 12 Chapter 14 Biomolecules

CBSE Case Study Questions Class 12 for Biology

There are lots of chapters in class 12 Biology from which Class 12 Case Study Questions can be framed. Going through such types of questions help the students to assess their understanding level in the topics discussed in NCERT Class 12 Biology Books. By practicing the Class 12 Case Study Questions for Biology students will be very confident to ace the board exam. Also the Biology case study will be very useful for the NEET exam preparation.

Doing a regular practice of Class 12 Biology Case Study questions is a great way to score higher marks in the board exams as it will help students to develop a grip on the concepts.

Case Study Questions Class 12 Chapter 2 Sexual Reproduction in Flowering Plants

Case Study Questions Class 12 Chapter 3 Human Reproduction

Case Study Questions Class 12 Chapter 4 Reproductive Health

Case Study Questions Class 12 Chapter 5 Principles of Inheritance & Variation

Case Study Questions Class 12 Chapter 6 Molecular Basic of Inheritance

Case Study Questions Class 12 Chapter 8 Human Health And Diseases

Case Study Questions Class 12 Chapter 10 Microbes in Human Welfare

Case Study Questions Class 12 Chapter 11 Biotechnology - Principles & Processes

Case Study Questions Class 12 Chapter 12 Biotechnology And Its Applications

Case Study Questions Class 12 Chapter 13 Organisms And Populations

Case Study Questions Class 12 Chapter 15 Biodiversity And Conversation

Case study types of questions are generally descriptive that helps to gather more information easily so, it is kinda easy to answer. However, our subject matter experts have given the solutions of all the CBSE Case Study Class 12 Biology questions.

Passage Based Class 12 Case Study Questions in PDF

CBSE Class 12 Case studies are known as Passage Based Questions. These types of problems usually contain a short/long paragraph with 4 to 5 questions.

Students can easily solve Passage Based Class 12 Case Study Questions by reading those passages. By reading the passage students will get the exact idea of what should be the answers. Because the passage already contains some vital information or data. However a better understanding of the basic concepts that can be learned from the NCERT Class 12 Textbooks will aid in solving the Case based questions or passage based questions.

How to Download CBSE Case Study of Class 12?

Follow the below given simple steps to know how to download CBSE Case Study of Class 12:-

Open Selfstudys website in your browser
Go to the navigation menu that look like this
Now, click on CBSE and then Case Study respectively
A new page will open, where you have to click on “Class 12”
Now, you are ready to select the subject for which you want to download the case study questions.

How to Solve Case Study Based Questions of Class 12?

There are very simple methods that a student should keep in mind while solving CBSE Case Study Class 12 for any subject:

Read each line of paragraph carefully and pay attention to the given data/numbers. Often questions are framed according to the highlighted data of the passage.
Since case study questions are often framed in Multiple choice questions, students should have the knowledge of elimination methods in MCQs.
Having a good understanding of the topics that are discussed in CBSE Class 12 Books are ideal to Solve Case Study Based Questions of Class 12.

Features Of Class 12 Case Study Questions And Answers PDF

The three most noticeable features of Class 12 Case Study Questions And Answers Pdf are -

It Is Free To Use: Keeping in mind the need of students and to help them in doing Self Study, our team has made all the PDF of CBSE Case Study Class 12 free of cost.
Answers Are Given: Not only the PDFs are free provided but answers are given for all the questions of CBSE Case Study Class 12.
PDF Can Be Downloaded Or Viewed Online: Many students don’t like to download the PDFs on their device due to the shortage of storage. Therefore, CBSE Class 12 Case Study questions are made available here in online format, so that students can view them online. However, through the Selfstudys app, a learner can download the PDFs too.

Benefits of Using CBSE Class 12 Case Study Questions and Answers

The CBSE Class 12 Case Study Questions and Answers can help a student in several ways:

In Exam Preparation: Those who go through the CBSE Case Study Class 12 will find support during the exam preparation as case based questions are also asked in the CBSE Class 12 Board examination.
Help in brushing up the previous learnings: No matter how brilliant you are, you have to revise the studied topics time and again to keep them refreshed. And in this task, the CBSE Class 12 Case Study Questions and Answers can help a lot.
To develop the critical thinking: Able to analyse information and make an objective judgement is a skill that is known as critical thinking. A student of class 12 can use CBSE Case Study Class 12 with answers to develop critical thinking so that they can make better decisions in their life and in the board examination.

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CASE STUDY-1 CHAPTER -1

Relations & functions.

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever

Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {( 𝑉 1, 𝑉 2) ∶ 𝑉 1, 𝑉 2 ∈ 𝐼 and both use their voting right in general election – 2019}

a) (X, Y) ∈ R

b) (Y, X) ∈ R

c) (X, X) ∉ R

d) (X, Y) ∉ R

a) both (X, W) and (W, X) ∈ R

b) (X, W) ∈ R but (W, X) ∉ R

c) both (X, W) and (W, X) ∉ R

d) (W, X) ∈ R but (X, W) ∉ R

a) (F1, F2 ) ∈ R, (F2, F3) ∈ R and (F1,F3) ∈ R

b) (F1, F2 ) ∈ R, (F2,F3) ∈ R and (F1,F3) ∉ R

c) (F1, F2 ) ∈ R, (F2,F2) ∈ R but (F3,F3) ∉ R

d) (F1, F2 ) ∉ R, (F2,F3) ∉ R and (F1,F3) ∉ R

a) Symmetric and transitive but not reflexive

b) Universal relation

c) Equivalence relation

d) Reflexive but not symmetric and transitive

a) All those eligible voters who cast their votes

b) Family members of Mr. Shyam

c) All citizens of India

d) Eligible voters of India


		(X, Y) ∉R
		both (X, W) and (W, X) ∈ R
		∈R, (F2, F3) ∈ R and (F1, F3) ∈ R

CASE STUDY-2 CHAPTER -1

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes

A = {S, D}, B = {1, 2, 3, 4, 5, 6}

a) Reflexive and transitive but not symmetric

b) Reflexive and symmetric and not transitive

c) Not reflexive but symmetric and transitive

d) Equivalence

a) Symmetric

b) Reflexive

c) Transitive

d) None of these three

b) Reflexive and Transitive

c) Transitive and symmetric

CASE STUDY-3 CHAPTER -1

Students of a school are taken to a railway museum to learn about railways heritage and its history.

An exhibit in the museum depicted many rail lines on the track near the railway station. Let L be the set of all rail lines on the railway track and R be the relation on L defined by

R = { (l 1 , l 2 ) : l 1 is parallel to l 2 }

On the basis of the above information, answer the following questions :

(iii) The set is {I : I is a line of type y = 3x + c, c ∈ R}

CASE STUDY-1 CHAPTER -3

A manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below

If the unit Sale price of Pencil, Eraser and Sharpener are Rs. 2.50, Rs. 1.50 and Rs. 1.00 respectively, and unit cost of the above three commodities are Rs. 2.00, Rs. 1.00 and Rs. 0.50 respectively, then,

Based on the above information answer the following:

1) Total revenue of market A

a) Rs. 64,000

b) Rs. 60,400

c) Rs. 46,000

d) Rs. 40600

2) Total revenue of market B

a) Rs. 35,000

b) Rs. 53,000

c) Rs. 50,300

d) Rs. 30,500

3) Cost incurred in market A

a) Rs. 13,000

b) Rs.30,100

c) Rs. 10,300

d) Rs. 31,000

4) Profit in market A and B respectively are

a) (Rs. 15,000, Rs. 17,000)

b) (Rs. 17,000, Rs. 15,000)

c) (Rs. 51,000, Rs. 71,000)

d) ( Rs. 10,000, Rs. 20,000)

5) Gross profit in both market

a) Rs.23,000

b) Rs. 20,300

c) Rs. 32,000

d) Rs. 30,200


		Rs. 46,000
		Rs. 53,000
		Rs.31,000
		Rs.15, 000, Rs.17, 000
		Rs. 32,000

CASE STUDY-2 CHAPTER -3

CASE STUDY 2:

Amit, Biraj and Chirag were given the task of creating a square matrix of order 2. Below are the matrices created by them. A, B , C are the matrices created by Amit, Biraj and Chirag respectively.