case study of class 12 maths

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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

More Case Study Questions

These are only some samples. If you wish to get more case study questions for CBSE class 12 maths, install the myCBSEguide App. It has class 12 Maths chapter-wise case studies with solutions.

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.

• 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

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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• 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 Expert

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 Case Study Questions for Class 12 Maths Matrices Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 12 Maths Matrices  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 Matrices PDF

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

• Chapter 1 Relations and Functions Case Study Questions
• Chapter 2 Inverse Trigonometric Functions 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

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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CBSE 12th Standard Maths Subject Continuity and Differentiability Case Study Questions 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

Cbse 12th standard maths continuity and differentiability case study questions 2021.

12th Standard CBSE

Final Semester - June 2015

Case Study Questions

Let f(x) be a real valued function, then its  Left Hand Derivative (L.H.D.) :  \(\begin{equation} \mathrm{L} f^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a-h)-f(a)}{-h} \end{equation}\)   Right Hand Derivative (R.H.D.) :  \(\begin{equation} \mathrm{Rf}^{\prime}(a)=\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h} \end{equation}\)   Also, a function jfx) is said to be differentiable at x = a if its L.H.D. and R.H.D. at x = a exist and are equal  For the function  \(\begin{equation} f(x)=\left\{\begin{array}{l} |x-3|, x \geq 1 \\ \frac{x^{2}}{4}-\frac{3 x}{2}+\frac{13}{4}, x<1 \end{array}\right. \end{equation}\)  answer the following questions (i) R.H.D. of f(x) at x = 1is

(ii) L.H.D. of f(x) at x = 1 is

(iii) f(x) is non-differentiable at

(iv) Find the value of f'(2).

(v) The value of f'( -1) is

The function f(x) will be discontinuous at x = a if f(x) has  (a) Discontinuity of first kind  \(\begin{equation} \lim _{h \rightarrow 0} f(a-h) \text { and } \lim _{h \rightarrow 0} f(a+h) \end{equation}\)  both exist but are not equal. If is also known as irremovable discontinuity. (b)  Discontinuity of second kind: If none of the limits  \(\begin{equation} \lim _{h \rightarrow 0} f(a-h) \text { and } \lim _{h \rightarrow 0} f(a+h) \end{equation}\)  exist. (c) Removable discontinuity:  \(\begin{equation} \lim _{h \rightarrow 0} f(a-h) \text { and } \lim _{h \rightarrow 0} f(a+h) \end{equation}\)  both exist and equal but not equal to f(a).  Based on the above information, answer the following questions. (i) If  \(\begin{equation} f(x)=\left\{\begin{array}{ll} \frac{x^{2}-9}{x-3}, & \text { for } x \neq 3 \\ 4, & \text { for } x=3 \end{array}\right. \end{equation}\)  ,then at x= 3

(ii) Let  \(\begin{equation} f(x)=\left\{\begin{array}{ll} x+2, & \text { if } x \leq 4 \\ x+4, & \text { if } x>4 \end{array}\right. \end{equation}\)  ,then at x = 4

(iii) Consider the function f(x) defined  \(\begin{equation} f(x)=\left\{\begin{array}{l} \frac{x^{2}-4}{x-2} \\ 5 \end{array}\right. \end{equation}\) , for  \(\begin{equation} x \neq 2 \end{equation}\)  

 (iv) If  \(\begin{equation} f(x)=\left\{\begin{array}{cc} \frac{x-|x|}{x}, & if\ x \neq 0 \\ 2, & if\ x=0 \end{array}\right. \end{equation}\)  ,then x = 0

(v) If  \(\begin{equation} f^{\prime}(x)=\left\{\begin{array}{cl} \frac{e^{x}-1}{\log (1+2 x)}, & \text { if } x \neq 0 \\ 7, & \text { if } x=0 \end{array}\right. \end{equation}\) , then at x = 0

(a) A function f(x) is said to be continuous in an open interval (a, b), if it is continuous at every point in this interval. (b) A function f(x) is said to be continuous in the closed interval [a, b], if f(x) is continuous in (a, b) and  \(\begin{equation} \lim _{h \rightarrow 0} f(a+h)=f(a) \text { and } \lim _{h \rightarrow 0} f(b-h)=f(b) \end{equation}\)   If function   \(\begin{equation} f(x)=\left\{\begin{array}{ll} \frac{\sin (a+1) x+\sin x}{x} & , x<0 \\ c & , x=0 \\ \frac{\sqrt{x+b x^{2}}-\sqrt{x}}{b x^{3 / 2}} & , x>0 \end{array}\right. \end{equation}\)  is continuous at x = 0, then answer the following questions. (i) The value of a is

(ii) The value of b is

(iii) The value of c is

(iv) The value of a + c is

(v) The value oi c - a is

If y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, then y = f[g(x)] is a differentiable function of x and  \(\begin{equation} \frac{d y}{d x}=\frac{d y}{d u} \times \frac{d u}{d x} \end{equation}\) . This rule is also known as CHAIN RULE. Based on the above information, find the derivative of functions w.r.t. x in the following questions (i)  \(\begin{equation} \cos \sqrt{x} \end{equation}\)  

(ii)  \(\begin{equation} 7^{x+\frac{1}{x}} \end{equation}\)  

(iii)  \(\begin{equation} \sqrt{\frac{1-\cos x}{1+\cos x}} \end{equation}\)  

(v) (d) : \(\begin{equation} \sec ^{-1} x+\operatorname{cosec}^{-1} \frac{x}{\sqrt{x^{2}-1}} \end{equation}\)   

If a relation between x and y is such that y cannot be expressed in terms of x, then y is called an implicit function of x. When a given relation expresses y as an implicit function of x and we want to find  \(\begin{equation} \frac{d y}{d x} \end{equation}\) .then we differentiate every term of the given relation w.r.t. x. remembering that a term in y is first differentiated w.r.t. y and then multiplied by  \(\begin{equation} \frac{d y}{d x} \end{equation}\) . Based on the above information, find the value of  \(\begin{equation} \frac{d y}{d x} \end{equation}\)  in each of the following questions  (i) x 3 +x 2 y+xy 2 +y3=81

(ii) x y = c- y

(iii) e siny = xy

(iv) sin 2 x + cos 2 y = 1

(v)  \(\begin{equation} y=(\sqrt{x})^{\sqrt{x}} \end{equation}\)  

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

Cbse 12th standard maths continuity and differentiability case study questions 2021 answer keys.

we have, \(\begin{equation} f(x)=\left\{\begin{array}{ll} x-3 & , x \geq 3 \\ 3-x & , 1 \leq x<3 \\ \frac{x^{2}}{4}-\frac{3 x}{2}+\frac{13}{4} & , x<1 \end{array}\right. \end{equation}\)   (i) (b) :  \(\begin{equation} \mathrm{R} f^{\prime}(1)=\lim _{h \rightarrow 0} \frac{f(1+h)-f(1)}{h} \end{equation}\)   \(\begin{equation} =\lim _{h \rightarrow 0} \frac{3-(1+h)-2}{h}=\lim _{h \rightarrow 0}-\frac{h}{h}=-1 \end{equation}\)   (ii) (b) :   \(\begin{equation} \mathrm{L}_{\mathrm{s}}^{\prime}(1)=\lim _{h \rightarrow 0} \frac{f(1-h)-f(1)}{-h} \end{equation}\)   \(\begin{equation} =\lim _{h \rightarrow 0} \frac{-1}{h}\left[\frac{(1-h)^{2}}{4}-\frac{3(1-h)}{2}+\frac{13}{4}-2\right] \end{equation}\)   \(\begin{equation} =\lim _{h \rightarrow 0}\left(\frac{1+h^{2}-2 h-6+6 h+13-8}{-4 h}\right) \end{equation}\)   \(\begin{equation} =\lim _{h \rightarrow 0}\left(\frac{h^{2}+4 h}{-4 h}\right)=-1 \end{equation}\)   (iii) (c) : Since, R.H.D. at x = 3 is 1 and L.H.D. at x = 3 is-1 \(\therefore\)   f(x) is non-differentiable at x = 3. (iv) (d) (v) (c) : From above, we have \(\begin{equation} f^{\prime}(x)=\frac{x}{2}-\frac{3}{2}, x<1 \end{equation}\)   \(\begin{equation} \therefore f^{\prime}(-1)=\frac{-1}{2}-\frac{3}{2}=-2 \end{equation}\)  

(i) (a) :  f(3) = 4 \(\begin{equation} \lim _{x \rightarrow 3} f(x)=\lim _{x \rightarrow 3} \frac{x^{2}-9}{x-3}=\lim _{x \rightarrow 3} \frac{(x+3)(x-3)}{(x-3)} \end{equation}\)   \(\begin{equation} =\lim _{x \rightarrow 3}(x+3)=6 \because \lim _{x \rightarrow 3} f(x) \neq f(3) \end{equation}\)   \(\therefore\)  f(x) has removable discontinuity at x = 3. (ii) (c) :   \(\begin{equation} \lim _{x \rightarrow 4^{-}} f(x)=\lim _{x \rightarrow 4}(x+2)=4+2=6 \end{equation}\)   \(\begin{equation} \lim _{x \rightarrow 4^{+}} f(x)=\lim _{x \rightarrow 4}(x+4)=4+4=8 \end{equation}\)   \(\begin{equation} \therefore \quad \lim _{x \rightarrow 4^{-}} f(x) \neq \lim _{x \rightarrow 4^{+}} f(x) \end{equation}\)   \(\begin{equation} \therefore f(x) \end{equation}\)  has an irremovable discontinuity at x = 4. (iii) (a) :    \(\begin{equation} \lim _{x \rightarrow 2} f(x)=\lim _{x \rightarrow 2} \frac{\left(x^{-4}-4\right)}{(x-2)}=\lim _{x \rightarrow 2}(x+2)=4 \end{equation}\)   \(\begin{equation} \therefore f(x) \end{equation}\)  has removable discontinuity at x = 2. (iv) (c) : f(0)=2 \(\begin{equation} \lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0} \frac{x+x}{x}=2 \end{equation}\)   \(\begin{equation} \lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0} \frac{x-x}{x}=0 \end{equation}\)   \(\begin{equation} \because \lim _{x \rightarrow 0^{-}} f(x) \neq \lim _{x \rightarrow 0^{+}} f(x) \end{equation}\) \(\begin{equation} \therefore f(x) \end{equation}\)  has an irremovable discontinuity at x = 0. (v) (d) : f(0) = 7 \(\begin{equation} \lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0} \frac{e^{x}-1}{\log (1+2 x)}=\lim _{x \rightarrow 0} \frac{\frac{\left(\frac{e^{x}-1}{x}\right)}{\log (1+2 x)}{2 x} \cdot 2}=\frac{1}{2} \end{equation}\)   \(\begin{equation} \because \ \lim _{x \rightarrow 0} f(x) \neq f(0) \end{equation}\)   \(\begin{equation} \therefore f(x) \end{equation}\)  has removable discontinuity at x = 0.

L.H.L (at x = 0) =  \(\begin{equation} \lim _{x \rightarrow 0} \frac{\sin (a+1) x+\sin x}{x}\left(\frac{0}{0} \text { form }\right) \end{equation}\)   Using L' Hospital rule, we get L.H.L.(at x = 0) \(\begin{equation} =\lim _{x \rightarrow 0}(a+1) \cos (a+1) x+\cos x=a+2 \end{equation}\)   R.H.L  \(\begin{equation} \text { (at } x=0)=\lim _{x \rightarrow 0} \frac{\sqrt{x+b x^{2}}-\sqrt{x}}{b x^{3 / 2}}=\lim _{x \rightarrow 0} \frac{\sqrt{1+b x}-1}{b x} \end{equation}\)   \(\begin{equation} =\lim _{x \rightarrow 0} \frac{1}{\sqrt{1+b x}+1}=\frac{1}{2} \end{equation}\)   Since,f(x) is continuous at x = 0. \(\therefore\)  From (i) and (ii), we get \(\begin{equation} a+2=c=\frac{1}{2} \Rightarrow a=-\frac{3}{2}, c=\frac{1}{2} \end{equation}\)   Also, value of b does not affect the continuity of f(x), so b can be any real number. (i) (a) (ii) (d)  (iii) (b) (iv) (c) :   \(\begin{equation} a+c=-\frac{3}{2}+\frac{1}{2}=-1 \end{equation}\)   (v) (d) :   \(\begin{equation} c-a=\frac{1}{2}+\frac{3}{2}=2 \end{equation}\)

(i) (a) : Let  \(\begin{equation} y=\cos \sqrt{x} \end{equation}\)   \(\begin{equation} \therefore \quad \frac{d y}{d x}=\frac{d}{d x}(\cos \sqrt{x})=-\sin \sqrt{x} \cdot \frac{d}{d x}(\sqrt{x}) \end{equation}\)   \(\begin{equation} =-\sin \sqrt{x} \times \frac{1}{2 \sqrt{x}}=\frac{-\sin \sqrt{x}}{2 \sqrt{x}} \end{equation}\)   (ii) (a) : Let  \(\begin{equation} y=7^{x+\frac{1}{x}} \quad \therefore \quad \frac{d y}{d x}=\frac{d}{d x}\left(7^{x+\frac{1}{x}}\right) \end{equation}\)   \(\begin{equation} =7^{x+\frac{1}{x}} \cdot \log 7 \cdot \frac{d}{d x}\left(x+\frac{1}{x}\right)=7^{x+\frac{1}{x}} \cdot \log 7 \cdot\left(1-\frac{1}{x^{2}}\right) \end{equation}\)   \(\begin{equation} =\left(\frac{x^{2}-1}{x^{2}}\right) \cdot 7^{x+\frac{1}{x}} \cdot \log 7 \end{equation}\)   (iii) (a) : Let  \(\begin{equation} y=\sqrt{\frac{1-\cos x}{1+\cos x}}=\sqrt{\frac{1-1+2 \sin ^{2} \frac{x}{2}}{2 \cos ^{2} \frac{x}{2}-1+1}}=\tan \left(\frac{x}{2}\right) \end{equation}\)   \(\begin{equation} \therefore \frac{d y}{d x}=\sec ^{2} \frac{x}{2} \cdot \frac{1}{2}=\frac{1}{2} \sec ^{2} \frac{x}{2} \end{equation}\)   (iv) (b) :  Let  \(\begin{equation} y=\frac{1}{b} \tan ^{-1}\left(\frac{x}{b}\right)+\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right) \end{equation}\)   \(\begin{equation} \therefore \quad \frac{d y}{d x}=\frac{1}{b} \times \frac{1}{1+\frac{x^{2}}{b^{2}}} \times \frac{1}{b}+\frac{1}{a} \times \frac{1}{1+\frac{x^{2}}{a^{2}}} \times \frac{1}{a} \end{equation}\)   \(\begin{equation} =\frac{1}{b^{2}+x^{2}}+\frac{1}{a^{2}+x^{2}} \end{equation}\)   (v) (d) :  Let  \(\begin{equation} y=\sec ^{-1} x+\operatorname{cosec}^{-1} \frac{x}{\sqrt{x^{2}-1}} \end{equation}\)   Put   \(\begin{equation} x=\sec \theta \Rightarrow \theta=\sec ^{-1} x \end{equation}\)   \(\begin{equation} \therefore \quad y=\sec ^{-1}(\sec \theta)+\operatorname{cosec}^{-1}\left(\frac{\sec \theta}{\sqrt{\sec ^{2} \theta-1}}\right) \end{equation}\)   \(\begin{equation} =\theta+\sin ^{-1}\left[\sqrt{1-\cos ^{2} \theta}\right] \end{equation}\)   \(\begin{equation} =\theta+\sin ^{-1}(\sin \theta)=\theta+\theta=2 \theta=2 \sec ^{-1} x \end{equation}\)   \(\begin{equation} \therefore \quad \frac{d y}{d x}=2 \frac{d}{d x}\left(\sec ^{-1} x\right)=2 \times \frac{1}{|x| \sqrt{x^{2}-1}}=\frac{2}{|x| \sqrt{x^{2}-1}} \end{equation}\)

(i) (b) :  x 3 + x 2 y+ xy 2 +y 3 = 81 \(\begin{equation} \Rightarrow 3 x^{2}+x^{2} \frac{d y}{d x}+2 x y+2 x y \frac{d y}{d x}+y^{2}+3 y^{2} \frac{d y}{d x}=0 \end{equation}\)   \(\begin{equation} \Rightarrow \left(x^{2}+2 x y+3 y^{2}\right) \frac{d y}{d x}=-3 x^{2}-2 x y-y^{2} \end{equation}\)   \(\begin{equation} \Rightarrow \frac{d y}{d x}=\frac{-\left(3 x^{2}+2 x y+y^{2}\right)}{x^{2}+2 x y+3 y^{2}} \end{equation}\)   (ii) (c) :  x y = e x-y ⇒y log x = x - y \(\begin{equation} \Rightarrow y \times \frac{1}{x}+\log x \cdot \frac{d y}{d x}=1-\frac{d y}{d x} \end{equation}\)   \(\begin{equation} \Rightarrow \frac{d y}{d x}[\log x+1]=1-\frac{y}{x} \Rightarrow \frac{d y}{d x}=\frac{x-y}{x[1+\log x]} \end{equation}\)   (iii) (d) :  \(\begin{equation} e^{\sin y}=x y \Rightarrow \sin y=\log x+\log y \end{equation}\)   \(\begin{equation} \Rightarrow \cos y \frac{d y}{d x}=\frac{1}{x}+\frac{1}{y} \frac{d y}{d x} \Rightarrow \frac{d y}{d x}\left[\cos y-\frac{1}{y}\right]=\frac{1}{x} \end{equation}\)   \(\begin{equation} \Rightarrow \frac{d y}{d x}=\frac{y}{x(y \cos y-1)} \end{equation}\)   (iv) (d) : sin 2 x + cos 2 y = 1 \(\begin{equation} \Rightarrow \quad 2 \sin x \cos x+2 \cos y\left(-\sin y \frac{d y}{d x}\right)=0 \end{equation}\)   \(\begin{equation} \Rightarrow \frac{d y}{d x}=\frac{-\sin 2 x}{-\sin 2 y}=\frac{\sin 2 x}{\sin 2 y} \end{equation}\)   (v) (d) :  \(\begin{equation} y=(\sqrt{x})^{\sqrt{x}} \quad \Rightarrow y=(\sqrt{x})^{y} \end{equation}\)   \(\begin{equation} \Rightarrow \log y=y(\log \sqrt{x}) \Rightarrow \log y=\frac{1}{2}(y \log x) \end{equation}\)   \(\begin{equation} \Rightarrow \frac{1}{y} \frac{d y}{d x}=\frac{1}{2}\left[y \times \frac{1}{x}+\log x\left(\frac{d y}{d x}\right)\right] \end{equation}\)   \(\begin{equation} \Rightarrow \frac{d y}{d x}\left\{\frac{1}{y}-\frac{1}{2} \log x\right\}=\frac{1}{2} \frac{y}{x} \end{equation}\)   \(\begin{equation} \Rightarrow \frac{d y}{d x}=\frac{y}{2 x} \times \frac{2 y}{(2-y \log x)}=\frac{y^{2}}{x(2-y \log x)} \end{equation}\)

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Case Study Questions for Class 12 Maths

Chapter 1 Relations and Functions Chapter 2 Inverse Trigonometric Functions Chapter 3 Matrices Chapter 4 Determinants Chapter 5 Continuity and Differentiability Chapter 6 Applications of Derivatives Chapter 7 Integrals Chapter 8 Applications of Integrals Chapter 9 Differential Equations Chapter 10 Vector Algebra Chapter 11 Three-dimensional Geometry Chapter 12 Linear Programming Chapter 13 Probability

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Class 12 Maths: Case Study of Chapter 3 Matrices 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 3 Matrices Case Study and Passage Based Questions with Answers were Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Matrices  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.

Matrices Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 12 Mathematics  Chapter 3 Matrices

Case Study/Passage-Based Questions

Three car dealers, say A, Band C, deals in three types of cars, namely Hatchback cars, Sedan cars, and SUV cars. The sales figure for 2019 and 2020 showed that dealer A sold 120 Hatchback, 50 Sedan, and 10 SUV cars in 2019 and 300 Hatchback, 150 Sedan, and 20 SUV cars in 2020; dealer B sold 100 Hatchback, 30 Sedan, and S SUV cars in 2019 and 200 Hatchback, 50 Sedan, 6 SUV cars in 2020; dealer C sold 90 Hatchback, 40 Sedan, 2 SUV cars in 2019 and 100 Hatchback, 60 Sedan,S SUV cars in 2020.

Based on the above information, answer the following questions.

(i) The matrix summarizing sales data for 2019 is

Answer: (b)

(ii) The matrix summarizing sales data of 2020 is

Answer: (a)

 (iii) The total number of cars sold in two given years, by each dealer, is given by the matrix

Answer: (c)

(iv) The increase in sales from 2019 to 2020 is given by the matrix

(v) If each dealer receives a profit of Rs.50000 on the sale of a Hatchback, Rs.100000 on the sale of a Sedan, and Rs. 200000 on the sale of an SUV (v) then the amount of profit received in the year 2020 by each dealer is given by the matrix.

Hope the information shed above regarding Case Study and Passage Based Questions for Class 12 Maths Chapter 3 Matrices with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 12 Mathematics Matrices 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 on Matrices Class 12 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Matrices Class 12 Maths can use this page to download the PDF file. 

The case study questions on Matrices are based on the CBSE Class 12 Maths Syllabus, and therefore, referring to the Matrices case study questions enable students to gain the appropriate knowledge and prepare better for the Class 12 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Matrices Class 12 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Matrices, therefore, they prepared a set of solutions along with the case study questions on Matrices.

The case study on Matrices Class 12 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Matrices case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Matrices Case Study Questions on Class 12 Maths?

There are three major reasons why one should solve Matrices case study questions on Class 12 Maths - all those major reasons are discussed below:

• To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 12 Maths students, therefore, it is important to solve Matrices Case study questions as it will help better prepare for the Class 12 board exam preparation.
• Develop Problem-Solving Skills: Class 12 Maths Matrices case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 12 students develop their problem-solving skills, which are essential for success in any profession rather than Class 12 board exam preparation.
• Understand Real-Life Applications: Several Matrices Class 12 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Matrices as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Matrices?

Students can choose their own way to answer Case Study on Matrices Class 12 Maths, however, we believe following these three steps would help a lot in answering Class 12 Maths Matrices Case Study questions.

• Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
• Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Matrices questions quickly.
• Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Matrices Class 12 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 12 Matrices?

 A few essential things to know to solve Case Study Questions on Class 12 Matrices are -

• Basic Formulas of Matrices: One of the most important things to know to solve Case Study Questions on Class 12 Matrices is to learn about the basic formulas or revise them before solving the case-based questions on Matrices.
• To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 12 Maths Matrices case study questions.
• Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

Where to Find Case Study on Matrices Class 12 Maths?

Use Selfstudys.com to find Case Study on Matrices Class 12 Maths. For ease, here is a step-wise procedure to download the Matrices Case Study for Class 12 Maths in PDF for free of cost.

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• Find CBSE from the given menu

• Click on Case Study

• Choose Class 12 
• Search Maths and then navigate to the Matrices Class 12 Maths Case Study

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• Simple Equations Class 7 Case Study Questions Maths Chapter 4

Last Updated on August 18, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 7 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 7 maths. In this article, you will find case study questions for CBSE Class 7 Maths Chapter 4 Simple Equations. It is a part of Case Study Questions for CBSE Class 7 Maths Series.

Table of Contents

Case Study Questions on Simple Equations

The teacher tells the class that the lowest marks obtained by a student in his class is half the highest marks plus 5. The lowest score is 45. What is the highest score ?

Q. 1. Find the marks which is 20 more than the lowest: (a) 25 (b) 65 (c) 70 (d) None of these

Difficulty Level: Easy

Ans. Option (b) is correct. Explanation: Given lowest marks is 45 and 20 more it is 45 + 20 = 65

Q. 2. Just to pass in the examination border line marks is just 12 less than the lowest marks obtained by the student in the class. Write the required passing marks. (a) 56 (b) 40 (c) 33 (d) 57

Difficulty Level: Medium

Ans. Option (c) is correct. Explanation: Given passing marks = lowest marks – 12 = 45 – 12 = 33

Q. 3. If one student Aavya of another class who scored 9 marks more than the doubled of lowest marks of this class, find the aavya’s marks: (a) 92 (b) 50 (c) 89 (d) 99

Ans. Option (d) is correct. Explanation: Aavya score = 2 × Lowest marks + 9 = 2(45) + 9 = 90 + 9 = 99

Q. 4. Find the highest marks.

Difficulty Level: Hard

Explanation: let the highest marks be $x$ according to the question, lowest marks

$$ \begin{aligned} & =\frac{1}{2} \text { (highest marks) }+5 \\ 45 & =\frac{1}{2}(x)+5 \\ 45-5 & =\frac{1}{2} x \text { [transposing } 5 \text { to LHS] } \\ 40 & =\frac{1}{2} x \\ 40 \times 2 & =x \text { [multiplying both sides by } 2] \\ 80 & =x \\ x & =80 \end{aligned} $$

• Comparing Quantities Class 7 Case Study Questions Maths Chapter 7
• Triangle and its Properties Class 7 Case Study Questions Maths Chapter 6
• Lines and Angles Class 7 Case Study Questions Maths Chapter 5
• Data Handling Class 7 Case Study Questions Maths Chapter 3

Fractions and Decimals Class 7 Case Study Questions Maths Chapter 2

Integers class 7 case study questions maths chapter 1, topics from which case study questions may be asked.

• Linear equation
• Solution of a linear equation
• Transposition

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

• An equation is a statement of equality which involves one or more literal numbers.
• The value of the variable which satisfies an equation is called the solution or the root of an equation.
• A term in an equation can be transposed from one side of an the sign of equality to another side by changing its sign.
• A number that divides a literal or another number on one side of an equation, when transposed multiplies the other side and viceversa.

A linear equation remains the same when the expression in the left and right are interchanged.

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Frequently Asked Questions (FAQs) on Simple Equations Case Study

Q1: what are simple equations.

A1: Simple equations are mathematical statements that express equality between two expressions. They usually involve a variable (like x) and can be solved to find the value of the variable that makes the equation true.

Q2: How do you solve a simple equation?

A2: To solve a simple equation, you need to isolate the variable on one side of the equation. This can be done by performing the same mathematical operations on both sides of the equation, such as addition, subtraction, multiplication, or division.

Q3: Can simple equations have more than one solution?

A3: Simple equations usually have a single unique solution. However, certain types of equations, like identities, can have infinite solutions, but those are not typically covered under “simple equations” in Class 7.

Q4: Why is it important to learn simple equations?

A4: Learning simple equations is important because it forms the foundation for more advanced topics in algebra and mathematics. It helps in developing problem-solving skills and understanding how to work with variables and mathematical relationships.

Q5: What are some real-life applications of simple equations?

A5: Simple equations can be used in various real-life situations, such as calculating expenses, determining distances, solving for unknown quantities in recipes, and even in basic physics problems involving speed, distance, and time.

Q6: What common mistakes should students avoid when solving simple equations?

A6: Common mistakes include not performing the same operation on both sides of the equation, incorrectly combining like terms, and forgetting to change the sign when moving terms from one side of the equation to the other.

Q7: What are some tips for mastering simple equations?

A7: To master simple equations, students should focus on understanding the basic principles of balancing equations, practice regularly, and check their solutions by substituting the value back into the original equation to ensure it holds true.

Q8: How can students practice solving simple equations effectively?

A8: Students can practice effectively by solving a variety of problems, starting with simple ones and gradually moving to more complex equations. They can also use online resources, worksheets, and practice tests to reinforce their learning.

Q9: Are there any online resources or tools available for practicing comparing quantities case study questions?

A9: We provide case study questions for CBSE Class 8 Maths on our  website . Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit  Physics Gurukul  website. they are having a large collection of case study questions for all classes.

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