case study questions class 12 maths

Class 12 Maths: Case Study Based Questions PDF Download

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You must practice some good Case Study questions of Class 12 Maths to boost your preparation to score 95+% on Boards. In this post, you will get Case Study Questions of All Chapters which will come in CBSE Class 12 Maths Board Exams.

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We have provided here Case Study questions for the Class 12 Maths exams. You can read these chapter-wise Case Study questions. 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 Board Final exams.

We are providing Case Study questions for class 12 Biology based on the latest syllabi. There is a total of 13 chapters included in CBSE class 12 Maths exams. Students can practice these questions for concept clarity and score better marks in their exams.

Table of Contents

CBSE Class 12th – MATHS : Chapterwise Case Study Question & Solution

CBSE will ask two Case Study Questions in the CBSE class 12 maths questions paper. Question numbers 15 and 16 are case-based questions where 5 MCQs will be asked based on a paragraph. Each theme will have five questions and students will have a choice to attempt any four of them.

Case Study Based Questions for Class 12 Maths

Class 12 Physics Case Study Questions Class 12 Chemistry Case Study Questions Class 12 Biology Case Study Questions Class 12 Maths Case Study Questions

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.

Class 12 Maths Syllabus 2022-23

Unit-i: relations and functions.

1. Relations and Functions (15 Periods)

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.

2. Inverse Trigonometric Functions (15 Periods)

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Unit-II: Algebra

1. Matrices (25 Periods)

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Oncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

2. Determinants 25 Periods

Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Unit-III: Calculus

1. Continuity and Differentiability (20 Periods)

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, 𝑙𝑖𝑘𝑒 sin −1  𝑥 , cos −1  𝑥 and tan −1  𝑥, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

2. Applications of Derivatives (10 Periods)

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations).

3. Integrals (20 Periods)

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Applications of the Integrals (15 Periods)

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

5. Differential Equations (15 Periods)

Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

Unit-IV: Vectors and Three-Dimensional Geometry

1. Vectors (15 Periods)

Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

2. Three – dimensional Geometry (15 Periods)

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.

Unit-V: Linear Programming

1. Linear Programming (20 Periods)

Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit-VI: Probability

1. Probability 30 (Periods)

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.

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Class 12 Maths Case Study Questions

Table of Contents

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

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 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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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 12th Standard Maths Subject Three Dimensional Geometry 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

12th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) The magnitude of the normal to the plane on which students of school B are seated, is

(iii) The intercept form of the equation of the plane on which students of school B are seated, is

(iv) Which of the following is a student of school B?

(v) The distance of the plane, on which students of school B are seated, from the origin is

(ii) The vector \(\overline{E D}\)  is

(iii) The length of the cable EB is

(iv) The length of cable EC is equal to the length of

(v) The sum of all vectors along the cables is

(ii) If the soldier decides to shoot the boat at given instant of time, where the distance measured in metres, then what is the distance that bullet has to travel?

(iii) If the speed of bullet is 30 m/sec, then how much time will the bullet take to hit the boat after the shot is fired?

(iv) At the given instant of time, the equation of line passing through the positions of helicopter and boat is

(v) At a different instant of time, the boat moves to a different position along the planar surface. What should be the coordinates of the location of the boat for the bullet to hit the boat if soldier shoots the bullet along the line whose equation is  \(\frac{x-1}{1}=\frac{y-1}{-2}=\frac{z-2}{3} ?\)

(ii) Which of the following points lie on the path of the rocket?

(iii) At what distance will the rocket be from the starting point (0, 0, 0) in 10 seconds?

(iv) If the position of rocket at certain instant of time is (3, -6, 6), then what will be the height of the rocket from the ground, which is along the xy-plane?

(v) At certain instant of time, if the rocket is above sea level, where equation of surface of sea is given by 3x - y + 4z = 2 and position of rocket at that instant of time is (1, -2,2), then the image of position of rocket in the sea is 

(ii) The height of the tower from the ground is

(iii) The equation of line of perpendicular drawn from the peak of tower to the ground is

(iv) The coordinates of foot of perpendicular drawn from the peak of tower to the ground are

(v) The area of \(\Delta\) ABC is

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Cbse 12th standard maths subject three dimensional geometry case study questions 2021 answer keys.

(i) (c): Clearly, the plane for students of school A is  \(\vec{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=5,\) which can be rewritten as \((x \hat{i}+y \hat{j}+z \hat{k}) \cdot(\hat{i}+\hat{j}+2 \hat{k})=5\) \(\Rightarrow \quad x+y+2 z=5\) , which is the required cartesian equation. (ii) (b): Clearly, the equation of plane for students of school B is  \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=6,\)  which is of the form  \(\vec{r} \cdot \vec{n}=d\) ∴ Normal vector to the plane is,  \(\vec{n}=2 \hat{i}-\hat{j}+\hat{k}\)  and its magnitude is  \(|\vec{n}|=\sqrt{2^{2}+(-1)^{2}+1^{2}}=\sqrt{6}\) (iii) (b): The cartesian form is 2x - y + z = 6, which can be rewritten as \(\frac{2 x}{6}-\frac{y}{6}+\frac{z}{6}=1 \Rightarrow \frac{x}{3}+\frac{y}{(-6)}+\frac{z}{6}=1\) (iv) (c): Since, only the point (3, I, 1) satisfy the equation of plane representing seating position of students of school B, therefore Khushi is the student of school B. (v) (d): Equation of plane representing students of school B is  \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=6,\)  which is not in normal form, as  \(|\vec{n}| \neq 1\) On dividing both sides by  \(\sqrt{2^{2}+(-1)^{2}+1^{2}}=\sqrt{6}\) , we get  \(\vec{r} \cdot\left(\frac{2}{\sqrt{6}} \hat{i}-\frac{1}{\sqrt{6}} \hat{j}+\frac{1}{\sqrt{6}} \hat{k}\right)=\frac{6}{\sqrt{6}}\) which is of the form  \(\vec{r} \cdot \hat{n}=d\) Thus, the required distance is  \(\sqrt 6\)  units.

(i) (b): Clearly, the coordinates of A are (8, -6, 0) and that of E are (0, 0, 24). Also, cartesian equation of line along EA is given by \(\frac{x-0}{8-0}=\frac{y-0}{-6-0}=\frac{z-24}{0-24}\) \(\Rightarrow \frac{x}{8}=\frac{y}{-6}=\frac{z-24}{-24} \Rightarrow \frac{x}{-4}=\frac{y}{3}=\frac{z-24}{12}\) (ii) (c): Clearly, the coordinates of Dare (-8, -6, 0) and that of E are (0, 0, 24) \(\therefore \text { Vector } \overline{E D} \text { is }(-8-0) \hat{i}+(-6-0) \hat{j}+(0-24) \hat{k} \ \text { i.e., }-8 \hat{i}-6 \hat{i}-24 \hat{k} \) (iii) (b): Since, the coordinates of Bare (8, 6, 0) and that of E are (0, 0, 24), therefore length of cable \(E B=\sqrt{(8-0)^{2}+(6-0)^{2}+(0-24)^{2}} \) \(=\sqrt{64+36+576}=\sqrt{676}=26 \text { units }\) (iv) (d): Since, the coordinates of Care (-8,6,0) therefore length of cable EC =  \(\sqrt{(-8-0)^{2}+(6-0)^{2}+(0-24)^{2}}\) \(=\sqrt{64+36+576}=\sqrt{676}=26 \mathrm{units}\) Similarly, length of cable EA = ED = 26 units. (v) (c): Sum of all vectors along the cables \(=\overrightarrow{E A}+\overrightarrow{E B}+\overrightarrow{E C}+\overline{E D}\) \( =(8 \hat{i}-6 \hat{j}-24 \hat{k})+(8 \hat{i}+6 \hat{j}-24 \hat{k})+(-8 \hat{i}+6 \hat{j}-24 \hat{k})+(-8 \hat{i}-6 \hat{j}-24 \hat{k}) \) \(=-96 \hat{k}\)

(i) (c) : Let P(2, 3, 5) and Q(1, 4, 2) be the positions of helicopter and boat respectively. Now, direction ratios of PQ are proportional to 1-2, 4-3, 2-5, i.e , -1, 1,-3. So, equation of plane passing through Q(1, 4, 2) and perpendicular to PQ is -(x - 1) + (y - 4) + (-3) (z - 2) = 0 ⇒ x - y + 3z = 3 (ii) (d) : Required distance = Distance between P and Q \(=\sqrt{(1-2)^{2}+(4-3)^{2}+(2-5)^{2}}=\sqrt{1+1+9}=\sqrt{11} \mathrm{~m}\) (iii) (d) : We know, Distance = Speed x Time ஃ  Required time =  \(\frac{\sqrt{11}}{30}\)   seconds (iv) (b) : Equation of line PQ is  \(\frac{x-1}{1}=\frac{y-4}{-1}=\frac{z-2}{3}\) (v) (b) : Any point on the line  \(\frac{x-1}{1}=\frac{y-1}{-2}=\frac{z-2}{3}\)  given by  \((\lambda+1,-2 \lambda+1,3 \lambda+2)\) Now, on substituting this point in the equation of plane x - y + 3z = 3, we get \( (\lambda+1)-(-2 \lambda+1)+3(3 \lambda+2)=3 \) \(\Rightarrow \lambda+1+2 \lambda-1+9 \lambda+6=3 \Rightarrow 12 \lambda=-3\) \(\Rightarrow \ \lambda=\frac{-1}{4}\) Thus, the required point is  \(\left(\frac{-1}{4}+1, \frac{1}{2}+1, \frac{-3}{4}+2\right)\)   i.e., \(\left(\frac{3}{4}, \frac{3}{2}, \frac{5}{4}\right)\)  

(i) (a): Eliminating 't' from the given equations, we get equation of path as,  \(\frac{x}{2}=\frac{y}{-4}=\frac{z}{4} \text { or } \frac{x}{1}=\frac{y}{-2}=\frac{z}{2}\) . Thus, the path of the rocket represents a straight line. (ii).(b) : Since, only (1, -2, 2) satisfy the equation of path of rocket therefore (1, -2, 2) lie on the path of rocket. (iii) (b): For t = 10 sec, we have x = 20,y = -40, z = 40  Now, required distance =  \(\sqrt{x^{2}+y^{2}+z^{2}}\) \(=\sqrt{20^{2}+(-40)^{2}+(40)^{2}}=\sqrt{400+1600+1600}\) \(=\sqrt{3600}=60 \mathrm{~km}\) (iv) (d) : Clearly, height of rocket from the ground = z-coordinate of given position = 6 km (v) (b) : Let Q be the image of point P(1, -2, 2) in the plane 3x - y + 4z = 2. Then, equation of PQ is \(\frac{x-1}{3}=\frac{y+2}{-1}=\frac{z-2}{4}\) Let the coordinates of Q be (3r +1, -r - 2, 4r + 2). Let R be the mid -point of PQ. Then, coordinates of R are \(\left(\frac{3 r+2}{2}, \frac{-r-4}{2}, \frac{4 r+4}{2}\right) \text { or }\left(\frac{3}{2} r+1, \frac{-r}{2}-2,2 r+2\right)\) Since, R lies on 3x - y + 4z = 2. \( \therefore \quad 3\left(\frac{3}{2} r+1\right)-\left(\frac{-r}{2}-2\right)+4(2 r+2)=2 \) \(\Rightarrow \frac{9 r}{2}+3+\frac{r}{2}+2+8 r+8=2 \\ \) \(\Rightarrow 13 r+13=2 \Rightarrow r=\frac{-11}{13}\) Hence, the coordinates of Q are \(\left(\frac{-33}{13}+1, \frac{11}{13}-2, \frac{-44}{13}+2\right) \text { i.e., }\left(\frac{-20}{13}, \frac{-15}{13}, \frac{-18}{13}\right)\)

(i) (b) : The equation of plane passing through three non - collinear points is given by \(\left|\begin{array}{ccc} x-x_{1} & y-y_{1} & z-z_{1} \\ x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \\ x_{3}-x_{1} & y_{3}-y_{1} & z_{3}-z_{1} \end{array}\right|=0\) \(\Rightarrow\left|\begin{array}{ccc} x & y-1 & z-2 \\ 3-0 & 4-1 & -1-2 \\ 2-0 & 4-1 & 2-2 \end{array}\right|=0\) \(\Rightarrow\left|\begin{array}{ccc} x & y-1 & z-2 \\ 3 & 3 & -3 \\ 2 & 3 & 0 \end{array}\right|=0\) \( \Rightarrow \ln x(0+9)-(y-1)(0+6)+(z-2)(9-6)=0 \) \(\Rightarrow 9 x-6 y+6+3 z-6=0 \Rightarrow 3 x-2 y+z=0\) (ii) (c) : Height of tower = Perpendicular distance from the point (6, 5, 9) to the plane 3x - 2y + z = 0 \(=\left|\frac{18-10+9}{\sqrt{3^{2}+(-2)^{2}+1^{2}}}\right|=\frac{17}{\sqrt{14}} \text { units }\) (iii) (b) : D.R.'s of perpendicular are < 3, -2, 1 > [ஃ Perpendicular is parallel to the normal to the plane] Since, perpendicular is passing through the point (6, 5, 9), therefore its equation is  \(\frac{x-6}{3}=\frac{y-5}{-2}=\frac{z-9}{1}\) (iv) (a) : Let the coordinates of foot of perpendicular  are Since, this point lie on the plane 3x - 2y + z = 0, therefore we get, \((3 \lambda+6,-2 \lambda+5, \lambda+9)\) \( 3(3 \lambda+6)-2(-2 \lambda+5)+(\lambda+9)=0 \) \(\Rightarrow 9 \lambda+4 \lambda+\lambda+18-10+9=0 \) \(\Rightarrow 14 \lambda=-17 \Rightarrow \lambda=\frac{-17}{14}\) Thus, the coordinates of foot of perpendicular are \(\left(\frac{-51}{14}+6, \frac{34}{14}+5, \frac{-17}{14}+9\right) \text { i.e., }\left(\frac{33}{14}, \frac{104}{14}, \frac{109}{14}\right)\) (v) (b) : Clearly, area of ABC = \(\frac{1}{2}|\overrightarrow{A B} \times \overrightarrow{A C}|\) \( =\frac{1}{2}|(3 \hat{i}+3 \hat{j}-3 \hat{k}) \times(2 \hat{i}+3 \hat{j})| \) \(=\frac{1}{2}\left\|\begin{array}{cc} \hat{i} & \hat{j} & \hat{k} \\ 3 & 3 & -3 \\ 2 & 3 & 0 \end{array}\right\|=\frac{1}{2}|9 \hat{i}-6 \hat{j}+3 \hat{k}|\) \( =\frac{1}{2} \sqrt{9^{2}+6^{2}+3^{2}}=\frac{1}{2} \sqrt{126}=\frac{3}{2} \sqrt{14} \text { sq. units } \)

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Case Study Questions for Class 12 Maths Chapter 10 Vector Algebra

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[PDF] Download Case Study Questions for Class 12 Maths Chapter 10 Vector Algebra

Here we are providing case study questions for class 12 maths. In this article, we are sharing Class 12 Maths Chapter 10 Vector Algebra case study questions. All case study questions of class 12 maths are solved so that students can check their solutions after attempting questions.

Case Study Questions for Class 12 Maths

Case study questions are a type of question that is commonly used in academic and professional settings to evaluate a person’s ability to analyze, interpret, and solve problems based on a given scenario or case study.

Typically, a case study question presents a real-world situation or problem that requires the individual to apply their knowledge and skills to identify the issues, consider various solutions, and recommend a course of action.

Case study questions are designed to test critical thinking skills, problem-solving abilities, and the capacity to work through complex and ambiguous situations.

Preparing for case study questions involves developing a deep understanding of the subject matter, being able to analyze and synthesize information quickly, and being able to communicate ideas clearly and effectively.

Importance of Solving Case Study Questions for Class 12 Maths

Solving case study questions for Class 12 Maths is extremely important as it provides students with an opportunity to apply the mathematical concepts they have learned to real-world scenarios. These questions present a situation or problem that requires students to use their problem-solving skills and critical thinking abilities to arrive at a solution.

The importance of solving case study questions for Class 12 Maths can be summarized as follows:

• Enhances problem-solving skills: Case study questions challenge students to think beyond textbook examples and apply their knowledge to real-world situations. This enhances their problem-solving skills and helps them develop a deeper understanding of the mathematical concepts.
• Improves critical thinking abilities: Case study questions require students to analyze and evaluate information, and draw conclusions based on their understanding of the situation. This helps them develop their critical thinking abilities, which are essential for success in many areas of life.
• Helps in retaining concepts: Solving case study questions helps students retain the concepts they have learned for a longer period of time. This is because they are more likely to remember the concepts when they have applied them to a real-world situation.
• Better preparation for exams: Many competitive exams, including the Class 12 Maths board exam, contain case study questions. Solving these questions helps students become familiar with the format of the questions and the skills required to solve them, which can improve their performance in exams.

In conclusion, solving case study questions for Class 12 Maths is important as it helps students develop problem-solving and critical thinking skills, retain concepts better, and prepare for exams.

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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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