class 12 maths case study questions pdf 2023

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

myCBSEguide App

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

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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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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Home > CBSE Class 12 Important Questions

Most Important Questions CBSE Class 12 Maths with Solutions

Cbse important questions for class 12 mathematics.

Mathematics improves the analytical and creative thinking of students and allows them to think differently. Concepts of class 12 Mathematics are directly asked in various competitive examinations like JEE and NDA. Therefore, it becomes really important for the students to have a good hold of the mathematical concepts.

At Educart, we provide our students with reliable resources so that they don’t get distracted from their journey and ace their examinations with flying colors.

In the table given below, we have provided the links to downloadable PDFs of chapter-wise important questions for class 12 Mathematics and that too for different categories of marks.

📈 Trending: Class 12 CBSE Syllabys 2024-25

📝 Recommended: Educart Class 12 Question Banks

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Benefits of CBSE Class 12 Mathematics Most Important Questions

A solid foundation in mathematics from classes 11 to 12 is necessary for students who wish to pursue careers in engineering research. Students can practice the associated questions by using NCERT books and appropriate study materials that help with idea clarification. The crucial questions for CBSE Class 12 Mathematics might aid in better comprehending the material and improve test preparation because the mathematics curricula for Classes 11 and 12 are extensive and divided into several areas and subtopics.

As per the updated CBSE Class 12 syllabus, the knowledgeable subject matter experts have compiled a list of all the crucial questions, broken down by chapter, along with clear explanations. To aid students in comprehending the questions stated and the intended responses, the explanations have been organized using a step-by-step approach. A variety of competency-based questions have been included, all while adhering to the most recent CBSE pattern. 

Why You Should Download CBSE Class 12 Mathematics Important Questions?

As exams start nearing, students try to adopt the best strategy to prepare for the exams to achieve good marks. Math is one of those subjects that give phobia mostly. To help students achieve the target, incorporating “Important Questions Practice” in the exam strategy is a vital step for many reasons.

• To have a deep understanding of topics in Class 12, understanding the topics from Class 12 will help in creating a strong base.
• These questions are curated to highlight the essential topics and principles and help students get the main idea behind that concept.
• Important questions provide extra help and work as important reference material to prepare well for exams.
• If any students want to appear for competitive exams like JEE, NEET, or any other exam, important questions will help in aligning with the exam pattern and strategy.
• You can curate a more effective study plan by shortlisting important topics.
• These questions will help you in boosting your confidence for the board exams.

CBSE Class 12 Important Questions will help students cover all the major topics and understand that chapter. At Educart, we have pledged to help students with the right material and help them in scoring their dream scores.

We hope that you practice the above important questions of mathematics and achieve your dream marks in it.

All the best! 

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CBSE Class 12 Maths Sample Question Paper 2023: Download Mathematics Sample Paper PDF Here

Cbse class 12 maths sample paper 2022-23: students of cbse class 12 can now check and download mathematics sample paper 2023 (code 041) for 2022-23 cbse board exams..

CBSE Class 12 Maths Sample Question Paper 2023: With the release of Class 12 Mathematics Sample Paper 2022-23 (code 041) by CBSE on their official website, it’s now time for the students of Class 12 Mathematics to start preparing for their exams. 

“The only way to learn mathematics is to do mathematics.” – Paul Halmos

• 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

In addition you can make use of previous year papers as well. Besides, now that the board has made available the latest sample papers, utilising these sample papers for 2022-23 and the marking scheme, students must practise the different kinds of questions that can be asked in the CBSE class 12 Mathematics board exams. 

If you are lacking any of these resources, Jagran Josh has the latest CBSE class 12 Mathematics syllabus , and the latest sample paper and marking scheme in one place.

Coming to the sample paper, the CBSE 12 Mathematics Sample Question Paper begins with the general instructions for the students to follow. 

The general instructions in the beginning of the CBSE Class 12 Mathematics Sample Question Paper 2022-23 are as follows:

TIME - 3 HOURS 

MAX. MARKS - 80

General Instructions: 

1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory. However, there are internal choices in some questions. 

2. Section A has 18 MCQ’s and 02 Assertion-Reason based questions of 1 mark each. 

3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each. 

4. Section C has 6 Short Answer (SA)-type questions of 3 marks each. 

5. Section D has 4 Long Answer (LA)-type questions of 5 marks each. 

6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each) with sub parts.  

CBSE Class 12 Maths Sample Question Paper 2023

(Multiple Choice Questions)

Each question carries 1 mark

Q1. If A =[a ij ] is a skew-symmetric matrix of order n, then

Q2. If A is a square matrix of order 3, |𝐴′| = −3, then |𝐴𝐴′| =

Q3. The area of a triangle with vertices A, B, C is given by

Q5. If 𝑓′(𝑥) = 𝑥 + 1/𝑥, then 𝑓(𝑥) is

(a) 𝑥 2 + log |𝑥| + 𝐶

(b) 𝑥 2 /2 + log |𝑥| + 𝐶

(c) 𝑥/2 + log |𝑥| + 𝐶

(d) 𝑥/2 − log |𝑥| + 𝐶

Q6. If m and n, respectively, are the order and the degree of the differential equation d/dx[(dy/dx)] 4 =0, then m + n =

 (d) 4

Q7. The solution set of the inequality 3x + 5y < 4 is

(a) an open half-plane not containing the origin.

(b) an open half-plane containing the origin.

(c) the whole XY-plane not containing the line 3x + 5y = 4.

(d) a closed half plane containing the origin.

Q9. The value of ∫ 3 2 x/x 2 +1dx is

(c) 1/2𝑙𝑜𝑔2

Q10. If A, B are non-singular square matrices of the same order, then (𝐴𝐵 -1 ) -1 =

(b)𝐴 -1 𝐵 -1

Q11. The corner points of the shaded unbounded feasible region of an LPP are (0, 4), (0.6, 1.6) and (3, 0) as shown in the figure. The minimum value of the objective function Z = 4x + 6y occurs at

(a)(0.6, 1.6) 𝑜𝑛𝑙𝑦

(b) (3, 0) only

(c) (0.6, 1.6) and (3, 0) only

(d) at every point of the line-segment joining the points (0.6, 1.6) and (3, 0)

Q13. If A is a square matrix of order 3 and |A| = 5, then |𝑎𝑑𝑗𝐴| =

Q14. Given two independent events A and B such that P(A) =0.3, P(B) = 0.6 and P(𝐴′ ∩ 𝐵′) is

Q15. The general solution of the differential equation 𝑦𝑑𝑥 − 𝑥𝑑𝑦 = 0 𝑖𝑠

(b) 𝑥 = 𝐶𝑦 2

(d) 𝑦 = 𝐶𝑥 2

Q16. If 𝑦 = 𝑠𝑖𝑛 -1 𝑥, then (1 − 𝑥 2 )𝑦 2 𝑖𝑠 equal to

Q18. P is a point on the line joining the points 𝐴(0,5, −2) and 𝐵(3, −1,2). If the x-coordinate of P is 6, then its z-coordinate is

ASSERTION-REASON BASED QUESTIONS

In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

(a) Both A and R are true and R is the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A.

(c) A is true but R is false.

(d) A is false but R is true.

SECTION - B

This section comprises of very short answer type-questions (VSA) of 2 marks each

Q22. A man 1.6 m tall walks at the rate of 0.3 m/sec away from a street light that is 4 m above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?

Find the direction ratio and direction cosines of a line parallel to the line whose equations are

6𝑥 − 12 = 3𝑦 + 9 = 2𝑧 − 2

SECTION - C

(This section comprises of short answer type questions (SA) of 3 marks each)

Q26. Find: ∫dx/√3-2x-x 2

Q27. Three friends go for coffee. They decide who will pay the bill, by each tossing a coin and then letting the “odd person” pay. There is no odd person if all three tosses produce the same result. If there is no odd person in the first round, they make a second round of tosses and they continue to do so until there is an odd person. What is the probability that exactly three rounds of tosses are made?

Find the mean number of defective items in a sample of two items drawn one-by-one without replacement from an urn containing 6 items, which include 2 defective items. Assume that the items are identical in shape and size.'

Q29. Solve the differential equation: 𝑦𝑑𝑥 + (𝑥 − 𝑦 2 )𝑑𝑦 = 0

Solve the differential equation: 𝑥𝑑𝑦 − 𝑦𝑑𝑥 = √𝑥 2 +𝑦 2 𝑑𝑥

Q30. Solve the following Linear Programming Problem graphically:

Maximize Z = 400x + 300y subject to 𝑥 + 𝑦 ≤ 200, 𝑥 ≤ 40, 𝑥 ≥ 20, 𝑦 ≥ 0

Q31. Find ∫(x 3 +x+1)/(x 2 -1)/dx

SECTION - D

(This section comprises of long answer-type questions (LA) of 5 marks each)

Q32. Make a rough sketch of the region {(𝑥, 𝑦): 0 ≤ 𝑦 ≤ 𝑥 2 , 0 ≤ 𝑦 ≤ 𝑥, 0 ≤ 𝑥 ≤ 2} and find the area of the region using integration.

Q33. Define the relation R in the set 𝑁 × 𝑁 as follows:

For (a, b), (c, d) ∈ 𝑁 × 𝑁, (a, b) R (c, d) iff ad = bc. Prove that R is an equivalence relation in 𝑁 × 𝑁.

Given a non-empty set X, define the relation R in P(X) as follows:

For A, B ∈ 𝑃(𝑋), (𝐴, 𝐵) ∈𝑅 iff 𝐴 ⊂ 𝐵. Prove that R is reflexive, transitive and not symmetric.

The equations of motion of a rocket are:

𝑥 = 2𝑡, 𝑦 = −4𝑡, 𝑧 = 4𝑡, where the time t is given in seconds, and the coordinates of a moving point in km. What is the path of the rocket? At what distances will the rocket be from the starting point O(0, 0, 0) and from the following line in 10 seconds?

SECTION - E

(This section comprises of 3 case-study/passage-based questions of 4 marks each with two sub-parts. First two case study questions have three sub-parts (i), (ii), (iii) of marks 1, 1, 2 respectively. The third case study question has two sub-parts of 2 marks each.)

Q36. Case-Study 1: Read the following passage and answer the questions given below.

The temperature of a person during an intestinal illness is given by

𝑓(𝑥) = −0.1𝑥 2 + 𝑚𝑥 + 98.6,0 ≤ 𝑥 ≤ 12, m being a constant, where f(x) is the temperature in °F at x days.

(i) Is the function differentiable in the interval (0, 12)? Justify your answer.

(ii) If 6 is the critical point of the function, then find the value of the constant m.

(iii) Find the intervals in which the function is strictly increasing/strictly decreasing.

(iii) Find the points of local maximum/local minimum, if any, in the interval (0, 12) as well as the points of absolute maximum/absolute minimum in the interval [0, 12]. Also, find the corresponding local maximum/local minimum and the absolute maximum/absolute minimum values of the function.

Q37. Case-Study 2: Read the following passage and answer the questions given below.

In an elliptical sport field the authority wants to design a rectangular soccer field with the maximum possible area. The sport field is given by the graph of x 2 /a 2 +y 2 /b 2 =1.

(i) If the length and the breadth of the rectangular field be 2x and 2y respectively, then find the area function in terms of x.

(ii) Find the critical point of the function.

(iii) Use First derivative Test to find the length 2x and width 2y of the soccer field (in terms of a and b) that maximize its area.

(iii) Use Second Derivative Test to find the length 2x and width 2y of the soccer field (in terms of a and b) that maximize its area.

Q38. Case-Study 3: Read the following passage and answer the questions given below.

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?

Download CBSE Class 12 Mathematics Sample Question Paper 2022-23

Download cbse class 12 mathematics marking scheme 2022-23.

Remember that “The only way to learn mathematics is to do mathematics.” – Paul Halmos. Thus , using both CBSE Class 12 Mathematics Sample Paper 2022-23 and the marking scheme, students should practice more to score higher in their board exams. 

Stay tuned to Jagran Josh for more content related to CBSE Class 12 board exams 2022-23.

Best of luck to all the candidates.

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• Will there be choices given in CBSE Class 12 Mathematics question paper? + No. Although internal choices of about 33% would be given, there would not be any overall choice in the question paper.
• Which is the most important unit in CBSE Class 12 Mathematics? + CBSE Class 12 Mathematics constitutes of 6 units. CBSE states that 'No chapter wise weightage. Care to be taken to cover all the chapters'. However, Calculus is the 3rd unit in the syllabus and has a total weightage of 35 marks out of 100. Thus, Calculus can be said to be the most important unit in CBSE Class 12 Mathematics.
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CBSE 12th Standard Maths Subject Case Study Questions with Solutions

By QB365 on 20 May, 2021

QB365 Provides the updated CASE Study Questions for Class 12 , 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

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CBSE Board Class 12 Maths Previous Year Question Paper 2023

• Cbse Previous Year Question Paper

Maths Class 12 Previous Year Question Paper 2023 with Solution

Maths is a crucial subject in Class 12 that requires both practical and theoretical expertise. To perform well in exams, students need to have a thorough understanding of the concepts. Solving previous year's question papers is an excellent method of exam preparation. This article emphasizes the importance of solving past year's question papers and offers solutions to Class 12 Maths' previous year's question papers.

Maths Board Exam Paper Class 12 2023- Set Wise Links Free PDF Download

Explore the CBSE Class 12 Maths Board Exam Paper 2023 with set-wise links for free PDF download. Enhance your preparation by practicing these papers aligned with the latest CBSE guidelines. Each set offers a comprehensive practice experience, covering various topics and question types. These resources aim to boost your confidence and ensure you're well-prepared for the Maths Board Exam Paper Class 12 . 

Importance of Solving Maths Previous Year Question Papers

Solving previous year's question papers is a beneficial method of exam preparation. The following are some reasons why solving previous year's question papers is crucial:

Provides Insight into the Exam Pattern : Solving previous year's question papers offers information on the question types, section weightage, and marking scheme utilized in the exam, assisting in understanding the exam format.

Builds Confidence : Solving the previous year's question papers instills confidence by providing an idea of what to expect in the exam and aiding in preparation.

Improves Time Management Skills : Solving the previous year's question papers helps estimate the time required for each section, enhancing time management skills and planning.

Identifies Areas of Weakness : It helps to identify the topics that need improvement and improves performance in the exam.

Maths Previous Year Question Paper Class 12 PDF

Candidates must practice previous years and sample question papers on Maths to enhance their chances of success in the class 12 exam. It is also important to evaluate their performance and recognize their strengths and weaknesses through answer checking. Adequate preparation and practice can lead to excellent results in Maths exams. Students may also consider practicing the JEE Maths Online Mock Test for Class 12 by Vedantu and enrolling in Vedantu's online Maths classes for Class 12 and ease of clearing the exam.

Practicing the previous year's Maths question papers for Class 12 is a crucial component of exam preparation, as it aids in comprehending the exam format.

FAQs on CBSE Board Class 12 Maths Previous Year Question Paper 2023

1. Where can I find Class 12 Maths previous year's question papers with solutions?

You can find Class 12 Maths previous year question papers with solutions on Vedantu and suggestions on preparation books.

2. How can solving Maths's previous year's question paper in class 12 help me in my exams?

Solving Maths's previous year's question paper in class 12 helps you understand the exam pattern and practice important concepts.

3. How did solving Class 12 Maths previous year question papers with solutions improve my problem-solving skills?

Solving Class 12 Maths previous year question papers with solutions can improve your problem-solving skills by providing you with practice on different types of questions and helping you understand how to approach them. It can also help you identify common mistakes and learn from them, improving your ability to solve similar problems in the future.

4. How do I analyse my performance while solving Maths's previous year's question paper in class 12?

You can start by reviewing the answers you got wrong and identifying the topics or concepts you need to work on. You can also check the time you took to solve each question and try to improve your time management. Additionally, you can compare your score with the average marks obtained by others who attempted the same paper to understand your performance.

CBSE Class 12 Maths Question Paper 2023 - PDF Download

CBSE Class 12 Maths Question Paper 2023 is a crucial material for preparing for the examination. Students who are preparing for class 12 maths board exam must be proficient in this subject. The simplest way to practice for exams is to go through the CBSE Maths Question Paper for Class 12. We've included the 2023 Maths Question Paper here, along with the marking scheme and solution PDF. 

The Maths exam usually consists of different questions that are based on theorems and formulas. All you have to do to ace the exam is to practice CBSE class 12 maths question paper 2023 as much as you can. The questions of the CBSE Class 12 Maths New Pattern question Paper are very important and different. This serves as a reference for students to understand the questions to be asked in their examination. Students can use the CBSE class 12 maths board question paper to gain a better understanding of the topics, the pattern and the marking system.

CBSE class 12 maths question paper 2023 PDF can be downloaded for free here. Students who are preparing for their Class 12 board exams can use the CBSE class 12 math question paper 2023 to get the best results in the exam. 

CBSE Class 12 Maths Question Paper Solutions 2023

The CBSE Class 12 Mathematics Question Paper 2023 is available for download along with the solutions. By practicing the mathematics question paper, students from the CBSE Board can ensure a successful outcome in the class 12 maths exam 2024. Therefore, it is recommended that students prepare for the exam by downloading and practicing the CBSE class 12 maths question paper Solution 2023 provided on eSaral. The solutions to class 12 maths question paper 2023 are available in PDF format so that the students can easily access the learning material from anywhere on any device.

The CBSE class 12 maths question paper & solutions 2023 will help students to prepare well and get good marks in the board examination. Students can download the class 12 mathematics question paper and solutions 2023 from the provided link here on eSaral and use it to create an effective exam plan to achieve higher marks.

CBSE Class 12 Maths Standard Question Paper 2023: Pattern and Marking Scheme

In order to score high marks in class 12, a student has to come up with some intelligent strategies and follow them consistently. Therefore, before that, the student has to have a thorough understanding of the exam pattern and marking scheme of CBSE class 12 board exam.

The duration of the CBSE class 12 maths question paper 2023 exam is 3 hours and the total marks are 80. The Maths 2023 question paper consists of 38 questions which are divided into 5 sections.

Section A: 18 multiple-choice questions and 2 Assertion-Reason questions of 1 mark each

Section B: 5 very short answer questions of 2 marks

Section C: 6 short answer questions of 3 marks each

Section D: 4 long answer questions of 5 marks each

Section E: 3 case study based questions of 4 marks

There was an internal option between questions. However, each question was mandatory to attempt.

CBSE Class 12 Maths Standard Question Paper 2023 Marking Scheme

Why should you solve the cbse class 12 board math 2023 question paper .

CBSE class 12 board maths questions papers 2023 from previous year will help in improving your score in the CBSE class 12 maths board exam 2024. Therefore, students are advised to solve the previous year CBSE class 12 maths question papers for the CBSE math board exam.

Here are the advantages of solving CBSE class 12 maths question paper from previous year.

By gaining a thorough understanding of the board exam structure, question format, marking scheme and more will help students prepare better for the board exam.

By solving the CBSE class 12 mathematics question paper, students can develop their time management skills and practice answering all the questions in the allotted time frame.

Solving question papers of CBSE class 12 maths question paper assists students to figure out their weak areas and enables them to adjust their approach to preparation.

CBSE class 12 previous year maths question paper will help students figure out which questions are most important and which question is more repeating.

Frequently Asked Questions

Question 1. What is the benefit of solving CBSE class 12 maths 2023 question paper ?

Answer 1. CBSE class 12 maths question Paper helps students to identify essential topics, provide guidance, and provide solutions to the questions and doubts.

Question 2. How can I download the CBSE class 12 maths question paper 2023 PDF?

Answer 2. You can download the CBSE class 12 maths question paper 2023 PDF from eSaral. We have also provided the CBSE class 12 maths question paper with solutions PDF.

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CBSE Class 12 Maths Question Papers 2023

CBSE Class 12 Maths Question Papers 2023 with solutions are available here for free download. Students preparing for their forthcoming Class 12 board exam can use the provided CBSE Class 12 Question Paper 2023 of Maths with solutions to maximise their exam preparation. The solutions for Class 12 Maths question paper 2023 is in PDF format, which makes it convenient for the students to access the learning material anytime from anywhere on any device.

Some benefits of reviewing the solutions of the Class 12 Maths 2023 question paper are as follows:

• Students are better prepared for the board exam by an in-depth understanding of the exam structure, the question format, the marking scheme and more.
• Solving previous years’ question papers helps students understand their weak areas and allows them to modify their preparation strategy accordingly.
• Students can learn time management and practise answering all the questions within the stipulated time.

The Class 12 Maths question paper and solutions 2023 can be easily downloaded from here and used by students to develop an effective exam strategy to help them score higher marks.

Download the CBSE Class 12 Maths Question Paper with Solutions 2023

Cbse class 12 maths question paper 2023.

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CBSE Question Paper and Solutions of Class 12 Maths 2023 will support students in preparing well and achieving good grades in the board exam.

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Case Study Questions for Class 12 Maths Chapter 13 Probability

• Last modified on: 1 year ago
• Reading Time: 6 Minutes

[PDF] Download Case Study Questions for Class 12 Maths Chapter 13 Probability

Here we are providing case study questions for class 12 maths. In this article, we are sharing Class 12 Maths Chapter 13 Probability 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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Class 12 - Maths

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Get NCERT solutions for Class 12 Maths free with videos. Solutions of all exercise questions, examples, miscellaneous exercise, supplementary exercise are given in an easy to understand way

The chapters and the topics in them are

• Chapter 1 Relation and Functions – Types of Relation - Reflexive, Symmetric, Transitive & Equivalence relation, Type of functions - One-one (injective), Onto (surjective) & Bijective, Composition of functions and Inverse of a function, Binary Operation - Commutative, Associative, Identity and Inverse.
• Chapter 2 Inverse Trigonometric Functions –  Finding principle value, solving identities using properties
• Chapter 3 Matrices – Order of matrix, Types of matrices - Column matrix, Row matrix, Square matrix, Diagnol matrix, Scalar Matrix, Identity matrix, Equal matrices, Addition, Subtraction and Multiplication of matrices, Transpose of a Matrix, Symmetric, Skew Symmetric Matrices, Finding inverse of matrix by elementary operations
• Chapter 4 Determinants – Evaluating 2 x 2, 3 x 3 Determinant, Properties of Determinant, Area of triangle, Minors and Cofactors, Adjoint and inverse of matrix, Solution of system of linear equations using matrix method
• Chapter 5 Continuity and Differentiability – Finding whether function is continuous, composition of continuous functions is continuous, Finding Derivative using chain rules, logarithmic and exponential differentiation, Mean value of theorem, Rolle's Theorem.
• Chapter 6 Application of Derivatives – Finding rate of change, Increasing & decreasing functions, Point of Inflexion, Finding slope of tangent  and normal, Finding approximate of functions and numbers, Finding maxima & minima using first derivative & second derivative test and Finding absolute maxima and minima
• Chapter 7 Integrals – Finding integration by substitution, trigonometric identities, Partial Fractions & using special formulas. Finding definite integrals as Limit as a Sum, Finding definite integral using indefinite integral and finding Definite Integral using properties
• Chapter 8 Application of Integrals –  Finding area of region of simple curve, curve and line. Finding area between two curves.
• Chapter 9 Differential Equations – Degree and order of differential equations, General & Particular Solutions of Differential Equation, Forming differential equation when general solution is equation, Solving by variable separating, solving homogeneous differential equations, Linear Differential Equation
• Chapter 10 Vector Algebra – What is vector, Difference between vector and scalar, Types of vector - Unit vector, Equal vector, Addition of vectors, Components of vector, Scalar(Dot) product of vectors, Projection of vector on line, Vector (Cross) product of vectors, Finding area of parallelogram
• Chapter 11 Three Dimensional Geometry – Direction Ratio & Direction cosines of line, Finding equation of line - given point & parallel vector, though two points, Angle between two lines, Distance between two skew lines, Distance between two parallel lines, Finding equation of plane - normal form, perpendicular to given vector & passing through point, through 3 non-collinear points, intercept form, through two planes. Coplanarity of two planes, Angle between two planes, Distance between point and plane, Angle between Line & Plane
• Chapter 12 Linear Programming  – Finding maximum or minimum value of Z using bounded or unbounded region of graphical inequality.  Solving Diet, Manufacturing & Transport problems.
• Chapter 13 Probability – Conditional Probability, Multiplication Theorem of Probability, Independent events, Bayes Theorem, Random Variable & its Probability Distributions, Mean & Variance of Random Variable, Bernoulli Trials & Binomial Distribution

Each chapter is divided into two parts - Serial Order Wise and Concept Wise.

• In Serial  Order Wise, the chapter is taught according to the NCERT Book with exercises, examples and miscellaneous. You should follow this when you are searching for a particular question
• In Concept Wise, we have divided the Chapter into topics. Concept is explained first, and then questions are ordered from easy to difficult. You should always follow this method to do the chapter. This is the Teachoo (टीचू) way of doing a chapter.

In addition to that, Important Questions are marked for your reference.

And, we have also solved Past Year Papers, and Sample Papers with step by step marking as well

Click on a Chapter below to begin

Chapter 1 Class 12 Relation and Functions

Chapter 2 class 12 inverse trigonometric functions, chapter 3 class 12 matrices, chapter 4 class 12 determinants, chapter 5 class 12 continuity and differentiability, chapter 6 class 12 application of derivatives, chapter 7 class 12 integrals, chapter 8 class 12 application of integrals, chapter 9 class 12 differential equations, chapter 10 class 12 vector algebra, chapter 11 class 12 three dimensional geometry, chapter 12 class 12 linear programming, chapter 13 class 12 probability, important questions for exams class 12, solutions of sample papers and past year papers - for class 12 boards.

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Class 11-12 Math MCQ PDF Book | College Math MCQ Questions and Answers PDF

Quiz questions chapter 1-14 & practice tests with answers key (grade 11-12 math textbook notes, mcqs & study guide), publisher description.

The Class 11-12 Math Multiple Choice Questions (MCQ Quiz) with Answers PDF (College Math MCQ PDF Download): Quiz Questions Chapter 1-14 & Practice Tests with Answers Key (Math Textbook MCQs, Notes & Study Guide) includes revision guide for problem solving with hundreds of solved MCQs. Class 11-12 Math MCQ with Answers PDF book covers basic concepts, analytical and practical assessment tests. "Class 11-12 Math MCQ" PDF book helps to practice test questions from exam prep notes. The Class 11-12 Math MCQs with Answers PDF eBook includes revision guide with verbal, quantitative, and analytical past papers, solved MCQs. Class 11-12 Math Multiple Choice Questions and Answers (MCQs) PDF : Free download chapter 1, a book covers solved quiz questions and answers on chapters: Application of basic identities, double angle identities, functions and limits, fundamentals of trigonometry, matrices and determinants, number system, partial fractions, permutations, combinations and probability, quadratic equations, sequences and series, sets, functions and groups, trigonometric functions and graphs, trigonometric identities, trigonometric ratios of allied angles tests for college and university revision guide. Class 11-12 Math Quiz Questions and Answers PDF download, free eBook’s sample covers beginner's solved questions, textbook's study notes to practice tests. The book Class 11-12 Math MCQs Chapter 1-14 PDF includes college question papers to review practice tests for exams. Class 11-12 Math Multiple Choice Questions (MCQ) with Answers PDF digital edition eBook, a study guide with textbook chapters' tests for NEET/GRE/SAT/CLEP/ACT/GED/Olympiad competitive exam. College Math Practice Tests Chapter 1-14 PDF covers problem solving exam tests from Math textbook and practical eBook chapter-wise as: Chapter 1: Application of Basic Identities MCQ Chapter 2: Double Angle Identities MCQ Chapter 3: Functions and Limits MCQ Chapter 4: Fundamentals of Trigonometry MCQ Chapter 5: Matrices and Determinants MCQ Chapter 6: Number System MCQ Chapter 7: Partial Fractions MCQ Chapter 8: Permutations, Combinations and Probability MCQ Chapter 9: Quadratic Equations MCQ Chapter 10: Sequences and Series MCQ Chapter 11: Sets, Functions and Groups MCQ Chapter 12: Trigonometric Functions and Graphs MCQ Chapter 13: Trigonometric Identities MCQ Chapter 14: Trigonometric Ratios of Allied Angles MCQ Practice "Application of Basic Identities MCQ" PDF, book's chapter 1 test to solve MCQ questions: Applied mathematics, and trigonometry basics. Practice "Double Angle Identities MCQ" PDF, book's chapter 2 test to solve MCQ questions: Double angle identities. Practice "Functions and Limits MCQ" PDF, book's chapter 3 test to solve MCQ questions: Introduction to functions and limits, exponential function, linear functions, logarithmic functions, concept of limit of function, algebra problems, composition of functions, even functions, finding inverse function, hyperbolic functions, inverse of a function, mathematical formulas, notation and value of function, odd functions, parametric functions, and trigonometric function. Practice "Fundamentals of Trigonometry MCQ" PDF, book's chapter 4 test to solve MCQ questions: Trigonometric function, fundamental identities, trigonometry formulas, algebra and trigonometry, mathematical formulas, measurements conversion, measuring angles units, radian to degree conversion, radians to degrees, and trigonometry problems. Practice "Matrices and Determinants MCQ" PDF, book's chapter 5 test to solve MCQ questions: Introduction to matrices and determinants, rectangular matrix, row matrix, skew-symmetric matrix, and symmetric matrix, addition of matrix, adjoint and inverse of square matrix, column matrix, homogeneous linear equations, and multiplication of a matrix. Practice "Number System MCQ" PDF, book's chapter 6 test to solve MCQ questions: Properties of real numbers, rational numbers, irrational numbers, complex numbers, basic function, binary operation, De Moivre's theorem, groups, linear and quadratic function, sets, operation on three sets, and relation. Practice "Partial Fractions MCQ" PDF, book's chapter 7 test to solve MCQ questions: Introduction of partial fractions, rational fractions, resolution of a rational fraction into partial fraction, when q(x) has non-repeated irreducible quadratic factors, when q(x) has non-repeated linear factors, and when q(x) has repeated linear factors. Practice "Permutations, Combinations and Probability MCQ" PDF, book's chapter 8 test to solve MCQ questions: Introduction to permutations, combinations, probability, circular permutation, combinations, complementary combination, and examples of permutation. Practice "Quadratic Equations MCQ" PDF, book's chapter 9 test to solve MCQ questions: Introduction to quadratic equations, examples of quadratic equations, nature of roots of quadratic equation, cube roots of unity, exponential equations, formation of equation whose roots are given, fourth root of unity, polynomial function, relation b/w roots and the coefficients of quadratic equations, remainder theorem, roots of equation, solution of a quadratic equations, and synthetic division. Practice "Sequences and Series MCQ" PDF, book's chapter 10 test to solve MCQ questions: Introduction of sequences and series, arithmetic mean, arithmetic progression, geometric mean, geometric progression, harmonic mean, harmonic progression, infinite geometric series, relation b/w AM, GM and HM, sigma notation, and sum of n terms of a geometric series. Practice "Sets, Functions and Groups MCQ" PDF, book's chapter 11 test to solve MCQ questions: Introduction to sets, functions, groups, basic function, biconditional, implication or conditional, and operation on sets. Practice "Trigonometric Functions and Graphs MCQ" PDF, book's chapter 12 test to solve MCQ questions: Period of trigonometric functions, applied mathematics, domains, ranges, tangent, and cotangent functions. Practice "Trigonometric Identities MCQ" PDF, book's chapter 13 test to solve MCQ questions: Trigonometric identities, basic trigonometric identities, basic trigonometry formulas, trigonometric ratios of allied angles, trigonometric function, sine cosine tangent, double angle identities, and triple angle identities. Practice "Trigonometric Ratios of Allied Angles MCQ" PDF, book's chapter 14 test to solve MCQ questions: Trigonometric ratios of allied angles, and triple angle identities.

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CBSE Class 12th Mathematics 2023 : Topic-Wise Self Practice Question With Detailed Solution

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CBSE Class 12th Mathematics 2023 : Topic-Wise Self-Practice Question With Detailed Solution

Here are the CBSE Class 12 Mathematics Topic-Wise Self-Practice Question With Detailed Solution which help the students to develop a deeper understanding of the concepts as well.

Mathematics in class 12th is very difficult for many students, they are intimidated by this subject. They struggle to solve physics questions not because it is difficult, it is because their basics are not clear.

These CBSE Class 12 Mathematics Revision Notes have been prepared by Mathematics experts to help students get rid of the phobia and explain all the Physics concepts in an easy to understand manner.

• Short Notes
• Solved Examples
• Objective Ques. (MCQs)
• Short & Long Answers Type Ques
• Case-Based Question
• Toppers Corner

CBSE Class 12 Study Materials

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