class 12 maths case study questions with answers pdf

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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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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Class 12 Maths Case Study Questions

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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 Case Study Questions for Class 12 Maths Matrices Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 12 Maths Matrices  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 12 Maths Matrices PDF

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

• Chapter 1 Relations and Functions Case Study Questions
• Chapter 2 Inverse Trigonometric Functions Case Study Questions
• Chapter 4 Determinants Case Study Questions
• Chapter 5 Continuity and Differentiability Case Study Questions

How should I study for my upcoming exams?

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

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

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

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

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

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CBSE Class 12 Maths Exam 2024 Important Case Study Based Questions

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

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

CBSE Class 12   Maths   Unit Wise Marks Distribution 2024

CBSE Maths Previous Year Question Paper Class 12

CBSE Class 12 Maths Case Study Questions 2023

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

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

Based on the above information answer the following :

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

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

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

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

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

(i) 4y = 10 - (2 + π)x

(ii) A = 10x - (2 + 12π)x 2

(iii) 50/4 + π

20/4 + π  

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

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

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

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

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

      Write the Maximum value of Area (A) .

(i) (10 + x)√100 - x 2

(iii) 5√3m OR 75√3/m.m2

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

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

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

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

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

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

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

(iii) 1/2  Or  2/3            

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

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

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

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

i)  12πh 3

(ii) 1/48 cm/s

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

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

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

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

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

By QB365 on 21 May, 2021

QB365 Provides the updated CASE Study Questions for Class 12 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

Cbse 12th standard maths probability case study questions with solution 2021.

12th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) What is the probability that the first ball is yellow and the second ball is red?

(iii) What is the probability that both the balls are red?

(iv) What is the probability that the first ball is green and the second ball is not yellow?

(v) What is the probability that both the balls are not blue?

(ii) When the doctor arrives late, what is the probability that he comes by cab?

(iii) When the doctor arrives late, what is the probability that he comes by bike?

(iv) When the doctor arrives late, what is the probability that he comes by other means of transport?

(v) What is the probability that the doctor is late by any means?

(ii) Probability that puzzle is solved by Ravi but not by Priya, is

(iii) Find the probability that puzzle is solved.

(iv) Probability that exactly one of them solved the puzzle, is

(v) Probability that none of them solved the puzzle, is

(ii) The probability that it does not rain on chosen day is

(iii) The probability that the weatherman predicts correctly is

(iv) The probability that it will rain on the chosen day, if weatherman predict rain for that day, is

(v) The probability that it will not rain on the chosen day, if weatherman predict rain for that day, is

(ii) Teacher ask Mivaan, what is the probability that both tickets drawn by Aadya shows odd number?

(iii) Teacher ask Deepak, what is the probability that tickets drawn by Mivaan, shows a multiple of 4 on one ticket and a multiple 5 on other ticket?

(iv) Teacher ask Archit, what is the probability that tickets are drawn by Deepak, shows a prime number on one ticket and a multiple of 4 on other ticket?

(v) Teacher ask Aadya, what is the probability that tickets drawn by Vrinda, shows an even number on first ticket and an odd' number on second ticket?

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

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

Let B, R, Y and G denote the events that ball drawn is blue, red, yellow and green respectively. \(\therefore P(B)=\frac{12}{35}, P(R)=\frac{8}{35}, P(Y)=\frac{10}{35} \text { and } P(G)=\frac{5}{35}\) \((i) \ (c): P(G \cap B)=P(B) \cdot P(G \mid B)=\frac{12}{35} \cdot \frac{5}{34}=\frac{6}{119}\) \((ii) \ (\mathbf{b}): P(R \cap Y)=P(Y) \cdot P(R \mid Y)=\frac{10}{35} \cdot \frac{8}{34}=\frac{8}{119}\) (iii) (a): Let E = event of drawing a first red ball and F = event of drawing a second red ball Here,  \(P(E)=\frac{8}{35} \text { and } P(E)=\frac{7}{34}\) \(\therefore \P(F \cap E)=P(E) \cdot P(F \mid E)=\frac{8}{35} \cdot \frac{7}{34}=\frac{4}{85}\) \(\text {(iv) }(c): P\left(Y^{\prime} \cap G\right)=P(G) \cdot\left(Y^{\prime} \mid G\right)=\frac{5}{35} \cdot \frac{24}{34}=\frac{12}{119}\) (v) (d): Let E = event of drawing a first non-blue ball and F = event of drawing a second non-blue ball Here, \(P(E)=\frac{23}{35} \text { and } P(F)=\frac{22}{34}\) \(\therefore \ P(F \cap E)=P(E) \cdot P(F \mid E)=\frac{23}{35} \cdot \frac{22}{34}=\frac{253}{595}\)

Let E be the event that the doctor visit the patient late and let A 1 , A 2 , A 3 , A 4 be the events that the doctor comes by cab, metro, bike and other means of transport respectively. \(P\left(A_{1}\right)=0.3, P\left(A_{2}\right)=0.2, P\left(A_{3}\right)=0.1, P\left(A_{4}\right)=0.4\) P(E I A 1 ) = Probability that the doctor arriving late when he comes by cab = 0.25 Similarly, P ( E I A 2 ) = 0.3, P (E I A 3 ) = 0.35 and P ( E I A 3 ) = 0.1 (i) (b): P(A 2  | E) = Probability that the doctor arriving late and he comes by metro \(=\frac{P\left(A_{2}\right) P\left(E \mid A_{2}\right)}{\sum P\left(A_{i}\right) P\left(E \mid A_{i}\right)}\) \(=\frac{(0.2)(0.3)}{(0.3)(0.25)+(0.2)(0.3)+(0.1)(0.35)+(0.4)(0.1)}\) \(=\frac{0.06}{0.21}=\frac{2}{7}\) (ii) (c): P(A 1 | E) = Probability that the doctor arriving late and he comes by cab \(=\frac{P\left(A_{1}\right) P\left(E \mid A_{1}\right)}{\Sigma P\left(A_{i}\right) P\left(E \mid A_{i}\right)}\) \(=\frac{(0.3)(0,25)}{(0.3)(0.25)+(0.2)(0.3)+(0.1)(0.35)+(0.4)(0.1)}\) \(=\frac{0.075}{0.21}=\frac{5}{14}\) (iii) (d): P(A 3 | E) = Probability that the doctor arriving late and he comes by bike \(=\frac{P\left(A_{3}\right) P\left(E \mid A_{3}\right)}{\sum P\left(A_{i}\right) P\left(E \mid A_{i}\right)}\) \(=\frac{(0.1)(0.35)}{(0.3)(0.25)+(0.2)(0.3)+(0.1)(0.35)+(0.4)(0.1)}\) \(=\frac{0.035}{0.21}=\frac{1}{6}\) (iv) (c): P(A 4 | E) = Probability that the doctor arriving late and he comes by other means of transport \(=\frac{P\left(A_{4}\right) P\left(E \mid A_{4}\right)}{\Sigma P\left(A_{i}\right) P\left(E \mid A_{i}\right)}\) \(=\frac{(0.4)(0.1)}{(0.3)(0.25)+(0.2)(0.3)+(0.1)(0.35)+(0.4)(0.1)}\) \(=\frac{0.04}{0.21}=\frac{4}{21}\) (v) (a): Probability that the doctor is late by any means \(=\frac{2}{7}+\frac{5}{14}+\frac{1}{6}+\frac{4}{21}=1\)

Let E 1 be the event that Ravi solved the puzzle and E 2 be the event that Priya solved the puzzle Then, p(E 1 ) = 1/4 and P(E2) = 1/5 (i) (b): Since, E 1 and E 2 are independent events. ∴ P(both solved the puzzle) \(=P\left(E_{1} \cap E_{2}\right)\) \(=P\left(E_{1}\right) \cdot P\left(E_{2}\right)=\frac{1}{4} \times \frac{1}{5}=\frac{1}{20}=\frac{1}{20} \times 100 \%=5 \%\) (ii) (b): P(puzzle is solved by Ravi but not by Priya) \(=P\left(\bar{E}_{2}\right) P\left(E_{1}\right)=\left(1-\frac{1}{5}\right) \cdot \frac{1}{4}=\frac{4}{5} \cdot \frac{1}{4}=\frac{1}{5}\) (iii) (c) : P(puzzle is solved) = P(E 1 or E 2 ) \(=P\left(E_{1} \cup E_{2}\right)=P\left(E_{1}\right)+P\left(E_{2}\right)-P\left(E_{1} \cap E_{2}\right)\) \(=\frac{1}{4}+\frac{1}{5}-\frac{1}{20}=\frac{8}{20}=\frac{2}{5}\) (iv) (c): P(Exactly one of them solved the puzzle) \(=P\left[\left(E_{1} \text { and } \bar{E}_{2}\right) \operatorname{or}\left(E_{2} \text { and } \bar{E}_{1}\right)\right] \) \(=P\left(E_{1} \cap \bar{E}_{2}\right)+P\left(E_{2} \cap \bar{E}_{1}\right) \) \(=P\left(E_{1}\right) \times P\left(\bar{E}_{2}\right)+P\left(E_{2}\right) \times P\left(\bar{E}_{1}\right) \) \(=\frac{1}{4} \times \frac{4}{5}+\frac{1}{5} \times \frac{3}{4} \quad\left[\because P\left(\bar{E}_{1}\right)=1-P\left(E_{1}\right)\right] \) \(=\frac{4}{20}+\frac{3}{20}=\frac{7}{20}\) (v) (b): P(none of them solved the puzzle) \(=P\left(\bar{E}_{1} \cap \bar{E}_{2}\right)=P\left(\bar{E}_{1}\right) \cdot P\left(\bar{E}_{2}\right)=\frac{3}{4} \times \frac{4}{5}=\frac{3}{5}\)

(i) (d): Since, it rained only 6 days each year, therefore, probability that it rains on chosen day is  \(\frac{6}{366}=\frac{1}{61}\) (ii) (c): The probability that it does not rain on chosen day =  \(1-\frac{1}{61}=\frac{60}{61}=\frac{360}{366}\) (iii) (c): It is given that, when it actually rains, the weatherman correctly forecasts rain 80% of the time. Required probability \( =\frac{80}{100}=\frac{8}{10}=\frac{4}{5}\) (iv) (a): Let A 1 be the event that it rains on chosen day, A 2 be the event that it does not rain on chosen day and E be the event the weatherman predict rain. Then we have, P(A 1 ) \(=\frac{6}{366}, P\left(A_{2}\right)=\frac{360}{366},\) \(P\left(E \mid A_{1}\right)=\frac{8}{10} \text { and } P\left(E \mid A_{2}\right)=\frac{2}{10}\) Required probability = P(A 1 I E) \(=\frac{P\left(A_{1}\right) \cdot P\left(E \mid A_{1}\right)}{P\left(A_{1}\right) \cdot P\left(E \mid A_{1}\right)+P\left(A_{2}\right) \cdot P\left(E \mid A_{2}\right)}\) \(=\frac{\frac{6}{366} \times \frac{8}{10}}{\frac{6}{366} \times \frac{8}{10}+\frac{360}{366} \times \frac{2}{10}}=\frac{48}{768}=0.0625\) (v) (a): Required probability = 1 - P(A 1 I E) = 1 - 0.0625 = 0.9375 ≈ 0.94.

(i) (b): Total number of tickets = 50 Let event A = First ticket shows even number and B = Second ticket shows even number Now, P(Both tickets show even number) = P(A)・P(B | A) \(=\frac{25}{50} \cdot \frac{24}{49}=\frac{12}{49}\) (ii) (c): Let the event A = First ticket shows odd number and B = Second ticket shows odd number P (Both tickets show odd number) \(=\frac{25}{50} \times \frac{24}{49}=\frac{12}{49}\) (iii) (c): Required probability = P(one number is a multiple of 4 and other is a multiple of 5) = P(multiple of 5 on first ticket and multiple of 4 on second ticket) + P(multiple of 4 on first ticket and multiple of 5 on second ticket) \(=\frac{10}{50} \cdot \frac{12}{49}+\frac{12}{50} \times \frac{10}{49}=\frac{12}{245}+\frac{12}{245}=\frac{24}{245}\) (iv) (d): Required probability = P(one ticket with prime number and other ticket with a multiple of 4) \(=2\left(\frac{15}{50} \times \frac{12}{49}\right)=\frac{36}{245}\) (v) (b): Let the event A = First ticket shows even number and B = Second ticket shows odd number. Now, P(First ticket shows an even number and second ticket shows an odd number) = P(A)・P(B | A) \(=\frac{25}{50} \times \frac{25}{49}=\frac{25}{98}\)

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• Class 12 Maths Important Questions 2024-25

CBSE Class 12 Important Questions Maths Chapterwise - Free PDF Download

Class 12 Mathematics is an important part of the syllabus. The chapters are included in the syllabus to develop mathematical concepts and problem-solving skills among the students. This is why the students will need a good practice ground to check their skills. The Class 12 Maths Important Questions with Solutions term 2 will be the best tool to practise and become better in this subject.

Overview of Class 12 Important Questions Maths

CBSE Class 12 Mathematics is a very crucial subject to master. This subject is the key to crack the entrance exams conducted nationwide for the selection of the best candidates. From trigonometry to integrals, determinants to probability, the syllabus has been perfectly formulated to create a strong base of mathematical concepts for the aspirants. To make your knowledge more profound, you need Class Maths Important Questions Class 12 PDF . All these questions have been formulated chapter-wise so that you can find the specific areas easily to practice.

Class 12 Maths Important Questions are framed by the top teachers of Vedantu with the sole aim to deliver a platform where students can assess their problem-solving skills. These sample questions can be a brilliant medium to judge your preparation. You can find out your weaknesses and work on them. Download Class 12th Maths Important Questions With Solutions and work hard to ace the board exams and to prepare for the entrance exams ahead.

Download CBSE Class 12 Maths Important Questions 2024-25 PDF

Also, check CBSE Important Questions for Class 12 Maths with Solutions PDF 2024-25 chapter-wise:

CBSE Class 12 Maths Weightage 2024-25

CBSE Class 12 Maths must be studied smartly. Students must give priority to those chapters primarily that consist of major weightage of marks. Algebra, Calculus, Vectors, and Three-Dimensional Geometry are the most vital chapters from this perspective.  Check out the chapters with their marks distribution and prepare accordingly.

Chapterwise Important Questions for CBSE Class 12 Maths

NCERT Important Questions for Class 12 Maths with Solutions PDF 2024-25: Summary

Class 12 CBSE Mathematics has a huge syllabus. It is quite intimidating to cover the entire syllabus of all subjects and to find time to practice. You need to be very organized to segregate your time to cover the entire syllabus. This is where NCERT Important Questions for Class 12 Maths Chapter Wise PDF fits into the study material perfectly. All these Maths Class 12 Important Questions follow the CBSE guidelines and provide a new way to understand the concepts. These Class 12th Maths Important Questions are designed to make the students aware of the various other patterns found in the board exams. Once they are accustomed to solving questions in these patterns, they will feel quite confident about their problem-solving skills. These Class 12 Important Questions Maths can be solved once you are done with the exercises in the textbook.

As per the CBSE syllabus , you will find Class 12th Maths Important Questions for 13 chapters here. A sample question paper can be downloaded for each chapter for free and can be used offline to practice. Every question has been solved step by step using the easiest method so that the students can easily understand it and grab the concept. You can use CBSE Class 12 Maths Important Questions 2024 as a suggestion for the upcoming exams. Learn what other kinds of question patterns can be formulated for a particular concept in a chapter from the NCERT Important Questions for Class 12 Maths Chapter wise PDF .

How Solving Class 12 Important Questions Maths Chapter Wise Can Give You a Competitive Edge?

Studying a new chapter and understanding the concepts is a process with an aim. The aim is to acquire knowledge and use it to solve problems. This process can be made even better with the assured outcomes by using the Important Questions for Class 12 Maths with solutions PDF.

Benefits of Using CBSE Class 12th Maths Important Questions for Board Exam

Developing core knowledge.

Mathematical concepts are used in the subjects of advanced professional courses. Studying all the chapters properly is a must for the development of core knowledge. The best way to do so is by solving the Class 12 Maths Chapter Wise Important Questions . These questions are designed to challenge the intellect of a student. Maths Important Questions Class 12 PDF also comes with solutions. You can check the ways the teachers have approached these questions and solved them.

Clarification of Doubts

Apart from solving the exercises in the textbook, students will need another medium to find challenging questions. These challenging Class 12 Important Questions Maths can be downloaded from here and solved at your convenience. You will find new doubts arising while solving these problems. The solution will then guide you to clarify your doubts once and for all. You will learn new approaches to answer Class 12 mathematical questions.

Increasing Your Efficiency

The only way to increase your problem-solving skill level is by practising new problems. Once you are done with the textbook chapters, you can proceed to solve the CBSE Class 12 Important Questions Maths and check your efficiency level. These CBSE Important Questions will give you an intelligent medium to assess your skills. You will be able to find your weak areas in the entire syllabus. Work on the weaknesses and make them your strength. These Class 12th Maths Important Questions will work as a diagnostic tool. Your efficiency level will automatically increase when you practice solving sample questions for all the chapters. You can also check your answering skills by comparing them with the solutions.

Importance of CBSE Class 12 Maths Important Questions with Solutions for Term 2 

All the chapters in the Class 12 Maths syllabus are studied by the students to increase their mathematical knowledge and deepen their concepts. The chapters have been designed with exercises so that students can check their preparation level by solving the problems. This is where the important questions framed by the experts for all the chapters will be very useful.

These questions have been set by following the latest CBSE syllabus and the solutions have been framed in a stepwise method for easy comprehension. Apart from the exercises, these important questions can be used to practise what they have studied in the chapters. After solving these questions, they can compare the answers to the solutions provided and find out which part of the chapters needs more attention.

Hence, these Class 12 Maths Important Questions for Term 2 with Solutions will act as the perfect guide to practise using mathematical concepts, formulas, and fundamental principles of the chapters and focus on the development of a conceptual foundation for this subject.

Download Class 12 Maths Important Questions with Answers PDF 2024-25

Get the free PDF version of these important questions for all the chapters. Learn from the experts how to solve these questions and increase your knowledge. Become better at solving Class 12 Mathematics problems by practising these questions during your study time and score more in the final exam.

CBSE Class 12 Maths Study Materials 2024-25

Other cbse class 12 important questions related links.

FAQs on Class 12 Maths Important Questions 2024-25

1. How can Maths Important Question Class 12 help you study?

Ans: Download chapter-wise Important Question of Maths Class 12 and practice. Solve the questions and compare your answers with the solution for the 12th Maths Important Questions. You will become much better in due course of time. You will be able to solve questions and save time. Your score will increase when you use the tactics shown in the solutions.

2. Why should you prefer Vedantu for Class 12 Maths Important Questions?

Ans: Trust Vedantu for downloading high-quality Important Questions of Maths Class 12. Most of the students of Class 12 prefer Vedantu for conceptual questions and accurate answers. They like to practice mathematics by using these fundamental questions.

3. What are the different chapters in Class 12 Maths? 

Ans: There are 13 chapters in the textbook of Class 12 Maths. The names of these chapters are as follows. 

Chapter 1 Relations and Functions

Chapter 2 Inverse Trigonometric Functions 

Chapter 3 Matrices

Chapter 4 Determinants 

Chapter 5 Continuity and Differentiability

Chapter 6 Application of Derivatives

Chapter 7 Integrals

Chapter 8 Application of Integrals 

Chapter 9 Differential Equations

Chapter 10 Vector Algebra

Chapter 11 Three Dimensional Geometry

Chapter 12 Linear Programming

Chapter 13 Probability 

4. How can you get good scores in Class 12 Maths? 

Ans: If you want to get good scores in Class 12 Maths then the first and foremost thing that you have to do is start your preparation at an early stage. Start preparing for your Maths examination when your academic session starts. This technique will help you to complete each chapter of the book on time without hustling. The next thing you should do is attend all the Maths classes. Try to ask your doubts from your Maths teacher if you face any. Asking your queries will make the concepts crystal clear in your brain. At the same time, practise questions at home related to the concepts or chapters for better comprehension.

5. What is the exam paper pattern of Class 12 Maths? 

Ans: As per the latest guidelines of CBSE, the latest exam paper pattern of Class 12 Maths is as follows- 

There are five sections in the Maths Class 12 exam paper. 

In section one, there are 16 questions of one mark each. 

In section two, the questions will be asked from the case studies. There will be two case studies in this section. Here, each case study will have five multiple choice questions and the student has to attempt only four. Each MCQ carries one mark. 

Ten questions will be there in section three. Each question will carry two marks. 

In section four, seven questions will be there. And each question is of three marks. 

There will be three questions of five marks each in section five.

6. How can you get the NCERT Solutions of Class 12 Maths? 

Ans: If you are preparing for the Class 12 Maths examination then you can get all the necessary study material including the NCERT Solutions on Vedantu. Here’s how you can download them. 

Click on the link of NCERT Solutions of Class 12 Maths. 

By clicking on this link you will land on the official significant question page of Vedantu. On this page, you will see a list of chapters that are given in the Maths NCERT textbook. 

Then select the topics for which you require the study materials including the NCERT Solutions, notes, important questions, topic and concept-wise brief explanations, etc. 

Click on the chapters icon to get the relevant content. 

Tap on the download button for downloading the PDFs of the chapters.

7. Is Class 12 Maths easy? 

Ans: Class 12 Maths is easy for those students whose concepts are clear. If your Class 11 concepts are well settled in your mind then you can easily understand the concepts of Class 12 Maths. However, if your Class 11 concepts are not that much clear then you may face some issues in studying Class 12 Maths. Still, you can avoid this situation if you start your preparation early. If you do this then you can take out some extra time to read your last year’s concepts along with your Class 12 chapters. 

These solutions are available on Vedantu's official website( vedantu.com ) and mobile app free of cost.

Important Questions for CBSE Class 12

Cbse class 12 study materials, home tuitions in india.

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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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