case study questions maths class 12

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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CBSE Class 12

CBSE Class 12 Maths Exam 2024 Important Case Study Based Questions

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

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

CBSE Class 12 Maths Unit Wise Marks Distribution 2024

CBSE Maths Previous Year Question Paper Class 12

CBSE Class 12 Maths Case Study Questions 2023

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

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

Based on the above information answer the following :

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

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

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

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

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

(i) 4y = 10 - (2 + π)x

(ii) A = 10x - (2 + 12π)x 2

(iii) 50/4 + π

20/4 + π

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

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

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

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

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

Write the Maximum value of Area (A) .

(i) (10 + x)√100 - x 2

(iii) 5√3m OR 75√3/m.m2

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

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

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

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

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

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

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

(iii) 1/2 Or 2/3

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

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

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

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

i) 12πh 3

(ii) 1/48 cm/s

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

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

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

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

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CBSE NCERT Solutions

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CBSE Class 12 Maths Case Study Problems

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

Here are some example questions Based On Case Study Problems:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answer the following questions using the matrix method:

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

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

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

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

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

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

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

Answer the following questions:

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

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

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

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

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

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

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

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

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

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

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

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

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CBSE 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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Case Study Questions for Class 12 Maths Chapter 10 Vector Algebra

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

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

Case Study Questions for Class 12 Maths

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

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

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

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

Importance of Solving Case Study Questions for Class 12 Maths

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

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

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

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

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Maths assignment class viii | quadrilateral, case study based questions class xii, mathematics.

Case study questions on Relations & Functions, Matrices, Determinants, Applications of Derivatives, Applications of Integral, Differential equations, Vector Algebra, three dimensional Geometry and Probability etc.

CASE STUDY-1 CHAPTER -1

Relations & functions.

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

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

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

Q1) Two neighbors X and Y ∈ I. X exercised his voting right while Y did not cast her vote in general election – 2019. Which of the following is true?

a) (X, Y) ∈ R

b) (Y, X) ∈ R

c) (X, X) ∉ R

d) (X, Y) ∉ R

2. Mr.’ 𝑋 ’ and his wife ‘ 𝑊 ’both exercised their voting right in general election -2019, Which of the following is true?

a) both (X, W) and (W, X) ∈ R

b) (X, W) ∈ R but (W, X) ∉ R

c) both (X, W) and (W, X) ∉ R

d) (W, X) ∈ R but (X, W) ∉ R

Q3) Three friends F1, F2 and F3 exercised their voting right in general election-2019, then which of the following is true?

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

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

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

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

4. The above defined relation R is ______

a) Symmetric and transitive but not reflexive

b) Universal relation

c) Equivalence relation

d) Reflexive but not symmetric and transitive

5. Mr. Shyam exercised his voting right in General Election – 2019, then Mr. Shyam is related to which of the following?

a) All those eligible voters who cast their votes

b) Family members of Mr. Shyam

c) All citizens of India

d) Eligible voters of India

CASE STUDY-2 CHAPTER -1

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

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

Q1. Let 𝑅 ∶ 𝐵 → 𝐵 be defined by R = {( 𝑥 , 𝑦 ): 𝑦 𝑖𝑠 𝑑𝑖𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏𝑦 𝑥 } is

a) Reflexive and transitive but not symmetric

b) Reflexive and symmetric and not transitive

c) Not reflexive but symmetric and transitive

d) Equivalence

2. Raji wants to know the number of functions from A to B. How many number of functions are possible?

3. Let R be a relation on B defined by R = {(1,2), (2,2), (1,3), (3,4), (3,1), (4,3), (5,5)}. Then R is

a) Symmetric

b) Reflexive

c) Transitive

d) None of these three

4. Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?

5. Let 𝑅 : 𝐵 → 𝐵 be defined by R={(1,1),(1,2), (2,2), (3,3), (4,4), (5,5),(6,6)}, then R is

b) Reflexive and Transitive

c) Transitive and symmetric

CASE STUDY-1 CHAPTER -3

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

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

Based on the above information answer the following:

1) Total revenue of market A

a) Rs. 64,000

b) Rs. 60,400

c) Rs. 46,000

d) Rs. 40600

2) Total revenue of market B

a) Rs. 35,000

b) Rs. 53,000

c) Rs. 50,300

d) Rs. 30,500

3) Cost incurred in market A

a) Rs. 13,000

b) Rs.30,100

c) Rs. 10,300

d) Rs. 31,000

4) Profit in market A and B respectively are

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

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

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

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

5) Gross profit in both market

a) Rs.23,000

b) Rs. 20,300

c) Rs. 32,000

d) Rs. 30,200

CASE STUDY-2 CHAPTER -3

CASE STUDY 2:

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