case study questions maths

• Class 10 Notes
• 9th IT CODE 402
• 10th IT CODE 402
• 10th Hindi Grammar MCQ
• 9th Hindi Grammar MCQ

Case Study Questions Class 10 Maths with Solutions PDF Download

 case study questions class 10 maths pdf, case study questions class 10 maths with solutions, case study questions class 10 maths cbse chapter wise pdf download, how to solve case-based question in maths.

• First of all, a student needs to read the complete passage thoroughly. Then start solving the question
• After reading the question try to understand from which topics the question is asked. and try to remember all the concepts of that topic.
• Sometimes the question is very tricky and you will find it very difficult to understand. In that case, Read the question and passage again and again.
• After solving the answer check your answer with the options given.
• Remember, write only answering your answer book

Link to Download Case-Study Questions of class 10

Post a comment, popular posts.

Communication Skills Class 9 Notes

Top 50+ MCQ on Communication Skills Class 10 for TERM 1- 2022 | IT Code 402

Set-1 | Padbandh MCQ Questions Class 10 - CBSE 2022

Information Technology Code 402 Class 10 Solutions

Self Management Skills Class 9 Notes | Employability Skills Unit - 2 Complete Notes

Self Management Skills Class 10 Notes PDF

Introduction to IT and ITes Industry Class 9 Notes

Menu footer widget.

• Privacy Policy

• Andhra Pradesh
• Chhattisgarh
• West Bengal
• Madhya Pradesh
• Maharashtra
• Jammu & Kashmir
• NCERT Books 2022-23
• NCERT Solutions
• NCERT Notes
• NCERT Exemplar Books
• NCERT Exemplar Solution
• States UT Book
• School Kits & Lab Manual
• NCERT Books 2021-22
• NCERT Books 2020-21
• NCERT Book 2019-2020
• NCERT Book 2015-2016
• RD Sharma Solution
• TS Grewal Solution
• TR Jain Solution
• Selina Solution
• Frank Solution
• Lakhmir Singh and Manjit Kaur Solution
• I.E.Irodov solutions
• ICSE - Goyal Brothers Park
• ICSE - Dorothy M. Noronhe
• Sandeep Garg Textbook Solution
• Micheal Vaz Solution
• S.S. Krotov Solution
• Evergreen Science
• KC Sinha Solution
• ICSE - ISC Jayanti Sengupta, Oxford
• ICSE Focus on History
• ICSE GeoGraphy Voyage
• ICSE Hindi Solution
• ICSE Treasure Trove Solution
• Thomas & Finney Solution
• SL Loney Solution
• SB Mathur Solution
• P Bahadur Solution
• Narendra Awasthi Solution
• MS Chauhan Solution
• LA Sena Solution
• Integral Calculus Amit Agarwal Solution
• IA Maron Solution
• Hall & Knight Solution
• Errorless Solution
• Pradeep's KL Gogia Solution
• OP Tandon Solutions
• Sample Papers
• Previous Year Question Paper
• Important Question
• Value Based Questions
• CBSE Syllabus
• CBSE MCQs PDF
• Assertion & Reason
• New Revision Notes
• Revision Notes
• HOTS Question
• Marks Wise Question
• Toppers Answer Sheets
• Exam Paper Aalysis
• Concept Map
• CBSE Text Book
• Additional Practice Questions
• Vocational Book
• CBSE - Concept
• KVS NCERT CBSE Worksheets
• Formula Class Wise
• Formula Chapter Wise
• JEE Previous Year Paper
• JEE Mock Test
• JEE Crash Course
• JEE Sample Papers
• Important Info
• SRM-JEEE Previous Year Paper
• SRM-JEEE Mock Test
• VITEEE Previous Year Paper
• VITEEE Mock Test
• BITSAT Previous Year Paper
• BITSAT Mock Test
• Manipal Previous Year Paper
• Manipal Engineering Mock Test
• AP EAMCET Previous Year Paper
• AP EAMCET Mock Test
• COMEDK Previous Year Paper
• COMEDK Mock Test
• GUJCET Previous Year Paper
• GUJCET Mock Test
• KCET Previous Year Paper
• KCET Mock Test
• KEAM Previous Year Paper
• KEAM Mock Test
• MHT CET Previous Year Paper
• MHT CET Mock Test
• TS EAMCET Previous Year Paper
• TS EAMCET Mock Test
• WBJEE Previous Year Paper
• WBJEE Mock Test
• AMU Previous Year Paper
• AMU Mock Test
• CUSAT Previous Year Paper
• CUSAT Mock Test
• AEEE Previous Year Paper
• AEEE Mock Test
• UPSEE Previous Year Paper
• UPSEE Mock Test
• CGPET Previous Year Paper
• Crash Course
• Previous Year Paper
• NCERT Based Short Notes
• NCERT Based Tests
• NEET Sample Paper
• Previous Year Papers
• Quantitative Aptitude
• Numerical Aptitude Data Interpretation
• General Knowledge
• Mathematics
• Agriculture
• Accountancy
• Business Studies
• Political science
• Enviromental Studies
• Mass Media Communication
• Teaching Aptitude
• NAVODAYA VIDYALAYA
• SAINIK SCHOOL (AISSEE)
• Mechanical Engineering
• Electrical Engineering
• Electronics & Communication Engineering
• Civil Engineering
• Computer Science Engineering
• CBSE Board News
• Scholarship Olympiad
• School Admissions
• Entrance Exams
• All Board Updates
• Miscellaneous
• State Wise Books
• Engineering Exam
• STATE WISE BOOKS
• ENGINEERING EXAM
• SCHOLARSHIP OLYMPIAD
• STATE BOOKS

CBSE Class 12 Maths Case Study Questions With Solutions

CBSE Class 12 Mathematics Case Study Questions are introduced this year in the updated CBSE Board Exam Pattern. According to that this year the candidates need to prepare for the case study problems along with the questions that are legacy of CBSE Board.

In Class XIIth Mathematics Case Study Questions there are problems based on Objective types of questions, Assertions and Reason, and cae based problems. These problems have the intention to examine the students' overall understanding of the subject. If you are preparing for the Maths board exam then this is the right place for you. 

Here, we have provided the complete set of CBSE class 12 maths case study questions With Solutions. These are developed by the subject matter expert. If you want to score good marks in the board papers then you should practice these Case based problems. It is absolutely free of cost. 

Download PDF CBSE Class 12 Maths Case Study From the Given links. It is in chapter wise format.

Class 12th Mathematics Important Formulas, MCQ, Case-Based, Assertion and Reason

Class 12th Maths Case Study

In class 12th Maths Case Study the questions are based on the real world scenarios. A passage filled with information or data is provided to the students. On the basis of that paragraph upto 5 questions are developed which should be answered by the students. To answer them they need to read the passage carefully and then pay attention to the given data to solve such questions.

These types of problems are generally known as case based questions which can be only solved by referring to the given paragraph.

Class 12 Maths Important Formulas

Knowing about the Maths Important Formulas is a crucial part of solving the Maths questions. Formulas help in solving the problems more efficiently and faster. Therefore the PDF file that we have provided here consists of all the basics and Important formulas of maths. It will help in revisions and solving the questions more accurately and easily.

Every chapter has its own topics and formulas so the PDF has been divided into chapter wise format. And if you access them from this place then you will be able to get all the formulas and other questions separately.

Class 12 Maths Assertion and Reason MCQs

Class 12th Maths Assertion and Reason MCQs PDF with Solutions are also given here. It is the most important part of Case Study Questions because scoring good marks in this section is not that much hard. If your basic concepts are clear. Because most of the time such types of questions are directly prepared by referring to the concepts.

Furthermore, the assertion and reason MCQs are solved by applying the distinct approaches. For instance, to answer these questions first candidates need to verify the Assertion (Statement) and then the reason if both are correct, then learners need to verify whether both statement and reason support each other or not.

There are a total of 5 sections in CBSE Class 12 Maths Questions Term 1. Section A contains 1 mark, Section B contains 2 marks, Section C contains 3 marks, Section D contains 4 marks and the last Section E contains 5 marks. A total of 5 questions are given in these sections.

No, In Term 1 exam there will be a total of 5 questions in each case study of class 12 maths, out of which 4 are compulsory to solve.

CBSE 12th 2024-25 : Physics Official Competency Focused Practice Questions released by CBSE

CBSE 12th 2024-25 : Chemistry Official Competency Focused Practice Questions released by CBSE

CBSE Class 12 Marks Verification Window Last Date Today: Apply Soon, Direct Link Here

CBSE Class 12 Result 2024: Application for Verification of Marks Starts; Last Date 21st May – Check Complete Process

CBSE Class 12 Result 2024 Latest Update : Verification of Marks, Revaluation & Photocopy of Answer Sheet; Check Complete Process

CBSE Class 12th Result 2024 Out : Supplementary, Re-verification & Re-evaluation Date Released; Check Details Here

• NCERT Solutions for Class 12 Maths
• NCERT Solutions for Class 10 Maths
• CBSE Syllabus 2023-24
• Social Media Channels
• Login Customize Your Notification Preferences

• Second click on the toggle icon

Provide prime members with unlimited access to all study materials in PDF format.

Allow prime members to attempt MCQ tests multiple times to enhance their learning and understanding.

Provide prime users with access to exclusive PDF study materials that are not available to regular users.

CBSE Case Study Questions for Class 6 – 10, 12 for Maths, Science, SST

Cbse case study questions for maths, science, social science.

CBSE Case Study Questions:   Case Study Questions for all Class 1, 2, 4, 5, 6, 7, 8, 9,10, 11 and 12 by Experienced Teachers. We Net Ex. Arranged here Important Case Based Questions for CBSE Board – Maths, Science, Social Science, English.

Leave a Reply Cancel reply

We have a strong team of experienced teachers who are here to solve all your exam preparation doubts, বিশাল ডানাওয়ালা এক থুত্থুরে বুড়ো class 11 mcq for semester 1, the gandhian era class 10 mcq, puimacha (পুঁইমাচা) class 11 mcq questions answers for semester 1, alias jimmy valentine class 11 long questions for semester 2.

Class 10 Maths Case Study Questions of Chapter 1 Real Numbers

• Post author: studyrate
• Post published:
• Post category: class 10th
• Post comments: 0 Comments

Case study Questions in the Class 10 Mathematics Chapter 1  are very important to solve for your exam. Class 10 Maths Chapter 1 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 1  Real Numbers

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Real Numbers Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 1 Real Numbers

Case Study/Passage-Based Questions

Case Study 1: Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. (i) For what value of n, 4 n  ends in 0?

Answer: (d) no value of n

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, a n  is a rational number?

Answer: (c) for all n > 1 

(iii) If x and yare two odd positive integers, then which of the following is true?

Answer: (d) both (a) and (b)

(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is

Answer: (a) always true

(v) If n is any odd integer, then n2 – 1 is divisible by

Answer: (d) 8

Case Study 2: HCF and LCM are widely used in number system especially in real numbers in finding relationship between different numbers and their general forms. Also, product of two positive integers is equal to the product of their HCF and LCM Based on the above information answer the following questions.

(i) If two positive integers x and y are expressible in terms of primes as x =p 2 q 3  and y=p 3 q, then which of the following is true? (a) HCF = pq 2  x LCM (b) LCM = pq 2  x HCF (c) LCM = p 2 q x HCF (d) HCF = p 2 q x LCM

Answer: (b) LCM = pq2 x HCF

ii) A boy with collection of marbles realizes that if he makes a group of 5 or 6 marbles, there are always two marbles left, then which of the following is correct if the number of marbles is p? (a) p is odd (b) p is even (c) p is not prime (d) both (b) and (c)

Answer: (d) both (b) and (c)

(iii) Find the largest possible positive integer that will divide 398, 436 and 542 leaving remainder 7, 11, 15 respectively. (a) 3 (b) 1 (c) 34 (d) 17

Answer: (d) 17

(iv) Find the least positive integer that on adding 1 is exactly divisible by 126 and 600. (a) 12600 (b) 12599 (C) 12601 (d) 12500

Answer: (b) 12599

(v) If A, B and C are three rational numbers such that 85C – 340A = 109, 425A + 85B = 146, then the sum of A, B and C is divisible by (a) 3 (b) 6 (c) 7 (d) 9

Answer: (a) 3

Case Study 3: Real numbers are an essential concept in mathematics that encompasses both rational and irrational numbers. Rational numbers are those that can be expressed as fractions, where the numerator and denominator are integers and the denominator is not zero. Examples of rational numbers include integers, decimals, and fractions. On the other hand, irrational numbers are those that cannot be expressed as fractions and have non-terminating and non-repeating decimal expansions. Examples of irrational numbers include √2, π (pi), and e. Real numbers are represented on the number line, which extends infinitely in both positive and negative directions. The set of real numbers is closed under addition, subtraction, multiplication, and division, making it a fundamental number system used in various mathematical operations and calculations.

Which numbers can be classified as rational numbers? a) Fractions b) Integers c) Decimals d) All of the above Answer: d) All of the above

What are rational numbers? a) Numbers that can be expressed as fractions b) Numbers that have non-terminating decimal expansions c) Numbers that extend infinitely in both positive and negative directions d) Numbers that cannot be expressed as fractions Answer: a) Numbers that can be expressed as fractions

What are examples of irrational numbers? a) √2, π (pi), e b) Integers, decimals, fractions c) Numbers with terminating decimal expansions d) Numbers that can be expressed as fractions Answer: a) √2, π (pi), e

How are real numbers represented? a) On the number line b) In complex mathematical formulas c) In algebraic equations d) In geometric figures Answer: a) On the number line

What operations are closed under the set of real numbers? a) Addition, subtraction, multiplication b) Subtraction, multiplication, division c) Addition, multiplication, division d) Addition, subtraction, multiplication, division Answer: d) Addition, subtraction, multiplication, division

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 1 Real Numbers with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Real Numbers Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

You Might Also Like

Class 10 Science Revision Notes PDF Download for FREE Chapterwise

Extra questions of class 10 science chapter 7 control and coordination pdf download, extra questions of class 10 maths chapter 4 quadratic equations pdf download, leave a reply cancel reply.

Save my name, email, and website in this browser for the next time I comment.

• Bihar Board

CFA Institute

Srm university.

• Shiv Khera Special
• Education News
• Web Stories
• Current Affairs
• School & Boards
• College Admission
• Govt Jobs Alert & Prep
• GK & Aptitude
• CBSE Class 10 Study Material

CBSE Class 10 Maths Case Study Questions for Chapter 14 - Statistics (Published By CBSE)

Case study question bank for cbse class 10 maths chapter 14 - statistics is available here. practice this new format of questions to score good marks in your board exam..

CBSE Class 10 Maths Case Study Questions for Chapter 14 - Statistics are published by the CBSE board itself. These questions are perfect to acquaint with the new format of the questions and make your board exam preparations. Questions are based on the real life situations. You can easily understand how concepts and logic are used in the case study questions. All the questions are provided with answers.  

Check Case Study Questions for Class 10 Maths Chapter 14 - Statistics

CASE STUDY 1:

COVID-19 Pandemic The COVID-19 pandemic, also known as coronavirus pandemic, is an ongoing pandemic of coronavirus disease caused by the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) among humans.

The following tables shows the age distribution of case admitted during a day in two different hospitals

Refer to table 1

1. The average age for which maximum cases occurred is

Answer: c) 36.82

2. The upper limit of modal class is

Answer: d) 45

3. The mean of the given data is

Answer: d) 35.4

Refer to table 2

4. The mode of the given data is

Answer: a) 41.4

5. The median of the given data is

Answer: b) 40.2

Electricity Energy Consumption

CASE STUDY 2:

Electricity energy consumption is the form of energy consumption that uses electric energy. Global electricity consumption continues to increase faster than world population, leading to an increase in the average amount of electricity consumed per person (per capita electricity consumption).

Refer to data received from Colony A

1. The median weekly consumption is

a) 12 units

b) 16 units

c) 20 units

d) None of these

Answer: c) 20 units

2. The mean weekly consumption is

a) 19.64 units

b) 22.5 units

c) 26 units

Answer: a) 19.64 units

3. The modal class of the above data is I

Answer: c) 20-30

Refer to data received from Colony B

4. The modal weekly consumption is

a) 38.2 units

b) 43.6 units

d) 32 units

Answer: b) 43.6 units

5. The mean weekly consumption is

a) 15.65 units

b) 32.8 units

c) 38.75 units

d) 48 units

Answer: c) 38.75 units

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

Tips to Solve Case Study Based Questions Accurately

Get here latest School , CBSE and Govt Jobs notification in English and Hindi for Sarkari Naukari and Sarkari Result . Download the Jagran Josh Sarkari Naukri App . Check  Board Result 2024  for Class 10 and Class 12 like  CBSE Board Result ,  UP Board Result ,  Bihar Board Result ,  MP Board Result ,  Rajasthan Board Result  and Other States Boards.

• SSC JE Answer Key 2024
• APSC PRO Admit Card 2024
• BSF SI Recruitment 2024
• Kerala PSC Staff Nurse Answer Key 2024
• IITM RA Recruitment 2024
• IAS Exam Last Minute Tips 2024
• NFL Engineer Recruitment 2024
• APSC SO Result 2024
• APSC SO Admit Card 2024
• UPSC CSE Admit Card 2024
• CBSE Study Material
• CBSE Class 10

Latest Education News

Visual IQ Challenge: Only highly attentive readers can spot three hidden faces in 6 seconds!

SSC GD Revised Vacancy 2204: एसएससी जीडी में पदों की संख्या बढ़कर हुई 46 हजार जानें कौन से फोर्सेस में बढ़ी है रिक्तियां

Modi Cabinet 2024 with Portfolios: किसे मिली किस मंत्रालय की कमान और किसका बदला मंत्रालय, कौन बनेगा स्पीकर? सब जानें

SSC GD Result 2024 Updates: Revised CRPF Constables Vacancies Released at ssc.gov.in

Top 10 Father’s Day Easy Card Making Ideas with Images

IQ Test: Which Number Will Come Next In This Series? Answer In 20 Seconds!

Record Surge in Indian Students Opting for U.S. Education: U.S. Mission to India Reports Growth in Student Visas

Current Affairs One Liners: 13 June 2024- G7 Summit 2024

SOA MAINTAINS PRE-EMINENT POSITION IN NIRF, THE & QS WORLD RANKING

Top 10 Father’s Day Easy Craft Ideas with Images and Fun Activities

Superbug in Space, Are Astronauts in Danger?

PSEB Class 9th Punjabi A&B Syllabus 2024-25: Download PDF for Exam

Current Affairs Quiz: 13 June 2024- Global Gender Gap Index 2024

Why did India Slip by 2 Ranks in WEF Report? Get Full Details Here

DBRAU Result 2024 OUT at dbrau.ac.in; Download Agra University UG and PG Semester Marksheet PDF

Current Affairs Hindi One Liners: 13 जून 2024- G7 Summit 2024

VMOU Result 2024 OUT at vmou.ac.in, Direct Link to Download UG and PG Marksheet

AAI AERO Result 2024 Declared at aai.aero: Download PDF Here

[LINK ACTIVE] JKBOSE Class 12th Result 2024 Declared at jkbose.nic.in, 74% Students Pass, Download JK Board Soft, Hard Zone Mark Sheet PDF

Today Current Affairs Quiz In Hindi: 13 जून 2024- Global Gender Gap Index 2024

myCBSEguide

• Mathematics
• Class 12 Maths Case...

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

Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

Related Posts

• CBSE Reduced Syllabus Class 10 (2020-21)
• CBSE Class 10 Maths Sample Paper 2020-21
• Case Study Class 10 Maths Questions
• Competency Based Learning in CBSE Schools
• Class 11 Physical Education Case Study Questions
• Class 11 Sociology Case Study Questions
• Class 12 Applied Mathematics Case Study Questions
• Class 11 Applied Mathematics Case Study Questions

1 thought on “Class 12 Maths Case Study Questions”

plz provide solutions too

Leave a Comment

Save my name, email, and website in this browser for the next time I comment.

CBSE Expert

Class 10 Maths: Case Study Questions of Chapter 4 Quadratic Equations PDF

Case study Questions on the Class 10 Mathematics Chapter 4  are very important to solve for your exam. Class 10 Maths Chapter 4 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 10 Maths Chapter 4 Quadratic Equations

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Quadratic Equations Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 4 Quadratic Equations

Case Study/Passage Based Questions

1)Formation of Quadratic Equation

Quadratic equations started around 3000 B.C. with the Babylonians. They were one of the world’s first civilizations and came up with some great ideas like agriculture, irrigation, and writing. There were many reasons why Babylonians needed to solve quadratic equations. For example to know what amount of crop you can grow on the square field. Now represent the following situations in the form of a quadratic equation.

The sum of squares of two consecutive integers is 650. (a) x 2 + 2x – 650 = 0 (b) 2x 2 +2x – 649 = 0 (c) x 2 – 2x – 650 = 0 (d) 2x 2 + 6x – 550 = 0

Answer: (b) 2×2 +2x – 649 = 0

The sum of two numbers is 15 and the sum of their reciprocals is 3/10. (a) x 2 + 10x – 150 = 0 (b) 15x 2 – x + 150 = 0 (c) x 2 – 15x + 50 = 0 (d) 3x 2 – 10x + 15 = 0

Answer: (c) x2 – 15x + 50 = 0

Two numbers differ by 3 and their product is 504. (a) 3x 2 – 504 = 0 (b) x 2 – 504x + 3 = 0 (c) 504x 2 +3 = x (d) x 2 + 3x – 504 = 0

Answer: (d) x2 + 3x – 504 = 0

A natural number whose square diminished by 84 is thrice of 8 more of a given number. (a) x 2 + 8x – 84 = 0 (b) 3x 2 – 84x + 3 = 0 (c) x 2 – 3x – 108 = 0 (d) x 2 –11x + 60 = 0

Answer: (c) x2 – 3x – 108 = 0

A natural number when increased by 12, equals 160 times its reciprocal. (a) x 2 – 12x + 160 = 0 (b) x 2 – 160x + 12 = 0 (c) 12x 2 – x – 160 = 0 (d) x 2 + 12x – 160 = 0

Answer: (d) x2 + 12x – 160 = 0

2)Nature of Roots A quadratic equation can be defined as an equation of degree 2. This means that the highest exponent of the polynomial in it is 2. The standard form of a quadratic equation is ax 2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Every quadratic equation has two roots depending on the nature of its discriminant, D = b 2 – 4ac

Which of the following quadratic equation have no real roots? (a) –4x 2 + 7x – 4 = 0 (b) –4x 2 + 7x – 2 = 0 (c) –2x 2 +5x – 2 = 0 (d) 3x 2 + 6x + 2 = 0

Answer: (a) –4×2 + 7x – 4 = 0

Which of the following quadratic equation have rational roots? (a) x 2 + x – 1 = 0 (b) x 2 – 5x + 6 = 0 (c) 4x 2 – 3x – 2 = 0 (d) 6x 2 – x + 11 = 0

Answer: (b) x2 – 5x + 6 = 0

Which of the following quadratic equation have irrational roots? (a) 3x 2 +2x + 2 = 0 (b) 4x 2 – 7x + 3 = 0 (c) 6x 2 – 3x – 5 = 0 (d) 2x 2 +3x – 2 = 0

Answer: (c) 6×2 – 3x – 5 = 0

Which of the following quadratic equations have equal roots? (a) x 2 – 3x + 4 = 0 (b) 2x 2 – 2x + 1 = 0 (c) 5x 2 – 10x + 1 = 0 (d) 9x 2 + 6x + 1 = 0

Answer: (d) 9×2 + 6x + 1 = 0

Which of the following quadratic equations has two distinct real roots? (a) x 2 + 3x + 1 = 0 (b) –x 2 + 3x – 3 = 0 (c) 4x 2 + 8x + 4 = 0 (d) 3x 2 + 6x + 4 = 0

Answer: (a) x2 + 3x + 1 = 0

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 4 Quadratic Equations with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 10 Maths Quadratic Equations Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

Leave a Comment Cancel reply

Save my name, email, and website in this browser for the next time I comment.

Download India's best Exam Preparation App Now.

Key Features

• Revision Notes
• Important Questions
• Previous Years Questions
• Case-Based Questions
• Assertion and Reason Questions

No thanks, I’m not interested!

CBSE Case Study Questions for Class 11 Maths Sets Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 11 Maths Sets 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 11 Maths Sets PDF

Checkout our case study questions for other chapters.

• Chapter 2 Relations and Functions Case Study Questions
• Chapter 3 Trigonometric Functions Case Study Questions
• Chapter 4 Principle of Mathematical Induction Case Study Questions
• Chapter 5 Complex Numbers and Quadratic Equations 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.

Contact Form

Privacy Policy

• New QB365-SLMS
• NEET Materials
• JEE Materials
• Banking first yr Materials
• TNPSC Materials
• DIPLOMA COURSE Materials
• 5th Standard Materials
• 1st Standard - CVBHSS Materials
• 2nd Standard - CVBHSS Materials
• 3rd Standard - CVBHSS Materials
• 4th Standard - CVBHSS Materials
• 5th Standard - CVBHSS Materials
• 12th Standard Materials
• 11th Standard Materials
• 10th Standard Materials
• 9th Standard Materials
• 8th Standard Materials
• 7th Standard Materials
• 6th Standard Materials
• 12th Standard CBSE Materials
• 11th Standard CBSE Materials
• 10th Standard CBSE Materials
• 9th Standard CBSE Materials
• 8th Standard CBSE Materials
• 7th Standard CBSE Materials
• 6th Standard CBSE Materials
• Tamilnadu Stateboard
• Scholarship Exams
• Scholarships

CBSE 12th Standard Maths Subject Determinants Case Study Questions With Solutions 2021

By QB365 on 21 May, 2021

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

QB365 - Question Bank Software

12th Standard CBSE

Final Semester - June 2015

Case Study Questions

Let  \(\begin{equation} A=\left[\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}\right] \end{equation}\)  , and U 1 U 2 are first and second columns respectively of a 2 x 2 matrix U. Also, let the column matrices U I and U 2 satisfying  \(\begin{equation} A U_{1}=\left[\begin{array}{l} 1 \\ 0 \end{array}\right] \end{equation}\)  and  \(\begin{equation} A U_{2}=\left[\begin{array}{l} 2 \\ 3 \end{array}\right] \end{equation}\)   Based on the above information, answer the following questions (i) The matrix U 1 + U 2 is equal to

(ii) The value of IUI is

(iii) If  \(\begin{equation} X=\left[\begin{array}{ll} 3 & 2 \end{array}\right] U\left[\begin{array}{l} 3 \\ 2 \end{array}\right] \end{equation}\) ,then the value of IXI =

(iv) The minor of element at the position a 22 in U is

(v) If  \(\begin{equation} U=\left[a_{i j}\right]_{2 \times 2} \end{equation}\)  , then the value of a 11 A 11 + a 12 A l2  where A ij  denotes the cofactor of a ij  is

(ii) What is the award money for Punctuality?

(iii) What is the award money for Hard work?

(iv) If a matrix P is both symmetric and skew-symmetric, then IPI is equal to

(v) If P and Q are two matrices such that PQ = Q and QP = P, then IQ 2 1 is equal to

(ii) What is the cost of one handmade bag?

(iii) What is the cost of one newspaper envelope

(iv) Keeping in mind the social conditions, which shopkeeper is better?

(v) Keeping in mind the environmental conditions, which shopkeeper is better?

Minor of an element aij of a determinant is the determinant obtained by deleting its ith row and /h column in a ij lies and is denoted by M ij . Cofactor of an element a ij' denoted by A ij ,is defined by  \(\begin{equation} A_{i j}=(-1)^{i+j} M_{i j} \end{equation}\) , where M ij is minor of a ij. Also, the determinant of a square matrix A is the sum of the products of the elements of any row (or column with their corresponding cofactors. For example if  \(\begin{equation} A=\left[a_{i j}\right]_{3 \times 3}, \text { then }|A|=a_{11} A_{11}+a_{12} A_{12}+a_{13} A_{13} \end{equation}\)  . Based on the above information, answer the following questions (i) Find the sum of the cofactors of all the elements of  \(\begin{equation} \left|\begin{array}{cc} 1 & -2 \\ 4 & 3 \end{array}\right| \end{equation}\)  

(ii) Find the minor of a 21 of  \(\begin{equation} \left|\begin{array}{ccc} 5 & 6 & -3 \\ -4 & 3 & 2 \\ -4 & -7 & 3 \end{array}\right| \end{equation}\)  

(iii) In the determinant  \(\begin{equation} \left|\begin{array}{ccc} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{array}\right| \end{equation}\)  find the value of a 32 ·A 32

(iv) If  \(\begin{equation} \Delta=\left|\begin{array}{lll} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{array}\right| \end{equation}\) , find the value of a 32 ·A 32  .

(v) If  \(\begin{equation} \Delta=\left|\begin{array}{ccc} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{array}\right| \end{equation}\) , then find the value of \(\begin{equation} |\Delta| \end{equation}\) .

(ii) What is the cost of one pen and one bag?

(iii) What is the cost of one pen and one instrument box?

(iv) Which of the following is correct?

(v) From the matrix equation AB = AC, it can be concluded that B = C provided

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

Cbse 12th standard maths subject determinants case study questions with solutions 2021 answer keys.

(i) (c) : we have  \(\begin{equation} A=\left[\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}\right] \end{equation}\)   Let  \(\begin{equation} U_{1}=\left[\begin{array}{l} a \\ b \end{array}\right] \end{equation}\)  then  \(\begin{equation} A U_{1}=\left[\begin{array}{l} 1 \\ 0 \end{array}\right] \end{equation}\)   \(\begin{equation} \Rightarrow\left[\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}\right]\left[\begin{array}{l} a \\ b \end{array}\right]=\left[\begin{array}{l} 1 \\ 0 \end{array}\right] \Rightarrow\left[\begin{array}{c} a \\ 2 a+b \end{array}\right]=\left[\begin{array}{l} 1 \\ 0 \end{array}\right] \end{equation}\)   \(\begin{equation} \Rightarrow \end{equation}\)  a = 1 and 2a + b = 0  \(\begin{equation} \Rightarrow \end{equation}\)  a = 1 and b = -2 Let  \(\begin{equation} U_{2}=\left[\begin{array}{l} c \\ d \end{array}\right] \end{equation}\)  then  \(\begin{equation} A U_{2}=\left[\begin{array}{l} 2 \\ 3 \end{array}\right] \end{equation}\)   \(\begin{equation} \Rightarrow\left[\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}\right]\left[\begin{array}{l} c \\ d \end{array}\right]=\left[\begin{array}{l} 2 \\ 3 \end{array}\right] \Rightarrow\left[\begin{array}{c} c \\ 2 c+d \end{array}\right]=\left[\begin{array}{l} 2 \\ 3 \end{array}\right] \end{equation}\)   \(\begin{equation} \Rightarrow \end{equation}\)  c = 2 and 2c + d = 3 \(\begin{equation} \Rightarrow \end{equation}\)  c = 2 and d = 3 - 4 = -1 Thus, \(\begin{equation} U_{1}+U_{2}=\left[\begin{array}{c} 1 \\ -2 \end{array}\right]+\left[\begin{array}{c} 2 \\ -1 \end{array}\right]=\left[\begin{array}{c} 3 \\ -3 \end{array}\right] \end{equation}\)   (ii) (c) : Clearly  \(\begin{equation} U=\left[\begin{array}{cc} 1 & 2 \\ -2 & -1 \end{array}\right] \end{equation}\)   \(\begin{equation} \therefore|U|=\left|\begin{array}{cc} 1 & 2 \\ -2 & -1 \end{array}\right|=-1+4=3 \end{equation}\)   (iii) (d) :   We have  \(\begin{equation} X=\left[\begin{array}{ll} 3 & 2 \end{array}\right]\left[\begin{array}{cc} 1 & 2 \\ -2 & -1 \end{array}\right]\left[\begin{array}{l} 3 \\ 2 \end{array}\right] \end{equation}\)   \(\begin{equation} =\left[\begin{array}{ll} 3 & 2 \end{array}\right]\left[\begin{array}{c} 7 \\ -8 \end{array}\right]=[21-16]=[5] \end{equation}\)   \(\therefore\)  IX|=5. (iv) (a) :  a 22 in U is -1 and its minor is 1. (v) (d) : Since, the sum of products of elements of any row (or column) with their corresponding cofactors is equal to the value of determinant  \(\begin{equation} \therefore \quad a_{11} A_{11}+a_{12} A_{12}=|U|=3 \end{equation}\)

Three equations are formed from the given statements : 3x + 2y + z = 2200 4x + y + 3z = 3100 and x + y + z = 1200 Converting the system of equations in matrix form, we get \(\begin{equation} \left[\begin{array}{lll} 3 & 2 & 1 \\ 4 & 1 & 3 \\ 1 & 1 & 1 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{l} 2200 \\ 3100 \\ 1200 \end{array}\right] \end{equation}\)   i.e., PX= Q, where  \(\begin{equation} P=\left[\begin{array}{lll} 3 & 2 & 1 \\ 4 & 1 & 3 \\ 1 & 1 & 1 \end{array}\right], X=\left[\begin{array}{l} x \\ y \\ z \end{array}\right] \end{equation}\)  and  \(\begin{equation} Q=\left[\begin{array}{l} 2200 \\ 3100 \\ 1200 \end{array}\right] \end{equation}\)   \(\begin{equation} |P|=3(1-3)-2(4-3)+1(4-1)=-6-2+3=-5 \neq 0 \end{equation}\)   \(\begin{equation} \Rightarrow X=P^{-1} \end{equation}\)  provided p -l exists \(\begin{equation} \therefore \text { adj } P=\left[\begin{array}{ccc} -2 & -1 & 5 \\ -1 & 2 & -5 \\ 3 & -1 & -5 \end{array}\right] \end{equation}\)   \(\begin{equation} \therefore \quad P^{-1}=\frac{1}{|P|}(\operatorname{adj} P) \end{equation}\)   \(\begin{equation} =\frac{1}{-5}\left[\begin{array}{ccc} -2 & -1 & 5 \\ -1 & 2 & -5 \\ 3 & -1 & -5 \end{array}\right]=\frac{1}{5}\left[\begin{array}{ccc} 2 & 1 & -5 \\ 1 & -2 & 5 \\ -3 & 1 & 5 \end{array}\right] \end{equation}\)   \(\begin{equation} \therefore \quad X=\frac{1}{5}\left[\begin{array}{ccc} 2 & 1 & -5 \\ 1 & -2 & 5 \\ -3 & 1 & 5 \end{array}\right]\left[\begin{array}{c} 2200 \\ 3100 \\ 1200 \end{array}\right] \end{equation}\)   \(\begin{equation} =\frac{1}{5}\left[\begin{array}{c} 4400+3100-6000 \\ 2200-6200+6000 \\ -6600+3100+6000 \end{array}\right]=\left[\begin{array}{l} 300 \\ 400 \\ 500 \end{array}\right] \end{equation}\)   \(\begin{equation} \Rightarrow x=300, y=400 \text { and } z=500 \end{equation}\)   Hence the money awarded for Honesty, Hardwork and Punctuality are Rs.300, Rs. 400 and Rs.500 respectively (i) (b) (ii) (d) . (iii) (b) (iv) (c) : If a matrix P is both symmetric and skew skewsymmetric then it will be a zero matrix. So, IPI = 0. (v) (a):  We have Q 2 = QQ = Q(PQ) = (QP) Q = PQ = Q \(\begin{equation} \therefore \end{equation}\)  IQ 2 | = IQI

Let the cost of a polythene bag = Rs. x, the cost of a handmade bag = Rs. y  and the cost of a newspaper bag = Rs. z According to question, 20x + 30y + 40z = 250, 30x + 40y + 20z = 270 40x + 20y + 30z .=. 200 This system can be written as AX = B, where \(\begin{equation} A=\left[\begin{array}{ccc} 20 & 30 & 40 \\ 30 & 40 & 20 \\ 40 & 20 & 30 \end{array}\right], X=\left[\begin{array}{l} x \\ y \\ \frac{1}{4} \end{array}\right] \end{equation}\)  and  \(\begin{equation} B=\left[\begin{array}{c} 250 \\ 270 \\ 200 \end{array}\right] \end{equation}\)   \(\begin{equation} |A|=\left|\begin{array}{ccc} 20 & 30 & 40 \\ 30 & 40 & 20 \\ 40 & 20 & 30 \end{array}\right| \end{equation}\)   = 20(1200 - 400) - 30(900 - 800) + 40(600 - 1600) = 20(800) - 30(100) + 40(-1000) = 16000 - 3000 - 40000 = -27000≠ 0 So, A -1 exists and system has a solution given by X = A -1 B. Now, \(\begin{equation} \operatorname{adj} A=\left[\begin{array}{ccc} 800 & -100 & -1000 \\ -100 & -1000 & 800 \\ -1000 & 800 & -100 \end{array}\right] \end{equation}\)   \(\begin{equation} =\left[\begin{array}{ccc} 800 & -100 & -1000 \\ -100 & -1000 & 800 \\ -1000 & 800 & -100 \end{array}\right] \end{equation}\)   \(\begin{equation} \therefore A^{-1}=\frac{1}{|A|}(\operatorname{adj} A)=\frac{1}{-27000}\left[\begin{array}{ccc} 800 & -100 & -1000 \\ -100 & -1000 & 800 \\ -1000 & 800 & -100 \end{array}\right] \end{equation}\)   Now   \(\begin{equation} X=\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\frac{1}{27000}\left[\begin{array}{ccc} -800 & 100 & 1000 \\ 100 & 1000 & -800 \\ 1000 & -800 & 100 \end{array}\right]\left[\begin{array}{c} 250 \\ 270 \\ 200 \end{array}\right] \end{equation}\)     \(\begin{equation} X=\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\frac{1}{27000}\left[\begin{array}{ccc} -800 & 100 & 1000 \\ 100 & 1000 & -800 \\ 1000 & -800 & 100 \end{array}\right]\left[\begin{array}{c} 250 \\ 270 \\ 200 \end{array}\right] \end{equation}\)   Hence, cost of a polythene bag, a handmade bag and a newspaper envelope is Rs. 1, Rs. 5 and Rs. 2 respectively. (i) (a) (ii) (d) (iii) (b ) (iv) (b) : Vijay investing most of the money on hand-rnade bags. (v) (a) : Salim investing less amount of money on polythene bags.

(i) (a) : Let  \(\begin{equation} \Delta=\left|\begin{array}{cc} 1 & -2 \\ 4 & 3 \end{array}\right| \end{equation}\)   Cofactor of 1 = 3, cofactor of -2 =-4 Cofactor of 4 = 2, cofactor of 3 = 1 \(\therefore\)  Required sum = 3 - 4 + 2 + 1 = 2 (ii) (b) :  Let  \(\begin{equation} \Delta=\left|\begin{array}{ccc} 5 & 6 & -3 \\ -4 & 3 & 2 \\ -4 & -7 & 3 \end{array}\right| \end{equation}\)   Minor of  \(\begin{equation} a_{21}=\left|\begin{array}{cc} 6 & -3 \\ -7 & 3 \end{array}\right|=18-21=-3 \end{equation}\)   (iii) (c) :  Let  \(\begin{equation} \Delta=\left|\begin{array}{ccc} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{array}\right| \end{equation}\)   Clearly, a 32 = 5 and A 32  = cofactor of a 32  in  \(\begin{equation} \Delta=(-1)^{3+2}\left|\begin{array}{ll} 2 & 5 \\ 6 & 4 \end{array}\right| \end{equation}\)   = (-1)(8-30) = 22 \(\begin{equation} \therefore \end{equation}\)  a 32 ·A 32 = 5 x 22 = 110 (iv) (d) : Here, \(\begin{equation} \Delta=\left|\begin{array}{lll} 5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3 \end{array}\right| \end{equation}\)   \(\therefore\)  Minor of   \(\begin{equation} a_{23}=\left|\begin{array}{ll} 5 & 3 \\ 1 & 2 \end{array}\right|=10-3=7 \end{equation}\)   (v) (b) : Here, \(\begin{equation} \Delta=\left|\begin{array}{ccc} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{array}\right| \end{equation}\)     \(\begin{equation} A_{11}=(-1)^{1+1}\left|\begin{array}{cc} 0 & 4 \\ 5 & -7 \end{array}\right|=1(0-20)=-20 \end{equation}\)   \(\begin{equation} A_{12}=(-1)^{1+2}\left|\begin{array}{cc} 6 & 4 \\ 1 & -7 \end{array}\right|=-1(-42-4)=46 \end{equation}\)   \(\begin{equation} A_{13}=(-1)^{1+3}\left|\begin{array}{ll} 6 & 0 \\ 1 & 5 \end{array}\right|=1(30-0)=30 \end{equation}\)   \(\begin{equation} \therefore \quad \Delta=a_{11} A_{11}+a_{12} a_{12}+a_{13} A_{13} \end{equation}\)   = 2(-20) -3(46) + 5(30) = -28 \(\begin{equation} \Rightarrow|\Delta|=28 \end{equation}\)

Let the cost of 1 pen = Rs. x, the cost of 1 bag = Rs. y, and the cost of 1 instrument box = Rs. z According to the question, we have 5x + 3y + z = 16, 2x + Y + 3z = 19, x + 2y + 4z = 25 This system of equation can be written as AX = B, where  \(A=\left[\begin{array}{lll} 5 & 3 & 1 \\ 2 & 1 & 3 \\ 1 & 2 & 4 \end{array}\right], B=\left[\begin{array}{l} 16 \\ 19 \\ 25 \end{array}\right] \)  and  \(X=\left[\begin{array}{l} x \\ y \\ z \end{array}\right]\)   IAI = 5(4 - 6) - 3(8 - 3) + 1(4 - 1) \(=-10-3(5)+3=-22 \neq 0\) \(\therefore\)   A -1 exists. Now, X = A -1 B, where  \(A^{-1}=\frac{1}{|A|} \operatorname{adj} A\)   Here,  \(\operatorname{adj} A=\left[\begin{array}{ccc} -2 & -5 & 3 \\ -10 & 19 & -7 \\ 8 & -13 & -1 \end{array}\right]^{\prime}=\left[\begin{array}{ccc} -2 & -10 & 8 \\ -5 & 19 & -13 \\ 3 & -7 & -1 \end{array}\right]\)   \(\therefore \quad A^{-1}=\frac{1}{-22}\left[\begin{array}{ccc} -2 & -10 & 8 \\ -5 & 19 & -13 \\ 3 & -7 & -1 \end{array}\right]\)   \(\therefore \quad X=\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\frac{1}{-22}\left[\begin{array}{ccc} -2 & -10 & 8 \\ -5 & 19 & -13 \\ 3 & -7 & -1 \end{array}\right]\left[\begin{array}{c} 16 \\ 19 \\ 25 \end{array}\right]\)   \(=\frac{1}{-22}\left[\begin{array}{c} -32-190+200 \\ -80+361-325 \\ 48-133-25 \end{array}\right]=\frac{-1}{22}\left[\begin{array}{c} -22 \\ -44 \\ -110 \end{array}\right]=\left[\begin{array}{l} 1 \\ 2 \\ 5 \end{array}\right]\)   \(\therefore\)  x = 1, y = 2, z = 5 Hence, cost of one pen, one bag and an instrument box isRs. 1, Rs. 2 and Rs. 5 respectively. (i) (c) : Cost of one pen is Rs. 1. (ii) (a) : Cost of one pen. and one bag = Rs. (1 + 2) = Rs. 3 (iii) (b) : Cost of one pen and one instrument box = Rs. (1 + 5) = Rs. 6 (iv) (c) : According to the definition of determinant, determinartt is a number associated to a square matrix. (v) (b) : Given matrix equation is AB = AC Pre-multiplying by A -I on both sides, we get \(A^{-1} A B=A^{-1} A C \Rightarrow\left(A^{-1} A\right) B=\left(A^{-1} A\right) C\)   \(\Rightarrow \quad I B=I C \quad\left(\because A A^{-1}=A^{-1} A=I\right)\)   \(\Rightarrow B=C\)   Since A -1 exists only if A i's non-singular \(\therefore\)  For B = C, A should be non-singular

Related 12th Standard CBSE Maths Materials

12th standard cbse syllabus & materials, cbse 12th physics wave optics chapter case study question with answers, cbse 12th physics ray optics and optical instruments chapter case study question with answers, cbse 12th physics nuclei chapter case study question with answers, cbse 12th physics moving charges and magnetism chapter case study question with answers, cbse 12th physics electromagnetic induction chapter case study question with answers, cbse 12th physics atoms chapter case study question with answers, 12th physics alternating current chapter case study question with answers cbse, 12th chemistry the d and f block elements chapter case study question with answers cbse, 12th chemistry haloalkanes and haloarenes chapter case study question with answers cbse, 12th chemistry coordination compounds chapter case study question with answers cbse, 12th chemistry chemical kinetics chapter case study question with answers cbse, 12th chemistry biomolecules chapter case study question with answers cbse, 12th chemistry amines chapter case study question with answers cbse, 12th aldehydes ketones and carboxylic acids chapter case study question with answers cbse, 12th chemistry alcohols phenols and ethers chapter case study question with answers cbse.

Class VI to XII

Tn state board / cbse, 3000+ q&a's per subject, score high marks.

12th Standard CBSE Study Materials

12th Standard CBSE Subjects

Premier Test Prep for NCLEX-RN®, NCLEX-PN®, and FNP

Exam success is just a click away.

UWorld is the nursing students’ choice for licensure exam preparation for a reason – our detailed explanations include the clinical reasoning behind the correct and incorrect answers ­– so you learn as you practice. Our concise but content-rich rationales, paired with vivid illustrations and images, will develop your clinical judgment and give you the confidence to pass the exam. Whether you are preparing to take the NCLEX-RN, NCLEX-PN, or the FNP certification exam, let our challenging practice questions, in-depth explanations, and detailed performance tracking prepare you for the next step in your career.

Why Choose UWorld Nursing?

Over a million nurses have trusted us for their licensing exam preparation because we help you study smarter not harder.

Next Generation NCLEX (NGN)

Challenging questions, you’ll understand the “why”, you’ll feel more relaxed, you’ll remember more easily, practice any time, anywhere, uworld nursing student testimonials.

Looking for Institutional Pricing?

We partner with academic programs to offer bulk pricing on our suite of nursing exam prep solutions. We’ll work with you to customize a package to fit your students’ needs and your institution’s goals.

Select Your Exam

• Clinical Med Math

We use cookies to learn how you use our website and to ensure that you have the best possible experience. By continuing to use our website, you are accepting the use of cookies. Learn More