case study questions number system

Class 8 Maths Chapter 1 Case Based Questions - Number System

Correct Answer is Option (a) Number system: A numeral system (or system of numeration) is a writing system for expressing numbers that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The number the numeral represents is called its value.

Correct Answer is Option (a) a p + q a p  . a q  = a p + q

Correct Answer is Option (b) r – s is rational number.

Reason  : This statement is false. The difference between a rational number (r) and an irrational number (s) can be either rational or irrational. There is no general rule that says the difference of a rational and an irrational number must be rational. Counterexamples can easily be constructed to show that the difference could be either rational or irrational.

Correct Answer is Option (a)

Q7:  In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities. How many rational numbers are there between 5 and 7.

(a)  0 (b)  1 (c)  2 (d)  infinite

Correct Answer is Option (d) There are an infinite amount of irrational numbers between 5 and 7.

Q8: In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities. What fraction of the students participated in the campaign. (a)  2/7 (b) 5/7 (c)  4/7 (d)  7/7

Correct Answer is Option (b)

Number of students participated in campaign = 5

Number of total students = 7

Therefore, fraction of the students participated in the campaign. = 5/7

Q9: In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities. What kind of decimal expansion it has. (a) Terminating (b)  non terminating (c)  terminating repeating (d)  non terminating repeating

Correct Answer is Option (d) A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly. Decimals of this type cannot be represented as fractions, and as a result are irrational numbers. Non-terminating, non-repeating decimals can be easily created by using a pattern.

Q10: In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities. Every rational number is a _______ number. (a) Prime (b)  Composite (c)  real (d)  even

Correct Answer is Option (c) Every rational number is a real number. It can be defined as any number that can be expressed in the p/q form where q ≠ 0. We can also say that any fraction falls under the class of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero.

Top Courses for Class 8

Faqs on class 8 maths chapter 1 case based questions - number system, extra questions, shortcuts and tricks, past year papers, previous year questions with solutions, video lectures, objective type questions, sample paper, mock tests for examination, practice quizzes, study material, semester notes, viva questions, important questions.

Number System- Case Based Type Questions Free PDF Download

Importance of number system- case based type questions, number system- case based type questions notes, number system- case based type questions class 8, study number system- case based type questions on the app, welcome back, create your account for free.

Forgot Password

Unattempted tests, change country.

• 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
• DK Goel Solution
• TR Jain Solution
• Selina Solution
• Frank Solution
• ML Aggarwal 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
• 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 Crash Course
• JEE Previous Year Paper
• Important Info
• JEE Mock Test
• JEE Sample Papers
• SRM-JEEE Mock Test
• VITEEE Mock Test
• BITSAT Mock Test
• Manipal Engineering Mock Test
• AP EAMCET Previous Year Paper
• COMEDK Previous Year Paper
• GUJCET Previous Year Paper
• KCET Previous Year Paper
• KEAM Previous Year Paper
• Manipal Previous Year Paper
• MHT CET Previous Year Paper
• WBJEE Previous Year Paper
• AMU Previous Year Paper
• TS EAMCET Previous Year Paper
• SRM-JEEE Previous Year Paper
• VITEEE Previous Year Paper
• BITSAT Previous Year Paper
• UPSEE Previous Year Paper
• 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

CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF

SHARING IS CARING If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

CBSE Class 9 Maths exam 2022-23 will have a set of questions based on case studies in the form of MCQs. CBSE Class 9 Maths Question Bank on Case Studies given in this article can be very helpful in understanding the new format of questions.

Each question has five sub-questions, each followed by four options and one correct answer. Students can easily download these questions in PDF format and refer to them for exam preparation.

CBSE Class 9 All Students can also Download here Class 9 Other Study Materials in PDF Format.

• NCERT Solutions for Class 12 Maths
• NCERT Solutions for Class 10 Maths
• CBSE Syllabus 2023-24
• Social Media Channels
• Login Customize Your Notification Preferences
• CBSE Class 9th 2023-24 : Science Practical Syllabus; Download PDF 19 April, 2023, 4:52 pm
• CBSE Class 9 Maths Practice Book 2023 (Released By CBSE) 23 March, 2023, 6:16 pm
• CBSE Class 9 Science Practice Book 2023 (Released By CBSE) 23 March, 2023, 5:56 pm
• CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF 10 February, 2023, 6:20 pm
• CBSE Class 9th Maths 2023 : Important Assertion Reason Question with Solution Download Pdf 9 February, 2023, 12:16 pm
• CBSE Class 9th Exam 2023 : Social Science Most Important Short Notes; Download PDF 16 January, 2023, 4:29 pm
• CBSE Class 9th Mathematics 2023 : Most Important Short Notes with Solutions 27 December, 2022, 6:05 pm
• CBSE Class 9th English 2023 : Chapter-wise Competency-Based Test Items with Answer; Download PDF 21 December, 2022, 5:16 pm
• CBSE Class 9th Science 2023 : Chapter-wise Competency-Based Test Items with Answers; Download PDF 20 December, 2022, 5:37 pm

• 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.

myCBSEguide

• Mathematics
• CBSE Class 9 Mathematics...

CBSE Class 9 Mathematics 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.

If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!

Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak,  Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of   XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

• Now he told Raju to draw another line CD as in the figure
• The teacher told Ajay to mark  ∠ AOD  as 2z
• Suraj was told to mark  ∠ AOC as 4y
• Clive Made and angle  ∠ COE = 60°
• Peter marked  ∠ BOE and  ∠ BOD as y and x respectively

Now answer the following questions:

• 2y + z = 90°
• 2y + z = 180°
• 4y + 2z = 120°
• (a) 2y + z = 90°

Class 9 Mathematics Case study question 3

• (a) 31.6 m²
• (c) 513.3 m³
• (b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

Mycbseguide: blessing in disguise.

Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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

• 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
• Class 11 Mathematics Case Study Questions
• Class 11 Biology Case Study Questions
• Class 12 Physical Education Case Study Questions

14 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

MATHS PAAGAL HAI

All questions was easy but search ? hard questions. These questions was not comparable with cbse. It was totally wastage of time.

Where is search ? bar

maths is love

Can I have more questions without downloading the app.

I love math

Hello l am Devanshu chahal and l am an entorpinior. I am started my card bord business and remanded all the existing things this all possible by math now my business is 120 crore and my business profit is 25 crore in a month. l find the worker team because my business is going well Thanks

Leave a Comment

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

CBSE Expert

CBSE Class 9 Maths Case Study Questions PDF Download

Download Class 9 Maths Case Study Questions to prepare for the upcoming CBSE Class 9 Exams 2023-24. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 9 so that they can score 100% in Exams.

Case study questions play a pivotal role in enhancing students’ problem-solving skills. By presenting real-life scenarios, these questions encourage students to think beyond textbook formulas and apply mathematical concepts to practical situations. This approach not only strengthens their understanding of mathematical concepts but also develops their analytical thinking abilities.

Table of Contents

CBSE Class 9th MATHS: Chapterwise Case Study Questions

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked. For Class 9 Maths Case Study Questions, there would be 5 case-based sub-part questions, wherein a student has to attempt 4 sub-part questions.

Chapterwise Case Study Questions of Class 9 Maths

• Case Study Questions for Chapter 1 Number System
• Case Study Questions for Chapter 2 Polynomials
• Case Study Questions for Chapter 3 Coordinate Geometry
• Case Study Questions for Chapter 4 Linear Equations in Two Variables
• Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
• Case Study Questions for Chapter 6 Lines and Angles
• Case Study Questions for Chapter 7 Triangles
• Case Study Questions for Chapter 8 Quadrilaterals
• Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
• Case Study Questions for Chapter 10 Circles
• Case Study Questions for Chapter 11 Constructions
• Case Study Questions for Chapter 12 Heron’s Formula
• Case Study Questions for Chapter 13 Surface Area and Volumes
• Case Study Questions for Chapter 14 Statistics
• Case Study Questions for Chapter 15 Probability

Checkout: Class 9 Science Case Study Questions

And for mathematical calculations, tap Math Calculators which are freely proposed to make use of by calculator-online.net

The above  Class 9 Maths Case Study Question s will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Study Questions have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

Class 9 Maths Syllabus 2023-24

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (18 Periods)

1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.

2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.

3. Definition of nth root of a real number.

4. Rationalization (with precise meaning) of real numbers of the type

(and their combinations) where x and y are natural number and a and b are integers.

5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

UNIT II: ALGEBRA

1. POLYNOMIALS (26 Periods)

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities:

RELATED STORIES

and their use in factorization of polynomials.

2. LINEAR EQUATIONS IN TWO VARIABLES (16 Periods)

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.

UNIT III: COORDINATE GEOMETRY COORDINATE GEOMETRY (7 Periods)

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.

UNIT IV: GEOMETRY

1. INTRODUCTION TO EUCLID’S GEOMETRY (7 Periods)

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom)

1. Given two distinct points, there exists one and only one line through them. (Theorem)

2. (Prove) Two distinct lines cannot have more than one point in common.

2. LINES AND ANGLES (15 Periods)

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse.

2. (Prove) If two lines intersect, vertically opposite angles are equal.

3. (Motivate) Lines which are parallel to a given line are parallel.

3. TRIANGLES (22 Periods)

1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).

2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).

3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)

5. (Prove) The angles opposite to equal sides of a triangle are equal.

6. (Motivate) The sides opposite to equal angles of a triangle are equal.

4. QUADRILATERALS (13 Periods)

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.

2. (Motivate) In a parallelogram opposite sides are equal, and conversely.

3. (Motivate) In a parallelogram opposite angles are equal, and conversely.

4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.

5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.

6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

5. CIRCLES (17 Periods)

1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.

2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.

3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.

4. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

5. (Motivate) Angles in the same segment of a circle are equal.

6. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.

7. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

UNIT V: MENSURATION 1.

1. AREAS (5 Periods)

Area of a triangle using Heron’s formula (without proof)

2. SURFACE AREAS AND VOLUMES (17 Periods)

Surface areas and volumes of spheres (including hemispheres) and right circular cones.

UNIT VI: STATISTICS & PROBABILITY

STATISTICS (15 Periods)

 Bar graphs, histograms (with varying base lengths), and frequency polygons.

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Benefits of Practicing CBSE Class 9 Maths Case Study Questions

Regular practice of CBSE Class 9 Maths case study questions offers several benefits to students. Some of the key advantages include:

• Deeper Understanding : Case study questions foster a deeper understanding of mathematical concepts by connecting them to real-world scenarios. This improves retention and comprehension.
• Practical Application : Students learn to apply mathematical concepts to practical situations, preparing them for real-life problem-solving beyond the classroom.
• Critical Thinking : Case study questions require students to think critically, analyze data, and devise appropriate solutions. This nurtures their critical thinking abilities, which are valuable in various academic and professional domains.
• Exam Readiness : By practicing case study questions, students become familiar with the question format and gain confidence in their problem-solving abilities. This enhances their readiness for CBSE Class 9 Maths exams.
• Holistic Development: Solving case study questions cultivates not only mathematical skills but also essential life skills like analytical thinking, decision-making, and effective communication.

Tips to Solve CBSE Class 9 Maths Case Study Questions Effectively

Solving case study questions can be challenging, but with the right approach, you can excel. Here are some tips to enhance your problem-solving skills:

• Read the case study thoroughly and understand the problem statement before attempting to solve it.
• Identify the relevant data and extract the necessary information for your solution.
• Break down complex problems into smaller, manageable parts to simplify the solution process.
• Apply the appropriate mathematical concepts and formulas, ensuring a solid understanding of their principles.
• Clearly communicate your solution approach, including the steps followed, calculations made, and reasoning behind your choices.
• Practice regularly to familiarize yourself with different types of case study questions and enhance your problem-solving speed.Class 9 Maths Case Study Questions

Remember, solving case study questions is not just about finding the correct answer but also about demonstrating a logical and systematic approach. Now, let’s explore some resources that can aid your preparation for CBSE Class 9 Maths case study questions.

Q1. Are case study questions included in the Class 9 Maths Case Study Questions syllabus?

Yes, case study questions are an integral part of the CBSE Class 9 Maths syllabus. They are designed to enhance problem-solving skills and encourage the application of mathematical concepts to real-life scenarios.

Q2. How can solving case study questions benefit students ?

Solving case study questions enhances students’ problem-solving skills, analytical thinking, and decision-making abilities. It also bridges the gap between theoretical knowledge and practical application, making mathematics more relevant and engaging.

Q3. How do case study questions help in exam preparation?

Case study questions help in exam preparation by familiarizing students with the question format, improving analytical thinking skills, and developing a systematic approach to problem-solving. Regular practice of case study questions enhances exam readiness and boosts confidence in solving such questions.

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!

Talk to our experts

1800-120-456-456

• Number System Questions

Solved Examples of the Number System along with the Practice Questions

Number System is one of the most important topics of the Maths subject which the students are required to master. And the best way to master the chapter on the number system is by practicing the questions from the said chapter. But along with the practice students do need the solution of the same so that they can be sure about their progress. Hence Vedantu provides to all the students the practice questions of the number system, as well as solved examples of the same so that before attempting the practise questions students can see the examples and have a mental preparation

An Overview of the Number System

Before going directly into the practice questions of the number system, let us first have a brief understanding of the number system, and revise the concepts of it, so that you find it easy to solve the practice questions.

A method of expressing the numbers on the number line, using numerical symbols, is known as Number System. As you can see there are two terms in particular in this definition to understand in a better manner, which are:

Number Line: it is a straight line that real numbers at a fixed interval. All the types of numbers are included in the number line, that is to say, natural numbers, rational numbers, integers etc.

Numerical Symbols: it simply means the mathematical digits, that represents the numbers, which are from 0 to 9.

An Overview of Different Types of Numbers

All the types of numbers are represented in the number line and hence they are all part of the number system, therefore, let us have a quick review of all the types of numbers.

Natural Number: These are the numbers that we use in our day-to-day life because it is widely used in counting, therefore natural numbers are also called counting numbers. It includes all the positive numbers which are not a fraction, and also, it does not include 0. The range of the natural number is 1 to infinity.

Whole Numbers: Add zero to the natural number and you have the whole numbers , that is to say, it includes all the natural numbers and also the 0. Therefore, from 0 to infinity all the numbers are whole numbers.

Integers: It includes all the whole numbers, along with the negative numbers, that is to say, -1, -2, -3. But it does not include the fractions. From the negative infinity number to the positive number in infinity, are all Integers.

Fractions: The numbers which are written in the form of, where b is always a natural number.

Rational Numbers: These numbers can also be represented in fractional form, the difference between rational numbers and fractions is that rational numbers can be any integers except for the 0 as the denominator.

Irrational Numbers: These are the numbers that cannot be represented in a fractional manner such as the root of 2 (\[\sqrt{2}\]) and pie (π)

Real Numbers: When we combine the whole numbers, integers, and fractions are all real numbers. In a simple manner, all the integers along with the decimals and fractions are real numbers.

Prime Numbers: The numbers which only have two factors, which are 1 and the number itself are called prime numbers. For example, 37, can only be divided by 1 and by 37 itself.

The Number System is an important chapter of mathematics. A student needs to be strong in the fundamentals of the number system to solve other problems related to Maths. Some students face difficulty in solving sums of the number system. So, here in this article, we have provided some crucial sums relating to the number system. A student can practice these questions, and it would be easy for him/her to understand the chapter. In this article, we have provided various questions based on number systems such as number system questions and answers, number system practice questions, MCQs on number systems and many other important questions.

Number System Questions and Answers

1. Determine whether the numbers are rational or irrational.

\[ \sqrt{2}\]

\[\sqrt{100}\]

Ans: A rational number is a number that can be represented in the form of p/q, whereas an irrational number cannot be represented in the form of p/q. So,

\[ \sqrt{2}\] is Irrational.

1.5 is Rational.

\[\sqrt{100}\] is Rational.

3.14 is Irrational.

2. Without Actual Division, a state which of the following is a terminating decimal.

\[\frac{9}{25}\]

\[ \frac{37}{78}\]

Ans: In \[\frac{9}{25}\], the prime factors of denominator 25 are 5,5. Thus, it is a terminating decimal. 

In \[ \frac{37}{78}\], the prime factors of denominator 78 are 2, 3, and 13. Thus, it is a non-terminating decimal.

3. Express each of the following as a rational number in the form of p/q, where q ≠ 0.

\[\overline{0.6}\]

\[ \overline{0.43}\]

Ans:   1. Let x = 0.6666 …..(i)

Multiplying both side of eqn (i) by 10 we get,

10x = 6.6666…..(ii)

Now, subtracting eqn (i) from eqn (ii) we get, 

10x = 6.6666

⇒ x = 6/9 which is equal to ⅔, So the required fraction is ⅔.

2. Let x = 0.43434343….(i)

Multiplying both sides of eqn (i) by 100 we get,

100x = 43.43434343…..(ii)

Now, subtracting eqn (i) from eqn (ii) we get,

100x = 43.43434343

x = 0.43434343

⇒ x = \[\frac{43}{99}\], Hence the fraction is \[\frac{43}{99}\].

4. Find 4 rational numbers between 1 and 2.

Ans: To find 4 rational numbers between 1 and 2, we need to divide and multiply both the numbers by (4 + 1) which is 5. So we get,

\[1 \times \frac{5}{5} = \frac{5}{5}\] and \[ 2 \times \frac{5}{5}\] = \[\frac{10}{5}\], Therefore the rational numbers are:

\[\frac{5}{5}\], \[\frac{6}{5}\], \[\frac{7}{5}\], \[\frac{8}{5}\], \[\frac{9}{5}\], \[\frac{10}{5}\].

5. Compare the following numbers.

(i) 0 and \[-\frac{9}{5}\].

(ii) \[-\frac{17}{20}\] and \[-\frac{13}{20}\].

(iii) \[\frac{40}{29}\] and \[\frac{141}{29}\].

Ans: (i) We know that a negative number is always less than 0. Therefore,

0 > - \[\frac{9}{5}\].

(ii) Here the denominator is the same and we know that -17 < -13. Therefore, 

\[\frac{-17}{20}\] < \[\frac{-13}{20}\].

(iii) Here the denominator is the same and we know that 40 < 141. Therefore,

\[\frac{40}{29}\] < \[\frac{141}{29}\].

6. Write the following in decimal numbers and state what expansion it is.

(i) \[\frac{40}{100}\]  (ii) \[\frac{9}{10}\]  (iii) \[\frac{9}{37}\] (iv) \[\frac{103}{5}\]

Ans: (i) \[\frac{40}{100}\] is 0.40, and it is terminating.

(ii) \[\frac{9}{10}\] is 0.9, and it is ending.

(iii) \[\frac{9}{37}\] is 0.243243… it is non-terminating.

(iv) \[\frac{103}{5}\] is 20.6, and it is terminating.

7. Insert one rational number between 3/5 and 7/9.

Ans:   If a and b are two rational numbers, then one rational number between these two will be \[\frac{a + b}{2}\]. Hence the required rational number will be 

\[\frac{1}{2} (\frac{3}{5} + \frac{7}{9}) = \frac{1}{2} (\frac{27 + 35}{45}) = \frac{1}{2} \times \frac{62}{45} = \frac{31}{45}\]

So, the rational number is \[\frac{31}{45}\].

Questions on Number System Conversion

Here, we have provided some number system math questions which are based on number system conversion. 

1. Convert each of the following into a decimal number.

(i) \[\frac{4}{15}\]

(ii) \[2\frac{5}{12}\]

(iii) \[\frac{9}{27}\]

(iv) \[5\frac{31}{55}\]

2. Convert the following into a rational number.

(i) \[0.\overline{227}\]

(ii) \[0.\overline{2104}\]

Number System Practice Questions

As we know, practice makes everyone perfect, so for the better understanding of students, we have provided some number system important questions for practice.

1. Show the number √5 on the number line.

\[\sqrt{2}\]

\[ \sqrt{100}\]

Ans: A rational number is a number which can be represented in the form of p/q, whereas an irrational number cannot be represented in the form of p/q. So,

\[\sqrt{2}\] is Irrational.

2. Insert three rational numbers between 4 and 5.

\[ \frac{37}{78} \]

Ans: In \[ \frac{9}{25}\], the prime factors of denominator 25 are 5,5. Thus, it is a terminating decimal. 

In \[\frac{37}{78} \], the prime factors of denominator 78 are 2, 3, and 13. Thus, it is a non-terminating decimal.

3. Represent the following rational numbers in decimal form

(i) \[\frac{18}{42}\]    (ii) \[-\frac{11}{13}\]

4. Rationalise the denominator of

\[ \frac{1}{3-\sqrt{5}} \]

5. Simplify the following expression (24 - 32)a. ( 5 + 23)

FAQs on Number System Questions

1. Give Some MCQs on the Number System.

Some important MCQs on Number System are:

1. From the following choose Co-prime numbers.

(a) 2, 3 (b) 2, 4 (c) 2, 6 (d) 2, 110

2. On adding \[2\sqrt{3}\] and \[3\sqrt{2}\] we get:

(a) \[5\sqrt{5}\] (b) \[5(\sqrt{3} + \sqrt{2})\] (c) \[ 2\sqrt{3} + 3\sqrt{2}\] (d) None of these

3. A rational number between \[\sqrt{2}\] and \[\sqrt{3}\].

(a) 1.9 (b) \[ \frac{( \sqrt{2}.\sqrt{3} )}{2}\] (c)1.5 (b) 1.8

4. Which of the following is irrational?

(a) \[ \frac{\sqrt{4}}{9} \] (b)\[ \frac{\sqrt{12}}{\sqrt{3}}\] (c) \[\sqrt{5}\] (d) \[\sqrt{81}\] 

5. The Value of (16) 3/4 is equal to:

(a) 2 (b) 4 (c) 8 (d) 16

2. What do you mean by Number System? What are its types?

The number system can be defined as the expression of numbers in a written format. These are a set of symbols and rules used to denote numbers. The number system is used to state how many objects are there in a given set. There are different types of number systems, and here we have mentioned some of the types of number systems for better knowledge of students. The following are the types of number systems:

Real Numbers.

Natural Numbers.

Whole Numbers.

Rational Number system.

Irrational Number system.

Complex Number system.

Binary Number system.

Decimal Number System.

Hexa-Decimal Number System.

Octal-Decimal Number System.

• New QB365-SLMS
• NEET Materials
• JEE Materials
• Banking first yr Materials
• TNPSC Materials
• DIPLOMA COURSE Materials
• 5th Standard 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

Class 11th Applied Mathematics - Numbers, Quantification and Numerical Applications Case Study Questions and Answers 2022 - 2023

By QB365 on 09 Sep, 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 11 Applied Mathematics Subject - Numbers, Quantification and Numerical Applications, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

QB365 - Question Bank Software

Numbers, quantification and numerical applications case study questions with answer key.

11th Standard CBSE

Final Semester - June 2015

Applied Mathematics

On the basis of the above information answer the following questions: (i) The value of base in binary system is

(ii) Which of the following is not a binary number?

(iii) Which of the following is the correct representation of binary number?

(iv) If the decimal number is a fraction then its binary equivalent is obtained by ____________ the number continuously by 2.

(v) The binary equivalent of the decimal number 10 is

(ii) The value of log 5 + log 2 is equal to

(iii)The value of log  \(\frac{10}{2}+\log \frac{22}{11} \text { is }\)  

(iv) log  \(\frac{32}{4}\)   is equal to

(v)  \(\log \frac{25}{27}+\log \frac{81}{125}+\log \frac{25}{3} \text { is }\) equal to 

(ii) What is difference of two binary numbers 1011 –101 ?

(iii) What is the value of 11011 + 10101?

(iv) What is the value of 1101101–11011 ?

(v)  Find decimal equivalent of Binary Number(1011.011) 2 ?

(ii) The value of log 23 16 9  is equal 

(iii)  \(\frac{\log 27 \times \log 16 \times \log 125}{4}=\alpha \text {, then the value of } \alpha \text { is }\)  

(iv) If log a bc = x, log b ca = y, log c ab = z,  \(\text { then } \frac{1}{x+1}+\frac{1}{y+1}=\frac{1}{z+1}=\)  

(v)  If 2 log a = 4 log 3, then find the value of

I In cricket matches, scores of all the players are recorded to find the average of their batting and bowling. Data of few batsmen are recorded as mentioned below:

On the basis of this information teacher ask students various questions as mentioned below: (i) What is the average score of Sachin Tendulkar?

(ii) What is the average score of Rahul Dravid ?

(iii) What is the average score of Virendra Sehwag ?

(iv) What is the approximate average of sum of average scores of Sachin Tendulkar and Rahul Dravid?

(v) If the second and third score of Virendra Sehwag is replaced from 56 to 95 and 63 to 89 what will be the new average score ?

(ii) 'A' can do a piece of work in 5 days and 'B' can do it in 6 days. How long will they take if both work together ?

(iii)  A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone ?

(iv) 'A' does a work in 10 days and ’B’ does the same work in 15 days. In how many days they together will do the same work ?

(v) ’A’ can finish a work in 18 days and ’B’ can do the same work in half the time taken by ’A’ then, working together, what part of the same work they can finish in a day.

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

Numbers, quantification and numerical applications case study questions with answer key answer keys.

(i) (a):  False According to Law 1 log a ( mn ) = log a m + log an. So, log( a + b) ≠ log a + log (ii) (a): 1 log 5 + log 2 = log 10 = 1 (iii) (b): 1 \(\log \frac{10}{2}+\log \frac{22}{11}=\log 5+\log 2\)   = log 10 = 1 (iv) (a):  log 32 – log 4 Using property log  \(\frac{a}{b}=\log a-\log b\)   (v) (d):  log 5   \(\log \frac{25}{27}+\log \frac{81}{125}+\log \frac{25}{3}=\log \left(\frac{25}{27} \times \frac{81}{125} \times \frac{25}{3}\right)\)   = log 5

(i) (d): 3 log 2 8 = 3 log 2 2 = 3 (ii) (d): 12 \(\log _{2} 316^{9}=\frac{9}{2} \log _{2} 16\)   = 3 log 2 2 4 = 12 log 2 2 = 12 (iii) (b): 36   \(\frac{\log 27 \times \log 16 \times \log 125}{\log 3 \times \log 2 \times \log 5}=\frac{3 \log 3 \times 4 \log 2 \times 3 \log 5}{\log 3 \times \log 2 \times \log 5}\)   = 36 (iv) (d): 1 x + 1 = log a bc + log a a = log a abc y+ 1 = log b ca+ log b b= log b abc z+ 1 = log c ab+ log c c= log c abc Therefore,  \(\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}=\frac{1}{\log _{a} a b c}+\frac{1}{\log _{b} a b c}+\frac{1}{\log _{c} a b c}\)   \(\begin{aligned} &=\log _{a b c} a+\log _{a b c} b+\log _{a b c} c \end{aligned}\)   \(\begin{aligned} &=\log _{\pi / v} a b c=1\end{aligned}\)   (v) (b): 9 2 loga= 4 log 3 ⇒ loga 2 = log3 4 ⇒ 2 = (3 2 )2 ⇒ a = 3 2 = 9

(i) (b): 79.2 Sum of all scores = 396 Average =  \(\frac{396}{5}\)   = 79.2 (ii) (b): 80.6 Sum of all scores = 403 Average =  \(\frac{403}{3}\)   = 80.6  (iii) (d): 69.8 Sum of scores = 349 Average Score  \(\frac{349}{5}\)   = 69.8 (iv) (c): 80 Sum = 80.6 + 79.2 = 159.8 Average =  \(\frac{159.8}{2}\)   = 79.9 = 80 (approx.) (v) (b): 82.8 New scores = 97 , 95 , 89, 44, 89 Total of scores = 414 Average Score =  \(\frac{414}{5}\)   = 82.8

(i) (c): 15  Here, M 1 = 15, D 1 = 16, T 1  = 9 hours, M 2  = 18 and T 2 = 8 hours Using formula, M 1 × D1 × T 1 = M 2 × D 2 × T D2 =  \(\frac{M_{1} \times D_{1} \times T_{1}}{M_{2} \times T_{2}}\)   \(\Rightarrow \quad D_{2}=\frac{15 \times 16 \times 9}{18 \times 8}=15 \text { days }\)   Hence, required number of days are 15. (ii) (c):   \(2 \frac{8}{11}\)   Suppose, A can do a piece of work in D 1 days and B can do the same work in D 2 days. Here, given D 1 = 5 days and D 2 = 6 days Thus, A and B can do this work in  \(\frac{D_{1} \times D_{2}}{D_{1}+D_{2}} \text { days }\)   i.e.,  \(\frac{5 \times 6}{5+6}=\frac{30}{11}=2 \frac{8}{11} \text { days. }\)   (iii) (c):   \(7 \frac{1}{2}\)   Son's 1 day's work =  \(\left(\frac{1}{3}-\frac{1}{5}\right)=\frac{2}{15}\)   ༜ The son alone can do the work in  \(\frac{15}{2}=7 \frac{1}{2} \text { days }\) (iv) (d): 6 A's 1 day's work =  \(\frac{1}{10}\)   B's 1 day's work =  \(\frac{1}{15}\)   ༜  ( A + B )'s 1 day's work =  \(\frac{1}{10}+\frac{1}{15}=\frac{1}{6}\)  

So, A and B together can be the work in 6 days (v)   (b):   \(\frac{1}{6}\)     \(\frac{1}{6} \text { th part, because }\)   \(A \text { 's } 1 \text { day's work }=\frac{1}{18}\)   \(B^{\prime} \text { s } 1 \text { day's work }=\frac{1}{9}\)   \(\therefore \ (A+B)^{\prime} \mathrm{s} 1 \text { work }=\left(\frac{1}{18}+\frac{1}{9}\right)=\frac{1}{6}\)   Hence, A and B together finish 16 th part of the work in a day.

Related 11th Standard CBSE Applied Mathematics Materials

11th standard cbse syllabus & materials, cbse 11th physics motion in a straight line chapter case study questions with answers, cbse 11th physics units and measurements chapter case study questions with answers, cbse 11th chemistry structure of atom chapter case study question with answers, cbse 11th chemistry some basic concept of chemistry chapter case study questions with answers, 11th biology biological classification chapter case study question with answers cbse, 11th biology the living world chapter case study question with answers cbse, class 11th business studies - internal trade case study questions and answers 2022 - 2023, class 11th business studies - social responsibilities of business and business ethics case study questions and answers 2022 - 2023, class 11th business studies - emerging modes of business case study questions and answers 2022 - 2023, class 11th business studies - business service case study questions and answers 2022 - 2023, class 11th business studies - private, public and global enterprises case study questions and answers 2022 - 2023, class 11th business studies - business, trade and commerce case study questions and answers 2022 - 2023, class 11th biology - chemical coordination and integration case study questions and answers 2022 - 2023, class 11th biology - neural control and coordination case study questions and answers 2022 - 2023, class 11th biology - locomotion and movement case study questions and answers 2022 - 2023.

Class VI to XII

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

11th Standard CBSE Study Materials

11th Standard CBSE Subjects

• Math Article

Number System Questions

Number systems questions are provided here with solutions. In Class 9, we will come across the Number System chapter where we learn the basics of different types of numbers and their applications. In number theory , you may have learned about the different classifications of numbers, such as whole and natural numbers, even and odd numbers, etc. Here, we will solve the problems based on rational and irrational numbers. Students can practice the questions and it would be helpful for the students to understand this chapter. Here, we have provided a variety of number system questions and some important questions for practice. Let us learn in brief about each concept covered in this chapter before we solve a question based on it.

Also, read: Number System For Class 9

Number System Questions with Solutions

1. What are the five rational numbers between 1 and 2?

Solution: We need to find 5 rational numbers between 1 and 2

Divide and multiply both the numbers by (5+1)

6/6 and 12/6 are rational numbers now.

Therefore, the required rational numbers between 1 and 2 are:

6/6, 7/6, 8/6, 9/6, 10/6, 11/6, 12/6.

2. Can we locate √3 on the number line?

Solution: Yes, we can locate it.

Follow the steps to locate it: Construct BD of unit length perpendicular to OB

Then using the Pythagoras theorem, we see that OD = √((√2) 2 +1 2 ) = √3

With centre O and radius OD, using a compass, draw an arc that cuts the number line at the point Q.

4. Show that 0.3333…, can be expressed in the form of rational number, i.e. p/q.

Solution: Let x = 0.33333

10 x = 10 × (0.333…) = 3.333…

We can write,

3.3333… = 3 + 0.3333… = 3 + x

10 x = 3 + x

5. Write the following in decimal form and mention what expansion it is.

(i) 36/100 = 0.36

It is terminating.

(ii) 1/11 = 0.09090909…

It is non-terminating and repeating

6. Add 2√2 + 5√3 and √2 – 3√3.

Solution: (2√2 + 5√3) + (√2 – 3√3)

= (2+1)√2+(5-3)√3

7. Multiply 6√2 by 2√2.

Solution: 6√2 x 2√2

6 x 2 x √2 x √2

8. Rationalise the denominator of 1/√3

Solution: To rationalise the denominator of 1/√3, we need to multiply the numerator and denominator by √3

1/√3 x (√3/√3) = √3/3

9. Rationalise the denominator of √2/(√3-√5).

Solution: Multiply both numerator and denominator by √3+√5

Numerator = √2(√3+√5)

Denominator = (√3-√5)(√3+√5) = (√3) 2 -(√5) 2 = 3-5 = -2

= [-√2(√3+√5)]/2

10. Simplify:

(i) 2 1/3 .2 2/3

(ii) (3 1/5 ) 4

(iii) 7 1/3 /7 1/5

(iv) 13 1/7 .17 1/7

(iii) (7 1/3 )/(7 1/5 )

= 7 ( 1/3)-(1/5)

= (13.17) 1/7

Video Lesson

Number system and factorisation.

Number System Questions for Practice

• If (p ×q) = 6p-4q+3pq, then find the value of [(6×3)+(4×3)]
• Find out which of the following numbers are prime numbers, given that “p” is a prime number.

(a) 2p  (b)p 2 (c)3p (d) p-2 (e) p-3

• Write down the five rational numbers between 6/5 and 7/5
• Express the decimal number 1.2343 in the form of a rational number (i.e p/q form)
• Simplify the expression (2 2 -3)x. (4+2 2 )

Frequently Asked Question on the Number System Questions

What is meant by number system.

In mathematics, a number system is defined as the way of expressing numbers. The number system provides a distinct way of expressing different types of numbers and it also provides the algebraic structure of the mathematical problem.

What are the different types of numbers?

The different types of numbers are: Natural Numbers Whole numbers Real Numbers Rational Numbers Irrational numbers Complex numbers

Why do we use numbers?

The numbers are used to count the surrounding thing. Numbers are used for expressing money, time, date, and so on. Without numbers, we could not be able to understand the value of many things

What are the four different types of number systems?

The four major types of number system are: Binary number system (base 2 number system) Octal number system (base 8 number system) Decimal number system (base 10 number system) Hexadecimal number system (base 16 number system)

What are the applications of the number system?

The most common application of the number system is found in computer technology. It uses the binary number system. The base 2 number system is used in the process of digital encoding

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Very nice questions with explaintion

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

• All Platforms
• First Naukri
• All Companies
• Cognizant GenC
• Cognizant GenC Next
• Cognizant GenC Elevate
• Goldman Sachs
• Infosys SP and DSE
• TCS CodeVita
• TCS Digital
• TCS iON CCQT
• TCS Smart Hiring
• Tech Mahindra
• Zs Associates

• Top 100 Codes
• Learn Python
• Learn Data Structures
• Learn Competitve & Advanced Coding
• Learn Operating System
• Software Engineering
• Online Compiler
• Microsoft Coding Questions
• Amazon Coding Questions

• Learn Logical
• Learn Verbal
• Learn Data Interp.
• Psychometric Test

• All Syllabus
• Cognizant-Off Campus
• L&T Infotech
• Mahindra ComViva
• Reliance Jio
• Wells Fargo
• ZS-Associates

• Interview Preparation
• HR Interview
• Virtual Interview
• Technical Interview
• Group Discussions

• All Interview Exp.
• Accenture ASE
• ZS Associates

• Get OffCampus updates
• On Instagram
• On LinkedIn
• On Telegram
• On Whatsapp
• AMCAT vs CoCubes vs eLitmus vs TCS iON CCQT
• Companies hiring via TCS iON CCQT
• Companies hiring via CoCubes
• Companies hiring via AMCAT
• Companies hiring via eLitmus
• Companies hiring from AMCAT, CoCubes, eLitmus
• Prime Video
• PrepInsta Prime
• The Job Company
• Placement Stats

Notifications Mark All Read

TCS NQT OffCampus Hiring Announced for 2024 Batch

• Get Prime
• Shortcuts, Tips & Tricks
• Shortcut, tips, and tricks
• Successive Discount 1
• Successive Discount 2
• Finding remainder of large powers

Number System Questions and Answers

March 6, 2024

Number System Questions and Answers for Competitive placement exams

On this page we are going to discuss Number System Questions with Solutions, with basic definition and practice examples.

Number system Questions with solution

Important definitions for solving number system questions:.

• Natural Numbers:  All positive integers are called natural numbers. All counting numbers from 1 to infinity are natural numbers. N = {1, 2, 3, 4, 5, 6……..∞}
• Whole Numbers:  The set of numbers that includes all natural numbers and the number zero are called whole numbers. They are also called as Non-negative integers. W = { 0,1,2,3,4,5,6,7,8,………∞}
• Integers:  All numbers that do not have the decimal places in them are called integers. Z = {∞…….-3, -2, -1, 0, 1, 2, 3………∞}
• Real Numbers:  All numbers that can be represented on the number line are called real numbers.
• Rational Numbers:  A rational number is defined as a number of the form a/b where ‘a’ and ‘b’ are integers and b ≠ 0. The rational numbers that are not integers will have decimal values. These values can be of two types
• Irrational Numbers:   It is a number that cannot be written as a ratio.An Irrational numbers are non-terminating and non-periodic fractions.

Formulas to solve Questions

Prime course trailer, related banners.

Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription

Also Check Out

Number System questions with solution

1. Find the L.C.M of 15, 30, 45

None of the above

2 | 15, 30, 45 3 | 15, 15, 45 3 | 5, 5, 15 5 | 5, 5, 5 | 1, 1, 1

L.C.M = 2*3*3*5 = 90

2. The given ratio of two numbers is 3:2. If the L.C.M of them is 30, then calculate their sum.

Ratio of the two numbers = 3: 2

LCM of two numbers = 30

To find: Sum of the two numbers

The formula used: Product of two numbers = LCM × HCF

Let the numbers be 3x and 2x

Product of two numbers = LCM × HCF

The HCF of two numbers will be x as the numbers are in ratio due to which it c an be conclude that their will be a HCF factor of x also.

The two numbers are 3x,2x

(3x )(2x) = 30 (x)

The first number is 3x

The first number is 15

The second number is 2x

The second number is 10

Therefore the two numbers are 15,10

The sum of two numbers = 15 + 10 = 25

The ratio of two numbers is 3 ratio 2 and the lcm of them is 30 then  the sum​ of the numbers is 25

3. Find the L.C.M of 25, 35, and 55

5 | 25, 35, 55 5 | 5, 7, 11 7 | 1, 7, 11 11 | 1, 1, 11 | 1, 1, 1

L.C.M = 5*5*7*11 = 1925

4. Calculate the HCF of 22 and 33

So the HCF will be 11

5. If 20 is the HCF of two particular numbers and the other two factors of their LCM are 10 and 12, find the larger number?

20* 10 = 200

20*12 = 240

So the larger number will be 240

HCF of two numbers is the number that is a common factor for both numbers given

Here 20 is the common factor.

Other than this common factor, we also will have the product of uncommon factors for the two numbers (10 and 12 here).

The first number = 20*10 = 200

and second number = 20 × 12 = 240

The greatest of two numbers is definitely 20 × 12 = 240

6. The HCF  of three specific numbers 6, 12, and 18 is 24 , find the LCM?

(6*12*18)/24

The next number will be = 54

7. The two specific numbers are in the ratio 6:7, if the HCF of the given numbers is 30, what will be the numbers?

Let the numbers be 6y and 7y

The numbers will be 6*30 = 180

And 7*30 = 210

8. Determine the largest length of the tape, which can measure tape of 5 cm, 7cm, and 13 cm?

As all these numbers have no factors and are considered as prime numbers so their HCF will be 1.

9. The HCF of two numbers is 45, and their LCM is 90, if one specific number is 9, find the other number.

HCF * LCM = Products of Numbers

45 * 90 = 9 * x

Another number will be = (45*90)/9 = 450

10. Street lamps start at the interval of 5, 10, 15, 20, and 25 seconds, calculate the number in which the street lamps began together in 40 minutes.

we need to calculate the number of occurrences when the time intervals (5 seconds, 10 seconds, 15 seconds, 20 seconds, and 25 seconds) align perfectly with each other within the 40-minute interval.

First, let's convert 40 minutes to seconds:

40 minutes * 60 seconds/minute = 2400 seconds

Now, let's find the least common multiple (LCM) of the given time intervals (5, 10, 15, 20, 25 seconds) to determine when the street lamps will start together. The LCM of these intervals is 150 seconds.

Next, we'll divide the total interval time (2400 seconds) by the LCM (150 seconds):

2400 seconds / 150 seconds = 16

So, the street lamps will start together 16 times within a 40-minute interval.

Therefore, the number of times the street lamps began together in 40 minutes is 16.

Please login to report

Get over 200+ course One Subscription

Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others

Checkout list of all the video courses in PrepInsta Prime Subscription

• HCF and LCM –  Questions     Formulas  |  How to Solve Quickly  |  Tricks & Shortcuts
• Number System –  Questions    |   Formulas  |  How to Solve Quickly  |  Tricks & Shortcuts
• Number Decimals & Fractions –   Questions    |  Formulas  |  How to Solve Quickly  |  Tricks & Shortcuts
• Surds and Indices –  Questions    |  Formulas  |  How to Solve Quickly  |  Tricks & Shortcuts
• Divisibility –  Questions    |  Formulas  |  How to Solve Quickly  |  Tricks & Shortcuts
• Ages –  Questions    |  Formulas  |  How to Solve Quickly  |  Tricks & Shortcuts
• LCM –   Questions    |  Formulas  |  How to Solve Quickly  |  Tricks & Shortcuts
• HCF –  Questions    |  Formulas  |  How to Solve Quickly  |  Tricks & Shortcuts
• Inverse –  Questions    |  Formulas  |  How to Solve Quickly  |  Tricks & Shortcuts
• HCF and LCM – Questions   Formulas | How to Solve Quickly | Tricks & Shortcuts
• Number Decimals & Fractions – Questions   | Formulas | How to Solve Quickly | Tricks & Shortcuts
• Surds and Indices- Questions   | Formulas | How to Solve Quickly | Tricks & Shortcuts
• Divisibility – Questions   | Formulas | How to Solve Quickly | Tricks & Shortcuts
• Ages – Questions   | Formulas | How to Solve Quickly | Tricks & Shortcuts
• LCM –  Questions   | Formulas | How to Solve Quickly | Tricks & Shortcuts
• HCF –   Questions   | Formulas | How to Solve Quickly | Tricks & Shortcuts
• Inverse – Questions   | Formulas | How to Solve Quickly | Tricks & Shortcuts

Login/Signup to comment

Class 9 Maths Case Study Questions of Chapter 1 Real Numbers

• Post author: studyrate
• Post published:
• Post category: class 9th
• Post comments: 0 Comments

Case study Questions in Class 9 Mathematics Chapter 1  are very important to solve for your exam. Class 9 Maths Chapter 1 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 9 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 9 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 9 Maths Chapter 1 Real Numbers

Case Study/Passage-Based Questions

Case Study 1: A Mathematics Exhibition is being conducted in your school and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.

Observe the following factor tree and answer the following:

1. What will be the value of x?

Answer: b) 13915

2. What will be the value of y?

Answer: c) 11

3. What will be the value of z?

Answer: b) 23

4. According to the Fundamental Theorem of Arithmetic 13915 is a

a) Composite number

b) Prime number

c) Neither prime nor composite

d) Even number

Answer: a) Composite number

5. The prime factorization of 13915 is

a) 5 × 11 3  × 13 2

b) 5 × 11 3  × 23 2

c) 5 × 11 2  × 23

d) 5 × 11 2  × 13 2

Answer: c) 5 × 112 × 23

Case Study 2: 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. Answer them.

(i) For what value of n, 4 n  ends in 0?

(a) 10 (b) when n is even (c) when n is odd (d) no value of n

Answer: (d) no value of n3

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

(a) when n is any even integer (b) when n is any odd integer (c) for all n > 1 (d) only when n=0

Answer: (c) for all n > 1

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

(a) x 2 +y 2  is even (b) x 2 +y 2  is not divisible by 4 (c) x 2 +y 2   is odd (d) both (a) and (b)

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

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

(a) always true (b) always false (c) sometimes true (d) None of these

Answer:(a) always true

(v) If n is any odd integer, then n 2 – 1 is divisible by

(a) 22 (b) 55 (c) 88 (d) 8

Answer: (d) 8

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 1 Real Numbers with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 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 9 science case study questions chapter 14 natural resources, mcq questions of class 9 social science history chapter 5 pastoralists in the modern world with answers, mcq class 9 social science economics people as resource quiz with answers, leave a reply cancel reply.

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

Please wait...

50 Important Number System Questions PDF – Download Here

The number system is an essential part of competitive exams like Banking, SSC, Railways & Insurance exams. Wondering what type of Number System questions are asked in different government exams? To help you with your preparation we have brought you the Important Number System Questions in this blog for the practice. We have covered every type of Number System question that can be asked in upcoming government exams.

Attempt Free CTET Mock Test 2024

Let us start with the blog and start solving “Important Number System Questions”. You can download the PDF for free and can attempt the questions according to your ease.

SSC CGL Syllabus 2024

1. Important Number System Questions PDF – Download Here

You can download Important Number System Questions and Answers PDF for free by clicking on the link given below:

To Download More Free Ebooks Click Here & Register Yourself

1.1 How to download 50 Important Number System Questions?

Step 1:  Click on the above-given  download link . You will be taken to Oliveboard’s FREE Ebooks Page.

Step 2: Register/Login to the Free E-Books Page of Oliveboard (It is 100% free, You just enter your valid email id and a password to be able to download the 50 Important Number System Questions).

Step 3:  After Logging in, you will see the list of Free Ebooks.

Step 4:  Click on the Solved Papers section under All ebooks sections.

Step 5: You will be able to download the 50 Important Number System Questions PDF.

Let’s have a look at the sample for the Important Number System Questions

Q1) The digits of a two-digit number are in the ratio of 2 : 3 and the number obtained by interchanging the digits is bigger than the original number by 27. What is the original number? 63 2. 48 3. 96 4. 69

Correct Answer: “4 ”

Q2) Three consecutive numbers such that twice the first, 3 times the second, and 4 times the third together make 182. The numbers in question are 18, 22 and 23 2. 18, 19 and 20 3. 19, 20 and 21 4. 20, 21 and 22

Correct Answer: “3″

Q3) A two-digit number is such that the sum of the digits is 11. When the number with the same digits is reversed is subtracted from this number, the difference is 9.What is the number? 1. 23 2. 24 3. 65 4. 14

Correct Answer: “3”

Q4) One-fifth of a number is equal to 5/8th of another number. If 35 is added to the first number, it becomes four times the second number. Find the second number. 39 2. 70 3. 40 4. 25

Q5) What least number would be subtracted from 427398 so that the remaining number is divisible by 15? 3 2. 10 3. 16 4. 11

Correct Answer: “1”

Q6) A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:

1. 3 2. 5 3. 9 4. 11

Correct Answer: “D”

• SSC CPO Final Result 2024 Out, Direct Link to Download
• Sarkari Result 2024, सरकारी नौकरी बम्पर भर्ती – 6th April
• 6 April 2024 Current Affairs in English
• SSC CHSL Salary 2024, Check Job Profile and Benefits
• SSC CHSL Quantitative Aptitude Syllabus 2024, Check the Details

Frequently Asked Questions

Ans. Candidates can download the Important Number Systems from the link mentioned in this blog.

Ans. Yes, the Important Number Systems PDF will have solutions.

Hey everyone, I’m Vaishnavi Kumari, an edtech writer and a dedicated aspirant for government exams, including banking and SSC exams. Having worked with several edtech platforms, I am committed to providing you with essential and accurate information to ace these exams. With my experience as both a writer and an aspirant, I understand your needs and challenges, and my aim is to make your preparation journey smoother. I’ll focus on specific sections of the exams, compiling comprehensive and helpful content that covers the crucial topics, tips, and strategies you need to succeed. Let’s conquer these exams together!

  Oliveboard Live Courses & Mock Test Series

• Download 500+ Free Ebooks for Govt. Exams Preparations
• Attempt Free SSC CGL Mock Test 2024
• Attempt Free IBPS Mock Test 2024
• Attempt Free SSC CHSL Mock Test 2024
• Download Oliveboard App
• Follow Us on Google News for Latest Update
• Join Telegram Group for Latest Govt Jobs Update

Leave a comment Cancel reply

Download 500+ Free Ebooks (Limited Offer)👉👉

Thank You 🙌

• Skip to main content
• Keyboard shortcuts for audio player

Millions of customers' data found on dark web in latest AT&T data breach

Chloe Veltman

An AT&T store in New York. The telecommunications company said Saturday that a data breach has compromised the information tied to 7.6 million current customers. Richard Drew/AP hide caption

An AT&T store in New York. The telecommunications company said Saturday that a data breach has compromised the information tied to 7.6 million current customers.

AT&T announced on Saturday it is investigating a data breach involving the personal information of more than 70 million current and former customers leaked on the dark web.

According to information about the breach on the company's website, 7.6 million current account holders and 65.4 million former account holders have been impacted. An AT&T press release said the breach occurred about two weeks ago, and that the incident has not yet had a "material impact" on its operations.

AT&T said the information included in the compromised data set varies from person to person. It could include social security numbers, full names, email and mailing addresses, phone numbers, and dates of birth, as well as AT&T account numbers and passcodes.

The company has so far not identified the source of the leak, at least publicly.

"Based on our preliminary analysis, the data set appears to be from 2019 or earlier," the company said. "Currently, AT&T does not have evidence of unauthorized access to its systems resulting in theft of the data set."

AT&T says cell service is back after a widespread outage and some disrupted 911 calls

The company said it is "reaching out to all 7.6 million impacted customers and have reset their passcodes," via email or letter, and that it plans to communicate with both current and former account holders with compromised sensitive personal information. It said it plans to offer "complimentary identity theft and credit monitoring services" to those affected by the breach.

External cybersecurity experts have been brought in to help investigate, it added.

NPR reached out to a few AT&T stores. The sales representatives in all cases said they were as yet unaware of the breach.

On its website, the telecommunications company encouraged customers to closely monitor their account activity and credit reports.

"Consumers impacted should prioritize changing passwords, monitor other accounts and consider freezing their credit with the three credit bureaus since social security numbers were exposed," Carmen Balber, executive director of the consumer advocacy group Consumer Watchdog, told NPR.

An industry rife with data leaks

AT&T has experienced multiple data breaches over the years.

In March 2023, for instance, the company notified 9 million wireless customers that their customer information had been accessed in a breach of a third-party marketing vendor.

In August 2021 — in an incident AT&T said is not connected to the latest breach — a hacking group claimed it was selling data relating to more than 70 million AT&T customers. At the time, AT&T disputed the source of the data. It was re-leaked online earlier this month. According to a Mar. 22 TechCrunch article , a new analysis of the leaked dataset points to the AT&T customer data being authentic. "Some AT&T customers have confirmed their leaked customer data is accurate," TechCrunch reported. "But AT&T still hasn't said how its customers' data spilled online."

AT&T is by no means the only U.S. telecommunications provider with a history of compromised customer data. The issue is rife across the industry. A 2023 data breach affected 37 million T-Mobile customers. Just last month, a data leak at Verizon impacted more than 63,000 people, the majority of them Verizon employees.

A 2023 report from cyber intelligence firm Cyble said that U.S. telecommunications companies are a lucrative target for hackers. The study attributed the majority of recent data breaches to third-party vendors. "These third-party breaches can lead to a larger scale supply-chain attacks and a greater number of impacted users and entities globally," the report said.

Government rules adapt

Meanwhile, last December, the Federal Communications Commission (FCC) updated its 16-year-old data breach notification rules to ensure that telecommunications providers adequately safeguard sensitive customer information. According to a press release , the rules aim to "hold phone companies accountable for protecting sensitive customer information, while enabling customers to protect themselves in the event that their data is compromised."

"What makes no sense is leaving our policies stuck in the analog era," said FCC Chairwoman Jessica Rosenworcel in a statement regarding the changes. "Our phones now know so much about where we go and who we are, we need rules on the books that make sure carriers keep our information safe and cybersecure."

• data breach