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CBSE Sample Papers for Class 5 Maths with Solution 2024-25

• CBSE Sample Papers

CBSE Sample Papers for Class 5 Maths - Free PDF Download

The sample papers in Maths will allow students to revise their subject concepts and score well in their exams by helping them to revise their basics. We at Vedantu have prepared these sample papers to help students improve their skills before their exams. In order to reflect all the significant questions asked in the class 5 Math examination, the sample paper is prepared in a way that covers all the topics. Class 5th maths sample paper includes not only the most relevant questions but also a variety of questions. This is so that students will be able to attempt any type of question with greater confidence in their exams.

The experts at Vedantu have prepared solutions to the sample papers according to the NCERT curriculum. The solutions to each significant question in the Sample Paper For Class 5 Maths are provided step-by-step. The Vedantu website provides free PDF downloadable sample papers for Class 5 Maths to help students improve their performance in the exam. They contain the most common questions that are commonly asked in exams. The sample paper for Class 5 Maths will help students ace their exams by answering these questions.

Download CBSE Class 5 Sample Papers 2024-25 PDF

Also, check CBSE Class 5 Sample Papers for other Subjects:

CBSE Sample Questions Paper for Class 5 Maths with Solutions

Benefits of Solving Class 5 Maths Sample Papers

The sample papers offer students an opportunity to review key concepts, as well as prepare them for final exams.

The students will be tested on their subject knowledge by solving a number of sample or mock papers before exams.

Students can improve their time management skills by solving Class 5 Maths Sample Papers and preparing accordingly for their exams.

Class 5 Maths sample papers can help students identify areas they are weak in as well as their strengths.

Feature of CBSE Class 5 Math Sample Paper 

Sample Paper for Class 5 Maths NCERT designed by Vedantu scholars will help you to solve plenty of sample questions and will cover all the patterns of questions that can appear in your exams. Sample Papers can guide you in preparing for your school exams.

You will improve your analytical and problem-solving skills when you practice these Sample Papers for Class 5th Maths.

Using the Sample Paper of 5th Maths NCERT you can review your entire math syllabus since it contains questions from all the topics.

After completing the sample paper, you will discover your weaknesses and make improvements. You will feel more confident about the exam. 

In addition, you can improve your chances of getting an overall high score by practising well in your strong areas with these sample papers.

As you practice your math skills, your speed and accuracy of solving problems also improve, which helps you manage your time during stressful exam periods.

Through Sample Papers of Class 5 Maths , you become familiar with the exam pattern.

Also, you can make a note of the key formulas and theorems from the sample paper in order to prepare for exams. Having a quick run-through of any chapter would be beneficial to you.

Class 5 Sample Papers are practice papers that help students prepare for their exams. There are lots of relevant questions in this Class 5 Maths Sample Paper . So, solving the sample papers before their exams will help students clear up all their doubts about the concepts so they can score good marks. Vedantu offers students a free PDF download of sample papers to help them excel in their exams.

Important Related Links for CBSE Class 5

FAQs on CBSE Sample Papers for Class 5 Maths with Solution 2024-25

1. What are the important chapters covered in the Sample paper Class 5 Maths?

The important chapters along with the breakage of the marks of each chapter asked in Class 5 Maths Sample Paper are given below:

Concept of Crore, Problems based on multiplication & Division - 16 marks

Concept of Angles, measurement and construction - 12 marks

Squares Perimeter and Area - 12 marks

Rational Numbers - 14 marks

Does it look the Same? - Problems based on Reasoning - 8 marks

Multiples & Factors - 12 marks

Can you See my pattern - Problems based on Reasoning - 6 marks

2. How important are Sample Paper For Class 5 Maths for students?

Sample papers provide a lot of practice on the concepts of Class 5 Maths before the exams. So, solving these Sample paper of Class 5 Maths will help students to brush up on their basic concepts and also make them confident about the subject before the exams.

3. Where can I find the Sample paper of Class 5th Maths?

Students can download the free PDF of Sample paper of Class 5th Maths available on Vedantu Platform. These sample papers are provided with solutions more descriptively to make students understand the concepts easily.

4. Why should students pay attention to Sample Paper For Class 5 Maths?

Practicing Class 5 Maths concepts with sample papers before the tests can be beneficial. Sample papers of Class 5 Maths will prepare students for their exams by brushing up on their math basics and boosting their confidence in the subject.

5. Could you please tell me where I can find a sample paper for maths class 5th?

Vedantu platform offers free copies of sample papers for Class 5th Maths. These sample papers include solutions that help students understand the concepts more easily. The purpose of this is for students to be more confident in their exam performance by attempting any type of question.

6. How many important concepts are there in the class 5 maths sample paper?

In this article, we will analyze important math concepts, along with the weightage of each chapter in the class 5 maths exams.

Concept of angles, measurement, and construction - 12 marks

Does it look the same? - Problems based on Reasoning - 8 marks

Can you see my pattern - Problems based on Reasoning - 6 marks

7. What topics are included in the sample paper for Maths for Class 5?

Numbers- Numbers in Roman numerals, numbers with underlines, numbers following, and numbers preceding.

Performing mathematical operations- multiplication, subtraction, addition, HCF, LCM, etc. 

Area and perimeter- describe important geometric shapes like triangles, rectangles, squares, and pentagons.

Miscellaneous questions- true and false, word problems, and definitions.

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Class 5 Maths Questions, Notes, Test Papers | NCERT Solutions

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User submitted papers, number systems, addition and subtraction, multiplication and division, lcm and hcf, fractional numbers, ratio and percentage, lines and angles, geometrical shapes, perimeter area and volume, measurements, time and calendar, money and bills, patterns and symmetry.

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Math Magic - The Fish Tale

Math magic - shapes and angles, math magic - how many squares, math magic - parts and wholes, math magic - does it look the same, math magic - be my multiple, i'll be your factor, math magic - can you see the pattern, math magic - mapping your way, math magic - boxes and sketches, math magic - tenths and hundredths, math magic - area and its boundary, math magic - smart charts, math magic - ways to multiply and divide, math magic - how big how heavy, cbse worksheets, other useful resourses,   online tests,   learning videos.

Get CBSE Class 5 Mathematics study material in PDF format. MyCBSEguide provides solved question papers, annual examination papers, revision notes, worksheets, and NCERT solutions for Class 5 Mathematics. 

CBSE Class 5 Mathematics Study Material & Detailed Syllabus

The upper primary syllabus attempts to highlight or give extra importance to the development of mathematical understanding and thinking in the child. Parents and teachers must be knowing that the upper primary stage is the transitional stage that takes their wards to a world of greater abstraction. At this level, children begin to move from concrete to abstract notions, wherein the child will learn to use and understand mathematical language, including symbols.

CBSE Class 5 Maths syllabus aims to help learners decode mathematics as a discipline. It has been integrated into our experiences and what we come across in our daily lives which may have an abstract basis. All tools that are used in the classroom are to scaffold the learning process at the intermediate stage of learning. The learning process takes a child from the process of generalisation to distinctivness. Helping the child to develop a better understanding of logic and appreciating the notion of proof is also stressed.

CBSE Class 5 Maths Resources

Our resources for Class 5 Maths like syllabus, practice questions, revision notes, test papers, sample papers, worksheets, etc. We also provide learning videos for each chapter where understanding the concepts and their application becomes pretty much easier. The  myCBSEguide App  is known for providing quality study material in all the subjects of CBSE. The senior-level teachers vouch for the sample papers of Mathematics provided by myCBSEguide. We aim to deliver the same quality of content at the junior level as well.

CBSE Class 5 Mathematics Syllabus

Geometry (Shapes and Spatial Understanding)

Numbers (Mental Arithmetic & Fractional Numbers)

• Measurement

CBSE Class 5 Maths Model Question Papers Test Papers

Leaning is not enough, so our kids need to need their progress. So, here we have all kinds of tests apt for Upper Primary level Mathematics students. The sample question papers for Class 5 Maths provided on  myCBSEguide  are mostly question papers from different schools. We also have a section of previous years' questions where you find assorted questions asked in various schools in various levels of class 5 Maths school examination. The idea is to make the students well aware of all possible question typologies for Class 5 Maths. 

CBSE Class 5 Maths MCQs and Online Tests

Being adept in objective-type questions right from a young age can prove to be extremely useful for students. This is because they will have to sit for various online tests or any other entrance or competitive tests, usually based on MCQs. So why not prepare from the primary stage itself? Our Students' Dashboard allows you to explore the maximum number of objective-type questions for any given chapter of Class 5 Maths. These questions cultivate a habit of time management in the students. You can also practice objective questions, which include MCQs of varied typologies. Download the app to get an experience of these fun tests for your young ones. 

CBSE Class 5 Maths Flashcards, Learning Videos, and CBQs

We at myCBSEguide keep making efforts to make our content most feasible and interesting for the learners. We keep updating as per the latest changes and developments in the curriculum strictly following the guidelines of CBSE . 

Here you can get Class 5 Maths Learning Videos for each chapter and their related topics. Our learning videos help students to understand the subjects conceptually. The Class 5 Mathematics Flashcards on our dashboard make the learning experience more fun as students learn the magic formulas and definitions in the play-way method.

CBSE Class 5 Maths Case Based Questions

The latest modification in the overall curriculum emphasises competency-based learning. Therefore, here we bring some of the finest Case-Based Questions for class 5 Maths which will develop a better understanding of the important chapters.  Some of the best CBSE teachers are associated with us. We assure you quality content in the form of notes and questions for Maths. Our resources will help the learner to get those insights that are generally skipped in simple pen-paper exercises.

The underlying philosophy of the course is to develop the child as being confident and competent in doing mathematics, having the foundations to learn more, and developing an interest in doing Mathematics. The focus is not on giving complicated arithmetic and numerical calculations but to develop a sense of estimation and an understanding of mathematical ideas.

Follow myCBSEguide to get all the relevant study materials for CBSE and other state boards along with ICSE/ICS, JEE and NEET.

• NCERT Solutions for Class 05

CBSE and many other state boards follow NCERT books. Here are NCERT chapter-end questions and their answers for class 5 English, EVS, Hindi, Maths and other subjects. NCERT Solutions – Class 5 NCERT Solutions for Class-5 English NCERT Solutions for Class-5 EVS NCERT Solutions for Class-5 Hindi NCERT Solutions for …

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CBSE Class 5 Worksheets for All Subjects

CBSE Class 5 Worksheets for All Subjects Maths, Science, Social Science, English and Hindi are available in myCBSEguide App for free download. Worksheets help students to practice the concepts. The most important thing about these practice sets is their composition. We know, creating worksheets is a time-consuming task. Sometimes, we …

NCERT Solutions for Class 5 Maths

NCERT Solutions for Class 5 Maths includes all the questions provided in NCERT Books for 5th Class Maths Subject. Here all questions are solved with detailed explanation and available for free to check mycbseguide.com. Book: National Council of Educational Research and Training (NCERT) Class: 5th Class Subject: Mathematics NCERT solutions …

NCERT Solutions for Class 5 Maths Smart Charts

NCERT Solutions for Class 5 Maths Smart Charts book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. …

NCERT Solutions for Class 5 Maths Ways of Multiply and Divide

NCERT Solutions for Class 5 Maths Ways of Multiply and Divide book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from …

NCERT Solutions for Class 5 Maths Can you See The Pattern

NCERT Solutions for Class 5 Maths Can you See The Pattern book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from …

NCERT Solutions for Class 5 Maths Mapping Your Way

NCERT Solutions for Class 5 Maths Mapping Your Way book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text …

NCERT Solutions for Class 5 Maths Boxes And Sketches

NCERT Solutions for Class 5 Maths Boxes And Sketches book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text …

NCERT Solutions for Class 5 Maths Tenths And Hundredths

NCERT Solutions for Class 5 Maths Tenths And Hundredths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text …

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NCERT Solutions for Class 5 Maths Free PDF Download

Ncert solutions for class 5 maths.

The Central Board of Secondary Education (CBSE) prescribes NCERT textbooks. We have compiled all the NCERT solutions for class 5 maths. These NCERT solutions for class 5 maths are chapter-wise and exercise-wise to help you prepare in the best possible manner for your exams.

Mathematics requires a clear understanding of the concepts, logic and a lot of practice. Hence, we are providing you all the NCERT solutions for class 5 maths. Our solutions cover all the basic concepts in NCERT solutions for class 5 maths.

NCERT solutions for class 5 maths are formed by our team of highly experienced and qualified faculties. Our NCERT solutions for class 5 maths will give you a complete grasp over the subject and shall help you in scoring higher marks. However, in case of doubts, in NCERT solutions for class 5 maths, we have a team of teachers who are ready to solve your doubts any time and are just a click away.

Download NCERT Solutions from the links, more links will be updated soon.

Chapter 1 – The Fish Tale

Chapter 2 – Shapes and Angles

Chapter 3 – How many Squares?

Chapter 4 – Parts and Wholes

Chapter 5 – Does it Look the Same

Chapter 6 – Be my Multiple, I’ll be your Factor

Chapter 7 – Can you see the Pattern?

Chapter 8 – Mapping your Way 

Chapter 9 – Boxes and Sketches

Chapter 10 – Tenths and Hundredths

Chapter 11 – Area and its boundary

Chapter 12 – Smart Charts

Chapter 13 – Ways to Multiply and Divide

Chapter 14 – How Big? How Heavy?

Download NCERT Solutions for Class of all subject here.

NCERT Solutions for Class 5 Maths Chapterwise

Ncert solutions for class 5 maths chapter 1 – the fish tale.

This chapter helps the students to develop their understanding of the Size and shapes of various objects and the Quantities of measurements of the various things.

NCERT Solutions for Class 5 Maths  Chapter 2 – Shapes and Angles

In this chapter, we shall study the various shapes of the things we use in our day to day life. Also, we shall study the angles between their sides or curves.

NCERT Solutions for Class 5 Maths Chapter 3 – How many Squares?

The size of an object depends on its perimeter and area. Thus, in this chapter, we shall study how to calculate perimeter and area of a given shape.

NCERT Solutions for Class 5 Maths Chapter 4 – Parts and Wholes

This chapter deals with the concept of equal and unequal parts of an article. Thus, here we will understand the concept of fractions.

NCERT Solutions for Class 5 Maths Chapter 5 – Does it Look the Same?

Some patterns may be similar and some may be different. In this chapter, we shall discuss the linear, reflectional and rotational symmetry of patterns.

NCERT Solutions for Class 5 Maths Chapter 6 – Be My Multiple, I’ll be Your Factor

When we have limited money and have to buy two or more things, then the question arises as to how much quantity of each thing to buy. This chapter thus deals with the multiples and factors of a number.

NCERT Solutions for Class 5 Maths Chapter 7 – Can You See the Pattern?

In this chapter, you will learn to observe patterns of the numbers and solve them. This has wide application in our daily lives.

NCERT Solutions for Class 5 Maths Chapter 8 – Mapping Your Way

Maps help you find your way when you need to go somewhere or you are lost. Nowadays GPS has made it very easy. Hence, this chapter guides you to understand mapping and scaling.

NCERT Solutions for Class 5 Maths Chapter 9 – Boxes and Sketches

This chapter teaches us to make the boxes of different shapes and sizes by joining rectangles and squares of corresponding sizes. Also, we shall study the visualization of 3D and 2D objects.

NCERT Solutions for Class 5 Maths Chapter 10 – Tenths and Hundredths

Use of fractions is quite common in day to day life. This chapter aims at making you understand the use of fractions and also the decimals.

NCERT Sols for Class 5 Maths Chapter 11 – Area and its Boundary

When we want to cover a wall with wallpaper we need to know the area of the wall. This chapter deals with the dimensions of the various shapes and their areas.

NCERT Sols for Class 5 Maths Chapter 13 – Ways to Multiply and Divide

We use multiplication and division number of times in a day. This chapter deals with the concepts of multiplication and division of numbers.

NCERT Sols for Class 5 Maths Chapter 14 – How Big? How Heavy?

In this chapter, you will study how to measure the volume and weights of the objects. For example, how many kilograms of sugar can be filled in a jar is decided by the volume of that jar.

Solved Questions for You

Question 1: A solid has how many dimensions ?

Answer:  A solid has 3 dimensions; length, breadth, height.

Question 2: The difference between a rectangle and a cube is

• Rectangle is B-dimensional and cube is 2-dimensional.
• Rectangle and cube are both 2-dimensional.
• Rectangle is 2-dimensional and cube is 3-dimensional.
• None of these

Answer: The difference in rectangle and cube is that a rectangle is a 2-dimensional figure where the length and the breadth of the geometry are specified.

A cube is a 3-dimensional figure where the length, breadth and depth of the geometry are specified.

Question 3: The side view of the pentagonal prism is

• parallelogram

Answer: Side view looks like this which is a parallelogram.

Question 4: A cylinder has two faces which are…………

Answer: A cylinder has two circular faces.

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NCERT Solutions for Class 5

• NCERT Solutions for Class 5 EVS Chapter 5 Free PDF Download
• NCERT Solutions for Class 5 Maths Chapter 6 Free PDF Download
• NCERT Solutions for Class 5 EVS Chapter 19 Free PDF Download
• NCERT Solutions for Class 5 EVS Chapter 20 Free PDF Download
• NCERT Solutions for Class 5 EVS Free PDF Download
• NCERT Solutions for Class 5 Maths Chapter 11 Free PDF Download
• NCERT Solutions for Class 5 Maths Chapter 9 Free PDF Download
• NCERT Solutions for Class 5 Maths Chapter 8 Free PDF Download
• NCERT Solutions for Class 5 Maths Chapter 2 Free PDF Download
• NCERT Solutions for Class 5 Maths Chapter 12 Free PDF Download

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Question Bank for 5th Class Mathematics

Select chapter, recent question banks, practice now, data handling, measurement, mensuration, fraction & decimals, factor & multiple, roman number, number system, reasoning and aptitude, applied mathematics: percentage, ratio and proportion, graphical representation of data, area, perimeter and volume of geometrical figures, geometrical figures, decimals and its operations, operation on fractions, factors and multiples, operation on numbers.

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CBSE Class 10 Maths Case Study Questions for Maths Chapter 5 - Arithmetic Progression (Published by CBSE)

Case study questions on cbse class 10 maths chapter 5 - arithmetic progression are provided here. these questions are published by cbse to help students prepare for their maths exam..

CBSE Class 10 Case Study Questions for Maths Chapter 5 - Arithmetic Progression are available here with answers. All the questions have been published by the CBSE board. Students must practice all these questions to prepare themselves for attempting the case study based questions with absolute correctness and obtain a high score in their Maths Exam 2021-22.

Case Study Questions for Class 10 Maths Chapter 5 - Arithmetic Progression

CASE STUDY 1:

India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year.

Based on the above information, answer the following questions:

1. Find the production during first year.

2. Find the production during 8th year.

3. Find the production during first 3 years.

4. In which year, the production is Rs 29,200.

5. Find the difference of the production during 7th year and 4th year.

2. Production during 8th year is (a+7d) = 5000 + 2(2200) = 20400

3. Production during first 3 year = 5000 + 7200 + 9400 = 21600

4. N = 12 5.

Difference = 18200 - 11600 = 6600

CASE STUDY 2:

Your friend Veer wants to participate in a 200m race. He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less. He wants to do in 31 seconds.

1. Which of the following terms are in AP for the given situation

a) 51,53,55….

b) 51, 49, 47….

c) -51, -53, -55….

d) 51, 55, 59…

Answer: b) 51, 49, 47….

2. What is the minimum number of days he needs to practice till his goal is achieved

Answer: c) 11

3. Which of the following term is not in the AP of the above given situation

Answer: b) 30

4. If nth term of an AP is given by an = 2n + 3 then common difference of an AP is

Answer: a) 2

5. The value of x, for which 2x, x+ 10, 3x + 2 are three consecutive terms of an AP

Answer: a) 6

CASE STUDY 3:

Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of Rs 1,18,000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month , answer the following:

1. The amount paid by him in 30th installment is

Answer: a) 3900

2. The amount paid by him in the 30 installments is

Answer: b) 73500

3. What amount does he still have to pay offer 30th installment?

Answer: c) 44500

4. If total installments are 40 then amount paid in the last installment?

Answer: a) 4900

5. The ratio of the 1st installment to the last installment is

Answer: b) 10:49

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

Tips to Solve Case Study Based Questions Accurately

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CBSE Class 10 Maths Case Study

CBSE Board has introduced the case study questions for the ongoing academic session 2021-22. The board will ask the paper on the basis of a different exam pattern which has been introduced this year where 50% syllabus is occupied for MCQ for Term 1 exam. Selfstudys has provided below the chapter-wise questions for CBSE Class 10 Maths. Students must solve these case study based problems as soon as they are done with their syllabus. 

These case studies are in the form of Multiple Choice Questions where students need to answer them as asked in the exam. The MCQs are not that difficult but having a deep and thorough understanding of NCERT Maths textbooks are required to answer these. Furthermore, we have provided the PDF File of CBSE Class 10 maths case study 2021-2022.

Class 10 Maths (Formula, Case Based, MCQ, Assertion Reason Question with Solutions)

In order to score good marks in the term 1 exam students must be aware of the Important formulas, Case Based Questions, MCQ and Assertion Reasons with solutions. Solving these types of questions is important because the board will ask them in the Term 1 exam as per the changed exam pattern of CBSE Class 10th.

Important formulas should be necessarily learned by the students because the case studies are solved with the help of important formulas. Apart from that there are assertion reason based questions that are important too. 

Assertion Reasoning is a kind of question in which one statement (Assertion) is given and its reason is given (Explanation of statement). Students need to decide whether both the statement and reason are correct or not. If both are correct then they have to decide whether the given reason supports the statement or not. In such ways, assertion reasoning questions are being solved. However, for doing so and getting rid of confusions while solving. Students are advised to practice these as much as possible.

For doing so we have given the PDF that has a bunch of MCQs questions based on case based, assertion, important formulas, etc. All the Multiple Choice problems are given with detailed explanations.

CBSE Class 10th Case study Questions

Recently CBSE Board has the exam pattern and included case study questions to make the final paper a little easier. However, Many students are nervous after hearing about the case based questions. They should not be nervous because case study are easy and given in the board papers to ease the Class 10th board exam papers. However to answer them a thorough understanding of the basic concepts are important. For which students can refer to the NCERT textbook.

Basically, case study are the types of questions which are developed from the given data. In these types of problems, a paragraph or passage is given followed by the 5 questions that are given to answer . These types of problems are generally easy to answer because the data are given in the passage and students have to just analyse and find those data to answer the questions.

CBSE Class 10th Assertion Reasoning Questions

These types of questions are solved by reading the statement, and given reason. Sometimes these types of problems can make students confused. To understand the assertion and reason, students need to know that there will be one statement that is known as assertion and another one will be the reason, which is supposed to be the reason for the given statement. However, it is students duty to determine whether the statement and reason are correct or not. If both are correct then it becomes important to check, does reason support the statement? 

Moreover, to solve the problem they need to look at the given options and then answer them.

CBSE Class 10 Maths Case Based MCQ

CBSE Class 10 Maths Case Based MCQ are either Multiple Choice Questions or assertion reasons. To solve such types of problems it is ideal to use elimination methods. Doing so will save time and answering the questions will be much easier. Students preparing for the board exams should definitely solve these types of problems on a daily basis.

Also, the CBSE Class 10 Maths MCQ Based Questions are provided to us to download in PDF file format. All are developed as per the latest syllabus of CBSE Class Xth.

Class 10th Mathematics Multiple Choice Questions

Class 10 Mathematics Multiple Choice Questions for all the chapters helps students to quickly revise their learnings, and complete their syllabus multiple times. MCQs are in the form of objective types of questions whose 4 different options are given and one of them is a true answer to that problem. Such types of problems also aid in self assessment.

Case Study Based Questions of class 10th Maths are in the form of passage. In these types of questions the paragraphs are given and students need to find out the given data from the paragraph to answer the questions. The problems are generally in Multiple Choice Questions.

The Best Class 10 Maths Case Study Questions are available on Selfstudys.com. Click here to download for free.

To solve Class 10 Maths Case Studies Questions you need to read the passage and questions very carefully. Once you are done with reading you can begin to solve the questions one by one. While solving the problems you have to look at the data and clues mentioned in the passage.

In Class 10 Mathematics the assertion and reasoning questions are a kind of Multiple Choice Questions where a statement is given and a reason is given for that individual statement. Now, to answer the questions you need to verify the statement (assertion) and reason too. If both are true then the last step is to see whether the given reason support=rts the statement or not.

CBSE Class 10 Results 2024 : CBSE Class 10 Answer Book Photocopy Applications Open

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Unit 1: Decimal place value

Unit 2: add decimals, unit 3: subtract decimals, unit 4: add and subtract fractions, unit 5: multi-digit multiplication and division, unit 6: multiply fractions, unit 7: divide fractions, unit 8: multiply decimals, unit 9: divide decimals, unit 10: powers of ten, unit 11: volume, unit 12: coordinate plane, unit 13: algebraic thinking, unit 14: converting units of measure, unit 15: line plots, unit 16: properties of shapes.

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• Geometry is the branch of mathematics that focuses on the measurement and relationship of lines, angles, surfaces, solids, and points.

• Angle is measured in degrees. A degree is denoted by °.

• A circle is a shape with all points the same distance from its centre. Area of a circle= X R 2

• A triangle is a plane figure with three straight sides and three angles.
• On the basis of sides, triangles are classified into: Scalene (all sides are different), Isosceles (Two sides are equal), Equilateral (All sides are equal)

• On the basis of angels, triangles are divided into: acute(all angles are acute), right(one angle is 90 degree), Obtuse(one angle is obtuse), Equiangular(all angles are equal).

• In geometry, a cube is a three-dimensional solid object bounded by six square faces, sides, with three meeting at each vertex.

EXAMPLE 1: The radius of the circle is 3 cm. Find its diameter, circumference, and area.

SOLUTION: Diameter= 2 X Radius = 2 X 3 = 6 cm

Circumference= 2 X X R = 2 X X 3= 18.84 cm Area= X R 2 = X (3) 2 = 28.27 cm 2

EXAMPLE 2: Find the number of triangles in the following figure and name them.

They are= triangle ABC, triangle CDE, triangle AEF triangle ABC= Right angle triangle triangle CDE= Isosceles Triangle triangle AEF= Right Angle Triangle

Perimeter and Area of Squares and Rectangles

• Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane.

Area of a rectangular surface= Length X Breadth units 2 Area of a square surface= a X a = a 2 units 2

EXAMPLE 1: Find the area and perimeter of a rectangle with length 1cm and breadth 2cm

SOLUTION: Perimeter= 2 X (Length + Breadth) = 2 X (1+2)= 6 cm Area= Length X Breadth= 1cm X 2cm= 2cm 2

EXAMPLE 2: Find the area and perimeter of a square with side 3cm.

Practice these questions

Q2) Classify the triangles.

Q3) Find the perimeter and area of the rectangle. (Hint: Divide the irregular rectangles into two regular rectangles.)

Q4) Find the area and perimeter of the square below.

• Only a surface can have area.
• Perimeter of rectangle= 2 X (Length + Breadth) Perimeter of square= 4 X a
• Area of rectangle= Length X Breadth Area of square= A 2
• Area of Circle=
• Circumference= 2 X X R
• Diameter = 2 X Radius
• There are 7 angles= acute, obtuse, reflex, complete, zero, right, and straight angle.
• On the basis of sides, there are 3 triangles= scalene, isosceles, equilateral triangle.
• On the basis of angle, there are 4 triangles = acute, obtuse, right, and equiangular triangle

Quiz for Geometry

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• CBSE Class 5 Maths

Class 5 Maths Parts And Wholes Important Questions For Exam

by Sanjusha · February 13, 2020

IMPORTANT QUESTIONS FOR CBSE EXAMINATION | CLASS 5 MATHEMATICS PARTS AND WHOLES – Lesson 4

Answer the following

1. The cost of 1 kg apple is 120 rupees and 1 kg orange is 80 rupees .Find the cost of ¾ kg apple and 1 ½ kg oranges?

2. Maya had 200 rupees with her. She spent ½ of it to buy chocolates, ¼ of it to buy a book and with the rest she bought a pouch. Find the amount she paid for

a) Chocolates b) Book c) Pouch

3. A Reduce to lowest form:

a) 24/48 b) 4/20

4. Manu had 20 rupees with him. He spent 16.50 rupees for buying snacks. He got the balance amount in 1 rupee and ½ rupee coins. What are the coins he got?

5. Write the next three like fractions:

a) 1/7, 2/7, 3/7 ………….. b) 1/3, 2/3, 3/3 …………………

6. Sonu has 10 toffees with him. He gave 2/5 of it to his sister. How many toffees are remaining with him?

7. There are 27 oranges in a basket. Kiran was given 4/9 of a basket of oranges. What number of oranges was left in the basket?

8. Lalitha has to travel 2 ¼ km to reach school. What distance does he travel to go to school and come back home?

9. Manju had 12 chocolates. She gave one fourth of it to Raji, one third to Sujatha and one sixth to Sheela. She ate the remaining part. How many chocolate did each get?

10. Sohan bought a dozen mangoes. ¼ of these mangoes are ripe. How many mangoes are ripe?

1. Cost of 1 kg apple = 120 rupees Cost of 1 kg orange = 80 rupees Cost of ¾ kg apple = ¾ of 120 = ¾ x 120 = 360/4 = 90 rupees Cost of ½ kg oranges = ½ x 80 = 80/2 = 40 rupees Cost of 1 ½ kg oranges = 80 + 40 = 120 rupees

2. a) Amount paid for chocolates = ½ of 200 = 100 rupees b) Amount paid for book = ¼ of 200 = 50 rupees c) Amount paid for pouch = ¼ of 200 = 50 rupees

3. a) 24/48 = ½ (24 is a common factor)

b) 4/20 = 1/5 (4 is a common factor)

4. The amount Manu had = 20 rupees Amount he spend = 16.50 rupees Remaining amount = 20 – 16.50 = 3.50 rupees So he will get 3 one rupee coins and 1 half rupee coin.

5. a) 1/7, 2/7, 3/7, 4/7, 5/7, 6/7……………. b) 1/3, 2/3, 3/3, 4/3, 5/3, 6/3 ………………

6. Total number of toffees = 10 Toffees given to his sister = 2/5 of 10 = 2/5 x 10 = 20/5 = 4 toffees Toffees remaining with him = 10 -4 = 6 toffees

7. Total number of oranges = 27 Number of oranges given to Kiran = 4/9 x 27 = 12 Oranges left in the basket = 27 -12 = 15

8. Total distance has to travel = 2 ¼ + 2 ¼ = 4 ½ km

9. Total number of chocolates = 12 Each one will get the following number of chocolates: Raji – ¼ of 12 = ¼ x 12 = 12/4 = 3 Sujatha – 1/3 of 12 = 1/3 x 12 = 12/3 = 4 Sheela – 1/6 of 12 = 1/6 x 12 = 12/6 =2 Manju – remaining 3 chocolates.

10. Number of mangoes that are ripe = ¼ of 12 = ¼ x 12 = 12/4 = 3 mangoes.

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Case Study Questions for Class 12 Maths Chapter 5 Continuity and Differentiability

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

Here we are providing case study questions for class 12 maths.

Case Study Questions for Class 12 Maths

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

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

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

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

Importance of Solving Case Study Questions for Class 12 Maths

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

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

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

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

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• NCERT Solutions
• NCERT Class 5
• NCERT 5 Maths
• Chapter 4: Parts And Wholes

NCERT Solutions Class 5 Maths Chapter 4 - Parts and Wholes

NCERT Solutions Class 5 Maths Chapter 4- Parts and Whole are provided here for students to prepare for exams. These solutions are prepared by subject experts with respect to the CBSE syllabus (2023-2024) published by the board.

Chapter 4 – Parts and Wholes is an interesting chapter. It deals with correctly representing and discovering fractions and their whole relationships. Here, students will be encouraged to use models to divide a whole into equal parts and record the fractions for parts. The solved questions provided for this chapter have been designed to help students practise the concepts which have been or may be asked in the upcoming examinations. Students will learn how to draw, determine as well as explain whether or not a given fraction and an area representation match.

Class 5 Maths NCERT Solutions for Parts and Wholes

Students are given NCERT solutions for Chapter 4 based on the points covered. They can also download NCERT textbooks Class 5 Maths subject and other study materials to prepare for exams. Solve sample papers and previous years’ question papers to get a brief idea of the types of questions asked from the chapter, Parts and Whole.

The Class 5 Maths, Chapter 4 – Parts and Wholes NCERT Solutions include different examples and questions, such as

• Bhupen had chocolate. He gave one-third to Sugam, one-fourth of it to Raji and one-sixth to Shri. He ate the remaining part. How many pieces of chocolate did each get?
• Various shapes, including shapes of flags, are used for the area models.
• Create patterns by marking some squares in grids A, B, C, D. What part of the grid did you mark? What part of the grid remained unmarked? Write.

These are some of the important topics and questions from Class 5 Maths Chapter 4 NCERT solutions. To know more, you can check out the solutions below.

NCERT Solutions Class 5 Maths Chapter 4 – Parts and Wholes

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1. Draw a rectangle of length 9 cm and width 6 cm. Divide it into three equal parts and complete the flag.

The top one-third of our flag is saffron (or orange).

(i) What is the colour of the middle one-third of the flag?

The colour of the middle one-third of the flag is white.

(ii) Where will you draw the Ashoka Chakra?

I will draw the Ashoka Chakra in the middle of the white portion of the flag.

(iii) How much of the flag will you colour green?

(1/3) rd portion of the flag will be coloured green.

(iv) Is the white colour now less than 1/3 of the flag? Why?

Yes, the white colour is less than 1/3 of the flag because the Ashoka Chakra is present in the white portion.

2. Now look at this flag. How much of it is black?

There are 3 portions, so the 1/3 rd portion of the flag contains black colour.

(i) The green part of the flag can be written as.

The green part of the flag can be written as one-third.

(ii) Is red less than one-third of the flag? Why?

Yes, the red colour is less than 1/3 of the flag because the white emblem is present in the red portion.

3. This is the flag of Myanmar, our neighbour.

(i) Is blue more than one-fourth of the flag or less?

The blue colour is less than one-fourth of the flag.

(ii) Guess how much of the flag is red. Is it more than ½? Is it more than three-fourths?

It is more than half and also it is more than three-fourths.

4. Practice time

(A) Chocolate bar

Manju had a chocolate. She gave one-fourth of it to Raji, one-third to Sugatha and one-sixth to Sheela. She ate the remaining part. How many pieces of chocolate did each get? Write here.

Manju had a chocolate.

Number of bites in the chocolate is 12.

She gave one-fourth of it to Raji = ¼ × 12

Sugatha got one-third of it = (1/3) × 12

Sheela got one-sixth of it = (1/6) × 12

(i) What part of the chocolate did Manju eat?

Part of the chocolate remains with Manju = 12 – (3 + 4 + 2)

Therefore, Manju ate 3 bites of chocolate.

(B) Colour the hats

(i) Colour 1/3 of the hats in red.

(ii) Colour three-fifth of the hats blue.

(iii) How many hats did you colour red?

(iv) How many hats did you colour blue?

(v) What part of the hats are not coloured?

The total number of hats in the given figure = 15

(i) Out of 15 colours, 1/3 of the hats are in red = 1/3 × 15

(ii) Out of 15 colours, three-fifth of hats are in blue = 3/5 × 15

(iii) 5 hats are coloured red.

(iv) 9 hats are coloured blue.

(v) Number of hats coloured = 14

Total number of hats = 15

So, the number of hats not coloured = 15 – 14

Therefore, (1/15) th part of the hats are not coloured.

Patterns in parts Page: 57

1) Make different patterns by colouring some squares in grids B, C, D. What part of the grid did you colour? What part of the grid remained white? Write.

2) Look at grid A again. Is the grid coloured

(a) ½ blue, ½ white? (b) 2/4 blue, 2/4 white?

(c) 3/8 blue, 5/8 white? (d) 4/8 blue, 4/8 white?

Mark (X) on the wrong answer.

(a) ½ blue, ½ white (b) 2/4 blue, 2/4 white

(c) 3/8 blue, 5/8 white (X) (d) 4/8 blue, 4/8 white

3) Draw grids of 16 squares and make patterns with

(a) 2/8 red, ½ yellow, ¼ green

(b) 3/16 blue, 5/16 red, ½ green

Out of 16 squares 2/8 red = 2/8 × 16

= 4 red squares

Out of 16 squares ½ yellow = ½ × 16

= 8 yellow squares

Out of 16 squares ¼ green = ¼ × 16

= 4 green squares

Out of 16 squares 3/16 blue = 3/16 × 16

= 3 blue squares

Out of 16 squares 5/16 red = 5/16 × 16

= 5 red squares

Out of 16 squares ½ green = ½ × 16

= 8 green squares

Ramu’s vegetable field Page: 58

Ramu’s vegetable field has 9 equal parts.

1. What vegetables does he grow?

Ramu grows chillis, potatoes, brinjals, tomatoes and spinach in his vegetable field.

i) Which vegetable grows in the biggest part of his field? What part?

He grows tomatoes in the biggest part of the field.

Out of 9 equal parts, 3 of them contain tomato, i.e., (3/9) th part of his field contains tomato.

ii) On what part of the field does he grow potatoes?

Out of 9 equal parts, 2 of them contain potatoes.

So, (2/9) th part of his field contains potatoes.

iii) What part of the field is used to grow spinach? What part is used for brinjals?

Out of 9 equal parts, only one part contains spinach.

So, (1/9) th part of his field contains spinach.

Out of 9 equal parts, 2 parts contain brinjals.

So, (2/9) th part of his field contains brinjals.

2. Ramu wanted to give these vegetables to his friends. He gave Aboobacker one-fifth of these tomatoes and 1/3 of the potatoes. Srija got 2/5 of the tomatoes and 3/6 of the potatoes. Nancy got the rest of these vegetables. Circle Aboobacker’s share in blue. Circle Srija’s share in yellow.

From the given figure,

Total number of potatoes = 18

Total number of tomatoes = 20

From the question,

Ramu wanted to give these vegetables to his friends.

Aboobacker got one-fifth of these tomatoes = (1/5) × 20

Aboobacker got 1/3 of the potatoes = (1/3) × 18

Srija got 2/5 of the tomatoes = (2/5) × 20

Srija got 3/6 of the potatoes = (3/6) × 18

Nancy got the rest of these vegetables.

Total number of vegetables, including potatoes and tomatoes = 20 + 18

Number of vegetables Aboobacker and Srija got = 4 + 6 + 8 + 9

So, Nancy got = 38 – 27

= 11 vegetables

(i) How many potatoes and tomatoes did Nancy get?

From the above solution,

Number of tomatoes Aboobacker and Srija got = 4 + 8

Number of potatoes Aboobacker and Srija got = 6 + 9

Number of tomatoes Nancy got = 20 – 12

= 8 tomatoes

Number of potatoes Nancy got = 18 – 15

Guess and Check Page: 61

A) What part of each shape is coloured?

First, guess the answer, then check.

By looking at the figure, we can say that 1/8 of the shape is coloured.

By looking at the figure, we can say that 1/6 of the shape is coloured.

By looking at the figure, we can say that 2/9 of the shape is coloured.

By looking at the figure, we can say that 3/12 of the shape is coloured.

2. Coloured Parts

Complete these

This circle is divided into two equal parts. Out of equal parts, one part is coloured blue.

This circle is divided into two equal parts. Out of equal 2 parts, one part is coloured blue.

Here, the circle is divided into equal parts. Out of equal parts, parts are coloured blue.

Here, the circle is divided into four equal parts. Out of four equal parts, two parts are coloured blue.

Here, the circle is…………………………………………………………

Here, the circle is divided into six equal parts. Out of six equal parts, three parts are coloured blue.

Here, the circle is divided into eight equal parts. Out of eight equal parts, four parts are coloured blue.

So, we can say that ½ = (2/4) = (3/6) = (4/8)

3. Cutting the Halwa

Ramesh bought a piece of halwa for his children Ammu and Anu.

He divided it equally for them.

(i) Each will get ________ part of halwa.

Each will get ½ part of the halwa.

This piece is too big. We can’t eat it, they said.

(ii) So he divided the pieces into half again. Now, how many pieces will Ammu get?

Ammu gets two pieces.

(iii) What part of the halwa is it?

2/4 part of halwa, or ½ part of halwa.

“Make it even smaller, Dad,” they asked.

So, he again cut the halwa into smaller pieces.

“Ok, thank you, Dad.”

(i) Now, how many pieces will each get?

Now, Ammu and Anu get four pieces each.

(ii) What part of the halwa is each piece now?

Each piece is now 1/8 part of halwa.

(iii) If Ramesh had cut the halwa into 6 equal parts, how many pieces each have got? Look at your answers for questions 1 to 4 and write — ½ = = =

If Ramesh had cut the halwa into 6 equal parts, each got 3 pieces of halwa.

½ = 2/4 = 3/6 = 4/8 = 5/10 = 6/12

4. Parts of the Strip

(i) Look at the picture. Write what part of the strip is each green piece. Write the part for a piece of each colour.

(ii) How many one-fourths will make a half?

Two one-fourth will make a half.

(iii) How many 1/8 will make ¼?

Two 1/8 will make ¼.

= 1/8 + 1/8

(iv) How many 1/8 are in ½?

Four 1/8 are in ½.

= 1/8 + 1/8 + 1/8 + 1/8

5. Patterns

Look at the square.

(i) What part is coloured blue?

From the above figure, we can say that out of 16 squares, 2 squares are coloured blue.

i.e. 2/16 or 1/8 part is coloured blue.

(ii) What part is green?

From the above figure, we can say that, out of 16 squares, 1 square is coloured green.

i.e., 1/16 part is coloured green.

6. From a Part to the Whole

(i) This show 1/5 petals of a flower. Complete the flower by drawing the other petals.

(ii) The picture shows one-third of the blades of a fan. Complete the picture by drawing the other blades.

(iii) Half of the blades of another fan are shown here. Complete the picture by drawing the other half. How many blades have you drawn?

7. Rupees and Paise

(i) How many will make one rupee?

Two 50 paise coins make one rupee coin.

(ii) Is 50 paise half of one rupee?

Yes, 50 paise is half of one rupee.

(iii) How many will make one rupee?

Four 25 paise coins make one rupee.

(iv) 25 paise is _________ part of one rupee

25 paise is ¼ part of one rupee.

(v) 20 paise is _________ part of one rupee

20 paise is 1/5 part of one rupee.

Five 20 paise coins make one rupee.

(vi) How many 10 paise will make one rupee?

Ten 10 paise coins make one rupee.

(vii) So, 10 paise is _____ part of one rupee.

So, 10 paise is 1/10 part of one rupee.

8. Arun’s TimeTable

Sleeping: One third of a day

Use different colours to show,

Playing: One eighth of a day

Studying: ¼ of a day

We know that, 24 hours in a day and above figure contains 25 box.

So, Arun spent one eighth of a day for playing = (1/8) × 24

= 3 hours = 3 box

He spent ¼ of a day for studying = ¼ × 24

= 6 hours = 6 box

Sleeping Playing Studying Other activities

(i). How many hours does Arun take for Sleeping, studying and Playing?

8 hours for sleeping, 6 hours for studying and 3 hours for playing.

(ii) What part of the day does he use for other activities?

He uses the 7/24 part of the day for other activities.

9. School Magazine

A school has decided to bring out a magazine every quarter of the year. How many magazines will they have in a year? If they want to print it at the end of each quarter of a year, which are the months for printing? Mark the number for those months.

From the question, it is given that the school has decided to bring out a magazine every quarter of the year.

We know that there are 12 months in a year.

Quarter of the year = ¼ × 12

So, every three months, the school has to bring out a new magazine.

10. Sleeping Beauty

Have you heard of Kumbhakarna, the brother of Ravana? He is famous for sleeping for half a year.

(i) Most people sleep about 8 hours a day. Then what part of the day is it?

We know that, 24 hours a day.

Given, most people sleep about 8 hours a day = 8/24

= 1/3 part of a day

(ii) So what part of the year do they sleep? A person 60 years old must have slept _______ years!!!

A person 60 years old must have slept for = 1/3 × 60

11. Keerti’s shopping list

Look at the yellow price list.

a) How much does 2 kg of tomato cost?

From the price list, 1 kg of tomato = ₹ 12

Then, the cost of 2 kg of tomato = 12 × 2

b) How much does kg of tomato cost?

c) Kiran wants 2½ kg of tomato. How much will it cost?

For ½ kg of tomato = ½ × 12

So, the cost of 2½ kg of tomato = 24 + 6

d) How much does 3½ kg potato cost?

From the price list, 1 kg of potato = ₹ 10

For ½ kg of potato = ½ × 10

Then, 3 kg of potato = 3 × 10

So, cost of 3½ kg of potato = 30 + 5

e) What is the price of 1¼ kg of carrot?

From the price list, 1 kg of Carrot = ₹ 18

For ¼ kg of carrot = ¼ × 18

Then, 1¼ kg of carrot = 18 + 4.5

f) She bought a gourd of weight 4¾ kg, and it costs?

From the price list, 1 kg of gourd = ₹ 8

For 4 kg of gourd = 8 × 4

For ¾ kg of gourd = ¾ × 8

Then, cost of 4¾ kg of gourd = 32 + 6

g) Look at the shopping list in Keerti’s hand. How much will she have to pay to buy all of these?

12. Raheem’s journey

Raheem has to travel 1¼ km to reach school. What distance does he travel to go to school and come back home?

From the question, it is given that

To reach the school Raheem has to travel = 1 ¼ km = 5/4 km

From school to home = 1 ¼ km = 5/4 km

Total distance travelled by Raheem = 5/4 + 5/4

Therefore, he travels to go to school and comes back home = 2 ½ km

13. What coins?

Latha bought a pencil and a pen for seven and a half rupees. She gave Rs 10/–. The shopkeeper gave back the money in half and quarter rupees. What are the coins she got?

Latha bought a pencil and a pen for = ₹ 7½

Money given by Latha to the shopkeeper = ₹ 10

Shopkeeper gave back the money = 10 – 7.5

So, the shopkeeper can return ₹ 2.5 in the following ways:

a) 1 half rupee coin and 8 quarter rupee coins

b) 2 half rupee coins and 6 quarter rupee coins

c) 3 half rupee coins and 4 quarter rupee coins

d) 4 half rupee coins and 2 quarter rupee coins

14. At the railway station

Your attention, please. Mangalore Express coming from Mangalore and going to Thiruvananthapuram, is now running late by half an hour.

Oh, the train is late today. The right time is a quarter to 7.

a) What time is the train expected to come today?

The right time is a quarter to 7, i.e., 6: 45

But, the train is delayed by half an hour, i.e., 30 minutes.

So, the exact time the train will arrive at 6: 45 + 0: 30 = 7: 15

b) Nazia gets off at a station after 2½ hours from this station. What time will she get off?

Nazia gets off at a station after = 2: 30 hours

Then, total time taken by Nazia to reach = 2: 30 + 7: 15

c) Shaji will take 5 hours to reach Ernakulam by this train. At what time will he reach there?

Shaji will take 5 hours to reach Ernakulam.

Then, the total time taken by Shaji to reach Ernakulam = 7: 15 + 5

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Mathematics > Dynamical Systems

Title: dynamic properties of a class of van der pol-duffing oscillators.

Abstract: In this paper, we study the existence of bifurcation of a van der Pol-Duffing oscillator with quintic terms and its quasi-periodic solutions by means of qualitative and bifurcation theories. Firstly, we analyze the autonomous system and find that it has two kinds of local bifurcations and a global bifurcation: pitchfork bifurcation, Hopf bifurcation, homoclinic bifurcation. It is worth noting that the disappearance of the homoclinic orbit is synchronized with the emergence of a large limit cycle. Then, by discussing the stability of equilibria at infinity and the orientation of the trajectory, the existence and stability of limit circles of the autonomous system are analyzed by combining the Poincaré-Bendixson theorem and the index theory. The global phase portrait and the numerical simulation of the autonomous system in different parameter values are given. Finally, the existence of periodic and quasi-periodic solutions to periodic forced system is proved by a KAM theorem.

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