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ncertsolutionsbook · 6 years ago

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NCERT Solutions for Class 10 Maths

NCERT Solutions for Class 10 maths covers all exercise questions given in the CBSE textbook. You can download this as free pdf from this page. Our best Mathematics master teachers have reviewed all the class 10 maths ncert solutions of exercise questions that will help you solve all the NCERT class 10 maths questions without any problem. We at Learncbse provide free PDF solutions for NCERT maths class 10 for your ease. You can also share the link of our Learncbse website with your classmates so that they can also download CBSE class 10th math NCERT solution. At any point of time, if you have any doubt while going through the class 10 maths NCERT solutions, The online classes will be conducted by one of our best mathematics teachers. You can even talk to the tutor as you would in a normal tuition class.

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NCERT Solutions for Class 10 Maths - Free PDF Download Class 10 being a whole new experience for you as it will be the very first time when you will be appearing for the board exams. Speaking of which, a thorough knowledge of all the chapters along with NCERT Solutions for Class 10 Maths can really help you to understand the subject better in less time. Below given are the chapters and the topics and exercises entailed in each of them. Scroll down to get well-versed with each and every chapter of CBSE Class 10 Maths.

Chapter 1 – Real Numbers

NCERT Class 10 Math Chapter 1, Real Numbers, is the extension of the topics learnt in 9th class. Sections 1.2 and 1.3 of this chapter contains some very important properties of positive integers, namely Euclid’s division algorithm and the Fundamental Theorem of Arithmetic. Furthermore, you will be revisiting Irrational Numbers in section 1.4 whereas Revisiting Rational Numbers and Their Decimal Expansions will be included in Section 1.5. Euclid’s division algorithm has a lot to do with divisibility of integers. It has plethora of applications associated with the divisibility properties of integers. NCERT Class 10 Maths Chapter 1, Real Numbers will be highly beneficial to compute the HCF of two positive integers.

Chapter 2 - Polynomials

Polynomials has total of four exercises however the last exercise is optional. In the first exercise, you need to find zeroes of polynomials p(x). In the second exercise, there are two questions. You have to verify the relationship between the zeroes and the coefficients in the first, while in the second, you have to find a quadratic polynomial. The third exercise has a total of five questions in which you have to do division of polynomials and obtain zeroes of polynomials. Then comes the optional exercise which has five questions in which you need to find zeroes of polynomials.

Chapter 3 - Pair of Linear Equations in Two Variables

There is an introduction part in the beginning of this chapter explaining the concepts of Linear equations in two Variables. You will learn some further complex topics while revising concepts that you have learned in class 9. This chapter has a total of seven exercises in which the last exercise is optional again. You will see three world problems given in the first exercise. In the second exercise, there are a total of seven questions. The third exercise has three questions. The fourth exercise has two questions. The fifth exercise has a total of` five questions in which you have to solve the pair of linear equations through various methods given. The sixth exercise has two questions. The last exercise is optional. Some important topics covered in this chapter are graphical representations, Pair of Linear Equations in Two Variables, Algebraic Methods of Solving a Pair of Linear Equations, Graphical Method of Solution of a Pair of Linear Equations, Elimination Method, Substitution Method, Cross-Multiplication Method and Equations Reducible to a Pair of Linear Equations in Two Variables.

Chapter 4 - Quadratic Equations

You will study quadratic equations and number of ways to find their roots. You will also get to learn some applications of quadratic equations in our daily life situations. There is a total of four exercises in this chapter. The first exercise has two questions, in the first you will need to find check whether equations are quadratic equations or not while in the second you have to convert world problem into quadratic equations. You need to find the roots of quadratic equations by factorisation in the second exercise. You will be finding the roots of quadratic equations in the third exercise also. The fourth exercise has five questions based on finding the roots. Solution of a Quadratic Equation by Completing the Square, Solution of a Quadratic Equation by Factorisation, and Nature of Roots are the main topics studied in this chapter.

Chapter 5 - Arithmetic Progressions

Arithmetic Progressions, chapter 5 of Class 10 Maths, deals with an introduction to Arithmetic Progression with the help of simple daily life examples and gradually deals with the topics entailed and their complexities. Four exercises are given in this chapter divided into various questions in which we have to find the term. Overall, you will learn how to find the nth terms and the sum of n consecutive terms, and in turn use the acquired knowledge in solving some daily life problems.

Chapter 6 - Triangles

There are six exercises in chapter 6, Triangles, including one optional having different set of questions based on the properties of triangles. This chapter has a total of 9 theorems and is very important for all the students of class 10 Maths for their class 10 Board exam.

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Chapter 7 - Coordinate Geometry

A total of four exercises are given in the chapter. The questions are based on finding the distance between the two points whose coordinates are provided and area of a triangle formed by three given points.

Chapter 8 - Introduction to Trigonometry

This chapter has a total of four exercises comprising of various questions mainly on finding trigonometric ratios of the sides of a right triangle with respect to the acute angles of that triangle, called trigonometric ratios. Trigonometric Ratios, Trigonometric Ratios of Specific Angles, Trigonometric Identities and Trigonometric Ratios of Complementary Angles are the main topics you will learn in this chapter.

Chapter 9 - Some Applications of Trigonometry

In this chapter, you will be studying about some very interesting ways in which trigonometry is uded in the daily life around you. This chapter has only one exercise and the questions of which are based on the practical applications of trigonometry.

Chapter 10 - Circles

Circles has just two exercises. The first exercise contains basic questions, while the second has various questions in which you have to prove the given equations.

Chapter 11 - Constructions

In this chapter, there are two exercise where you have to draw various constructions such as division of line segments, construction of Tangents to a Circle and the questions are based on them.

Chapter 12 - Areas related to Circles

There are three exercises that cover all the questions of the area of a circle and finding the areas of two special ‘parts’ of a circular region.

Chapter 13 - Surface Areas and Volumes

In this chapter, there are five exercises and all of them will deal with the problems of finding areas and volumes of different solids such as cube, cuboid and cylinder.

Chapter 14 - Statistics

You will see a total of four exercises in this chapter. The questions will be based on finding mean, median and mode from ungrouped data to that of grouped data. You will also be solving questions related to cumulative frequency, how to draw cumulative frequency curves and the cumulative frequency distribution topics.

Chapter 15 - Probability

Out of the two exercise in this chapter, one is optional. The questions are based on finding the probability of getting a situation mostly on coins and dice.

Why Learncbse.in

Learncbse.in NCERT Solutions for Class 10 Maths enables you to understand all the basic & advance level concepts after solving each & every exercise question. Our Maths teachers especially focus on clearing out your concepts and providing you with a thorough understanding of all the topics. You are taught on a one-to-one basis by our most dedicated teachers. We at Learncbse.in don't believe in just recorded lectures as they don't prove helpful in solving doubts related to any of the book solutions.

To assess your progress on a regular basis, you are tested by our maths tutors at a definite interval of time. The results are shared with your parents to keep them on the same page as well. Another benefit of Learncbse.in is that you get to choose the pace of the learning of the lesson and the timing of the live tutoring session. The lesson plan is customized according to your requirements. The live sessions are also recorded and are available free of cost to all the students and their parents later for review and revision purposes. Another biggest advantage of studying with Learncbse.in is that you can choose to study class 10 maths ncert solutions either on your PC or through your Android mobile devices after downloading our Instant doubt solving app! You can either join us as a regular student or contact us whenever you have doubts and want to prepare for your tests or examinations! We want our NCERT solutions for class 10 maths to prove highly beneficial for you!

There are several ways with which you can avail the benefits of our NCERT Class 10 Maths Solutions. Let’s see what they are after a brief description. Stepping into Class 10 is the best experience of your life as you will be experimenting and facing new things which might appear very exciting to you. As mentioned already that it will be the first time in your life when you will be appearing for the class 10 board exams. Maths is counted among the most dreadful subjects which is feared by a lot of the students. This is the reason why along with NCERT Solutions for class 10 Maths, we have provided the detailed chapter-wise content so that you face no problem while solving the tricky questions of class 10 Maths. Students are advised to keep the Maths NCERT Solutions class 10 handy so that they can prepare short notes that are highly beneficial for class 10 Maths exam. You can include important formulas and theorems and make short notes of it. Chapters like Coordinate Geometry and Constructions need undivided attention which can be gained by solving NCERT Solutions for class 10 Maths and going through the root cause of each and every problem you are facing problem with. We wish you all the best for your journey along with the preparation of Class 10 Maths and good fortune to all your endeavours.

#NCERT Solutions #class 10 maths #learncbse

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learnsarthaks · 2 years ago

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Mastering JEE Main 2024: Tips and Tricks for Acing the Exam and Securing Your Future

If you're a student looking to pursue a career in engineering, then there's no doubt that the Joint Entrance Examination (JEE) is one of the most important exams you'll ever take. With the JEE Main 2024 just around the corner, it's time to buckle down and start preparing. But where do you start? How do you ensure that you're fully equipped to ace the exam and secure your future? That's where this guide comes in. In this article, we'll be sharing tips and tricks that will help you master the JEE Main Exam 2024 and get one step closer to your dream of becoming an engineer. From effective study techniques and time management strategies to expert advice on how to approach the exam, we've got you covered. So, let's dive in and get you on the path to success!

Understanding the JEE Main Exam Pattern

JEE Main is a national level entrance exam conducted by the National Testing Agency (NTA) for admission to undergraduate engineering courses in various colleges and universities across India. The exam is conducted twice a year, in January and April, and is divided into two papers - Paper 1 and Paper 2.

Paper 1 is for admission to B.E/B.Tech courses and is conducted in online mode. It consists of 90 multiple-choice questions from Physics, Chemistry, and Mathematics, with 30 questions from each subject. Each question carries 4 marks, and for every incorrect answer, 1 mark is deducted. The total duration of the exam is 3 hours.

Paper 2 is for admission to B.Arch/B.Planning courses and is conducted in both online and offline modes. It consists of three parts - Mathematics, Aptitude Test, and Drawing Test. Mathematics and Aptitude Test are conducted in online mode, while Drawing Test is conducted in offline mode. The total duration of the exam is 3 hours.

Understanding the JEE Main Exam Pattern is the first step towards cracking the JEE Main Exam. It helps you understand the structure of the exam and the number of questions you need to attempt from each subject. Once you have a clear understanding of the exam pattern, you can start preparing for the exam accordingly.

Syllabus for JEE Main 2024

The JEE Main syllabus is based on the NCERT syllabus of Classes 11 and 12. It covers topics from Physics, Chemistry, and Mathematics, and it's important to have a thorough understanding of all the topics in the syllabus to crack the exam. Here's a brief overview of the Syllabus for JEE Main 2024:

### Physics

- Kinematics

- Laws of Motion

- Work, Energy, and Power

- Rotational Motion

- Gravitation

- Properties of Solids and Liquids

- Thermodynamics

- Kinetic Theory of Gases

- Oscillations and Waves

- Electrostatics

- Current Electricity

- Magnetic Effects of Current and Magnetism

- Electromagnetic Induction and Alternating Currents

- Electromagnetic Waves

- Optics

- Dual Nature of Matter and Radiation

- Atoms and Nuclei

- Electronic Devices

### Chemistry

- Basic Concepts of Chemistry

- States of Matter

- Atomic Structure

- Chemical Bonding and Molecular Structure

- Chemical Thermodynamics

- Solutions

- Equilibrium

- Redox Reactions and Electrochemistry

- Chemical Kinetics

- Surface Chemistry

- Hydrogen

- s-Block Elements

- p-Block Elements

- d- and f-Block Elements

- Coordination Compounds

- Environmental Chemistry

- Some Basic Principles of Organic Chemistry

- Hydrocarbons

- Organic Compounds Containing Halogens, Oxygen, Nitrogen, and Sulphur

- Polymers

- Biomolecules

- Chemistry in Everyday Life

### Mathematics

- Sets, Relations, and Functions

- Complex Numbers and Quadratic Equations

- Matrices and Determinants

- Permutations and Combinations

- Mathematical Induction

- Binomial Theorem and Its Simple Applications

- Sequences and Series

- Limit, Continuity, and Differentiability

- Integral Calculus

- Differential Equations

- Coordinate Geometry

- Three-Dimensional Geometry

- Vector Algebra

- Statistics and Probability

- Trigonometry

Tips for Effective Time Management during JEE Main Preparation

Effective time management is crucial when it comes to preparing for JEE Main. With a vast syllabus to cover, it's important to make the most of the time you have. Here are some tips for effective time management during JEE Main preparation:

Create a study schedule: Create a study schedule that covers all the topics in the syllabus and allocate time for each topic based on its importance. Make sure to include breaks in your schedule to avoid burnout.

Prioritize topics: Prioritize the topics based on your strengths and weaknesses. Spend more time on the topics you find difficult and less time on the topics you're good at.

Take breaks: Take regular breaks to avoid burnout. Use your break time to relax, exercise or pursue a hobby.

Avoid distractions: Avoid distractions such as social media, TV, and video games during your study time. Keep your phone on silent mode and keep it away from your study area.

Stay organized: Keep your study area clean and organized. Make sure you have all the study material you need within reach.

Effective time management is the key to success when it comes to JEE Main Preparation. By following these tips, you can make the most of the time you have and stay on track with your preparation.

Effective Study Techniques to Ace JEE Main

Studying for JEE Main requires a lot of hard work and dedication. Here are some effective study techniques that can help you ace the exam:

Understand the concepts: Don't just memorize the formulas and equations. Understand the concepts behind them. This will help you solve problems more effectively and efficiently.

Practice regularly: Practice is the key to success when it comes to JEE Main. Solve as many problems as you can from different sources, including previous year question papers and mock tests.

Take short notes: Taking short notes while studying can help you remember important points and formulas. Use diagrams and flowcharts to simplify complex concepts.

Revise regularly: Revision is crucial when it comes to retaining information. Make sure to revise regularly to avoid forgetting what you've learned.

Seek help: Don't be afraid to seek help if you're stuck on a particular topic. Ask your teachers or peers for help, or join an online discussion forum to get your doubts cleared.

Effective study techniques can help you stay focused and motivated during your JEE Main Preparation. By following these techniques, you can improve your understanding of the concepts and increase your chances of acing the exam.

Importance of Solving Previous Year Question Papers

Solving previous year question papers is one of the most effective ways to prepare for JEE Main. Here's why:

Helps you understand the exam pattern: Solving previous year question papers can help you understand the exam pattern and the types of questions asked in the exam.

Helps you identify your strengths and weaknesses: By solving previous year question papers, you can identify the topics you're good at and the topics you need to work on.

Helps you manage time: Solving previous year question papers can help you develop time management skills and learn how to solve problems quickly and accurately.

Helps you build confidence: Solving previous year question papers can help you build confidence and reduce exam anxiety.

Make sure to solve as many previous year question papers as you can during your JEE Main preparation. This will help you get a feel for the exam and increase your chances of success.

Recommended Books and Resources for JEE Main Preparation

Choosing the right books and resources is crucial when it comes to JEE Main preparation. Here are some recommended books and resources that can help you ace the exam:

1. Physics:

- Concepts of Physics by H.C. Verma

- Problems in General Physics by I.E. Irodov

- Fundamentals of Physics by Halliday, Resnick, and Walker

2. Chemistry:

- Organic Chemistry by Morrison and Boyd

- Physical Chemistry by P. Bahadur

- Inorganic Chemistry by J.D. Lee

3. Mathematics:

- Mathematics by R.D. Sharma

- Higher Algebra by Hall and Knight

- Problems Plus in IIT Mathematics by A. Das Gupta

Apart from these books, there are several online resources and coaching institutes that can help you with your JEE Main preparation. Make sure to do your research and choose the resources that work best for you.

Online Coaching and Mock Tests for JEE Main

Online coaching and mock tests can be a great way to supplement your JEE Main preparation. Here's how:

Provides flexibility: Online coaching and mock tests provide flexibility in terms of timing and location. You can access the resources from anywhere and at any time.

Provides personalized learning: Online coaching and mock tests provide personalized learning based on your strengths and weaknesses.

Helps you track your progress: Online coaching and mock tests help you track your progress and identify areas where you need to improve.

Provides expert guidance: Online coaching and mock tests provide expert guidance from experienced teachers and mentors.

There are several online coaching institutes and websites that offer Mock Tests and study materials for JEE Main preparation. Make sure to choose the ones that provide quality resources and have a good track record.

Common Mistakes to Avoid during JEE Main Preparation

Avoiding common mistakes can help you stay on track with your JEE Main preparation and increase your chances of success. Here are some common mistakes to avoid:

Procrastination: Procrastination can lead to poor time management and lack of preparation. Make sure to start your preparation early and stick to your study schedule.

Lack of focus: Lack of focus can lead to poor retention of information. Make sure to avoid distractions and stay focused during your study time.

Lack of practice: Lack of practice can lead to poor problem-solving skills. Make sure to solve as many problems as you can from different sources.

Overconfidence: Overconfidence can lead to complacency and lack of preparation. Make sure to stay humble and avoid underestimating the exam.

By avoiding these common mistakes, you can stay on track with your JEE Main preparation and increase your chances of success.

Exam Day Strategies for JEE Main

Exam day can be stressful, but with the right strategies, you can stay calm and focused. Here are some exam day strategies for JEE Main:

1. Get enough sleep: Make sure to get enough sleep before the exam to avoid fatigue and lack of concentration.

2. Eat a healthy breakfast: Eating a healthy and nutritious breakfast can help you stay alert and focused during the exam.

3. Arrive early: Arrive at the exam centre early to avoid rushing and to familiarize yourself with the surroundings.

4. Read the instructions carefully: Read the instructions carefully before starting the exam to avoid making mistakes.

5. Manage time effectively: Manage your time effectively during the exam. Don't spend too much time on a single question and make sure to attempt all the questions within the given time frame.

6. Stay calm: Stay calm and avoid panicking during the exam. Take deep breaths and stay focused on the task at hand.

By following these strategies, you can stay calm and focused during the JEE Main exam and increase your chances of success.

Conclusion

Preparing for JEE Main can be challenging, but with the right strategies and techniques, you can ace the exam and secure your future as an engineer. Understanding the JEE Main Exam Pattern, covering the syllabus, effective time management, and regular practice are some of the key factors that can help you succeed in the exam. Make sure to follow the tips and advice shared in this article to stay on track with your preparation and increase your chances of success. Good luck!

#JEE Main Exam 2024 #JEE Main Exam Pattern #JEE Main Syllabus 2024 #JEE Main Preparation #JEE Main Online Mock Tests

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doubtapp · 3 years ago

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JEE MAIN 2022: IMPORTANT TOPICS FOR MATHEMATICS

In this article, we will go through all the important chapters and topics of mathematics that carry high weightage in the exam and will help you score high.

The JEE Main test, a national-level entrance exam, is conducted by the National Testing Agency (NTA). JEE Mains Paper 1 is for undergraduate engineering admissions, whilst Paper 2 is for undergraduate architecture admissions. Every engineering student’s dream is to be admitted to a prestigious university and pursue a career in their chosen engineering world. This can be achieved with a basic understanding of major concepts and chapters.

Understanding the complete JEE Main 2022 syllabus with weightage aids preparation. The JEE Main 2022 syllabus includes the NCERT Class 11 and Class 12 Physics, Chemistry, and Mathematics courses. Mastering the most important JEE Mains 2022 chapters will give you a substantial advantage in the JEE Main exam. In this article, we will go through all the important chapters and topics of mathematics that carry high weightage in the exam and will help you score high.

Mathematics chapters and their weightage-

Chapters

Total Questions

Weightage

Sets

3.3%

Permutations & Combinations

3.3%

Probability

3.3%

Complex Numbers

3.3%

Binominal Theorem

3.3%

Limits

3.3%

Differentiability

3.3%

Indefinite Integration

3.3%

Definite Integration

3.3%

Differential Equations

3.3%

Height & Distance

3.3%

Trigonometric Equations

3.3%

The Area under the Curve

3.3%

Quadratic Equations

3.3%

Vectors

3.3%

Tangents and Normals

3.3%

Maxima and Minima

3.3%

Statistics

3.3%

Parabola

3.3%

Ellipse

3.3%

Hyperbola

3.3%

Mathematical Reasoning

3.3%

Sequences & Series

6.6%

Straight Lines

6.6%

3-D Geometry

6.6%

Determinants

6.6%

Important topics-

Quadratic Equations & Expressions

Complex Numbers, Probability

Vectors & 3D Geometry

Matrices in Algebra

Circle, Parabola, Hyperbola in Coordinate Geometry

Functions

Limits

Continuity and Differentiability

Application of Derivatives

Definite Integral in Calculus

This subject takes a lot of practice. The questions are of high quality and will necessitate some effort on your part to answer them. The more you learn and practice mathematics, the better your analytical and problem-solving skills will become. Math problems in JEE can be lengthy and it is important to learn all the formulas and concepts as they are the key element in this subject.

If you preparing for the JEE exam and are facing doubts related to any topic, do check out the doubt buddy app. It is the best doubt-solving app that provides instant and 24/7 solutions to all your problems. It has the best tutors that will guide you through your studies and will strengthen your preparation.

Check out more articles from us- https://blog.doubtbuddy.com

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juniperpublishers-ttsr · 5 years ago

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Using Data Science to Establish Relationships between Key Railroad Engineering Parameters and Behavior

Abstract

The railroad industry is an infrastructure intensive industry that has found itself collecting large volumes of data due in part to the implementation of a new generation of sophisticated inspection and monitoring systems. These systems, which are being utilized to monitor infrastructure condition, optimize and plan maintenance, and improve safety, have resulted in an exponential growth in data collected. While traditional analysis of data, particularly "threshold” based analysis, are still being used, there is a growing awareness of and use of "Data Science” to provide new and innovative insights and an improved understanding of maintenance and safety issues [1,2].

Keywords: Data science; Railroad engineering; Infrastructure intensive industry; Big data

Introduction

Data Science is an interdisciplinary field using evolving analysis tools and techniques to extract knowledge or insights from data in various forms, either structured or unstructured. Data Science provides ways (and tools) to deal with and benefit from "Big Data”, to include ways to see patterns, discover relationships, and develop predictive analytic capabilities and to make sense of varied images, data streams and information. Data Science in railway engineering applications attempts to represent the complexities of huge volumes of both structured and unstructured data collected by the full range of inspection and management systems with the goal of obtaining new and useful insights into such phenomenon as track and equipment component degradation and failure.

Recent studies looking at the relationship between several key track measurement and failure parameters have provided such insights [3-6]. Two such studies will be briefly discussed here as examples of how Big Data can lead to not just insights, but actually predictive relationships that have direct and practical application in railroad engineering.

One such study examined the relationship between track geometry defects and rail defects, two separate and distinct classes of defects associated with different parts of the railroad track structure [3,4]. Rail defects are associated with failure in the rail itself, while track geometry defects, which represent degradation of the track geometry in either the vertical or lateral planes, are most commonly associated with failure in the rail supporting structure, such as the cross-ties, ballast or sub grade (soil).

In order to examine this relationship, the study correlated multiple years of track geometry with a data base of several years of rail defects obtained from a major US railroad. The railroad system data represented more than 35,000 track km, and included three years of rail defect data, representing approximately 50,000 defect records (which was subsequently narrowed to approximately 26,000 defects of "interest”), five years of track geometry data representing approximately 335,000 defect records, and traffic/tonnage data (in annual Million Gross Tonnes or MGT) [3,4].

Correlation and statistical analyses were performed and two sets of analyses relationships were developed. The first was a relationship between the life of rail (in cumulative MGT) and the presence of geometry defect(s). The second was a relationship between the probability of a rail defect occurring at a given location and the presence of one of more geometry defects at that location.

Initial correlation analysis showed that 11&percnt; of all rail defects were preceded by one or more track geometry defects. In contrast, if the relationship between rail defects and geometry defects were purely random the probability of a match at a given location was calculated to be 1.4&percnt; on curves; the results were even more dramatic, with 21&percnt; of all rail defects preceded by one or more geometry defects. Thus, the actual percentages of matches were of the order of 7 to 20 times that which would occur purely by random chance.

A series of statistical analyses, using Multivariate Adaptive Regressive Splines (MARS) analysis, were performed examining the relationship between the 'age” of the rail, at the time of defect occurrence and the presence of track geometry defects. The results showed a reduction in the time it took a rail defect to develop of between 20&percnt; and 44&percnt;, if a track geometry defect was present.

In addition to this reduction in "life” of the rail, a second series of analyses were performed looking at the probability of a rail defect occurring given a geometry defect preceding it. The Probability analysis approaches used included Random Analysis and Conditional Probability Analysis (Bayes' Theorem probability analysis, Naive Bayes probability analysis, and Bayesian network analysis). Figure 1 illustrates the Bayesian network model structure. The presence of four geometry defects (though not necessarily at the same time) prior to the development of the rail defect results in a probability of a rail defect occurring of 88.6&percnt; (about 500 times random).

The results of the analysis showed that the presence of a geometry defect has a strong and well-defined effect, with the probability of a rail defect occurring at the location where there was one of more preceding geometry defects being strong and significant. Thus, a single geometry defect increases the probability of a rail defect (from random) by 6 to 13 times, while multiple geometry defects will increase the probability of a rail defect (from random) by factors of up to 600 times. Thus 2 geometry defects increase the probability of a rail defect to approximately 10 to 20&percnt; depending on defect type, 3 geometry defects increase probability of a rail defect to approximately 40 to 50&percnt;, and 4 geometry defects increase probability of a rail defect to approximately 80 to 90&percnt;.

The second analysis looked at the relationship between missing ballast and the development of track geometry defects. This was a two-phase analysis with the initial phase [5] looking at ballast data taken from a major US railroad consisting of 187,025 segments, each approximately 15 meters in length, for a total length of approximately 2800 km of track. A total of 5440 geometry defects were reported within that stretch of track, distributed over 2278 segments, with many segments having multiple reported geometry defects. The second phase [6] broadened the analysis, looking at missing ballast volume data on 105,416 segments of data. The length of the segments had an average and median value of 5.6m (18.74 feet) and 15m (49.98 feet) respectively. A total of 22,919 track geometry exceptions were included in the data set.

Figure 2 shows the results of the first phase analysis, where the rate of development of ballast-related defects is positively correlated to the volume of missing ballast in a non-linear relationship Thus, this data strongly supports the idea that missing ballast section (specifically shoulder ballast) will contribute to the development of ballast related track geometry defects).

Figure 3 presents the results of the second phase analysis where a Logistics Regression Model is used to define the probability that a ballast related geometry exception or defect will develop in a given segment as a function of the volume of missing ballast and the annual traffic level (in MGT). Note that as a segment has increased volume of missing ballast, the probability the segment will contain a ballast related exception increases. This is also the case as annual traffic increases.

Thus, the second study shows that increasing volumes of missing ballast results in increases in the occurrence of track geometry defects, and in particular the ballast related track geometry defects, in those segments that have the missing ballast. The results provide a quantifiable relationship, in form of first a quadratic equation, and then a Logistics Regression model between missing ballast and the rate of development of segments with geometry defects.

These are but two examples of the increasing use of Data Science in the analysis of railroad inspection and condition data. They illustrate how "Big Data' analysis techniques are effective in dealing with large volumes and with large scale data bases where relationships between parameters are not always intuitively obvious. As such these "data science” tools (e.g. MARS, Bayesian analysis, Logistic Regression, etc.) within the Big Data paradigm can be applied to other areas where large scale data bases are available but have not been used for anything but the most basic exception reporting and data base uses.

Furthermore, the results presented here show that Data Science can be used to provide models to predict the probability that a given track segment will generate defects or exceptions as a function of key independent variables such as currently obtained by railroad inspection vehicles. This methodology shows real promise in its potential for development of "practical” tools that can be used by railroads in their maintenance planning and management processes. Such "practical” models would allow railways to plan and prioritize maintenance based on a number of factors, such as component condition, annual tonnage, curvature and other data to be explored. This allows for proper prioritization by considering interactivity of predictors which is inherent to Data Science models, and not just looking at simple threshold exceedances.

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extramarksonlinestudymaterial · 5 years ago

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ICSE Class 12th Mathematics Study Materials and Video Lectures at Extramarks Study Application

ICSE Syllabus for Class 11 Maths includes all necessary topics to clear major entrance exams and conquer the ICSE board exams as well. The syllabus includes topics such as Sets, Relations & Functions, Trigonometric Functions, Principle of Mathematical Induction, Complex Numbers and Quadratic Equations. The content of these topics are the basics to various other topics that students study in higher classes, and hence, have been explained in good detail in the ICSE Syllabus for Class 11 Maths. Aims: 1. To allow applicants to acquire knowledge and establish understanding in high-level secondary mathematical terms, concepts, symbols, meanings, values, processes and formulas. 2. Develop the ability to apply knowledge and understanding of mathematics to unfamiliar situations or new challenges. 3. To develop skills of (a) computation. (b) Reading tables, charts, graphs, etc. 4. Develop an appreciation of the role of mathematics in everyday life. 5. To develop an interest in Mathematics. 6. Develop a scientific attitude through the study of mathematics. There will be a paper with a duration of three hours of 100 marks. A, B, and C divide the curriculum into three parts. Section A is compulsory for all candidates. Candidates have the option of either Section B or Section C to attempt questions. Section A will consist of 9 questions. Section B / C Candidates will be required to answer two questions out of three from either Section B or Section C. Students should complete their ICSE Syllabus for Class 11 Maths in time so they can start revision in time.

#icse syllabus for class 11 maths

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vidyakul-blog · 7 years ago

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Download NCERT Solutions Class 11 Free

Vidyakul gives NCERT solutions class 11 Maths, NCERT solutions class 11 Physics and NCERT solutions class 11 Chemistry in PDF frame. NCERT Solutions being a fundamental asset for the individuals who need to score well in their class 11 PCM exam. The solutions of parts incorporate answers for each inquiry and help understudies to plan well and score great imprints. Presently get simple access to class 11 PCM NCERT solutions of the considerable number of sections in a part astute way. For those understudies who experience difficulty discovering answers for their activity can allude to the NCERT solutions that are given as these solutions are set up by master instructors. Fathoming these activities and honing them will assist the understudies with achieving most extreme stamps in their exam. Subsequently, understudies who need to score well in their exam ought to get ready by utilizing the NCERT books.

Free Download NCERT Solutions Class 11 Chemistry PDF

NCERT Solution Chapter 1 Some Basic Concepts of Chemistry NCERT Solution Chapter 2 Structure of Atom NCERT Solution Chapter 3 Classification of Elements and periodicity in properties NCERT Solution Chapter 4 Chemical Bonding and Molecular Structure NCERT Solution Chapter 5 States of Matter NCERT Solution Chapter 6 Thermodynamics NCERT Solution Chapter 7 Equilibrium NCERT Solution Chapter 8 Redox Reaction NCERT Solution Chapter 9 Hydrogen NCERT Solution Chapter 10 The S-Block Element NCERT Solution Chapter 11 The P-Block Element NCERT Solution Chapter 12 Organic Chemistry- Some Basic Principle and Techniques NCERT Solution Chapter 13 Hydrocarbons NCERT Solution Chapter 14 Environmental Chemistry

Free Download NCERT Solutions Class 11 Maths PDF

NCERT Solution Chapter 1 Sets NCERT Solution Chapter 2 Relations & Functions NCERT Solution Chapter 3 Trigonometric Functions NCERT Solutions Chapter 4 Principle of Mathematical Induction NCERT Solution Chapter 5 Complex Numbers and Quadratic Equations NCERT Solution Chapter 6 Linear Inequalities NCERT Solution Chapter 7 Permutations and Combinations NCERT Solution Chapter 8 Binomial Theorem NCERT Solution Chapter 9 Sequence and Series NCERT Solution Chapter 10 Straight Lines NCERT Solution Chapter 11 Conic Sections NCERT Solution Chapter 12 Introduction to Three dimensional Geometry NCERT Solution Chapter 13 Limits and Derivatives NCERT Solution Chapter 14 Mathematical Reasoning NCERT Solution Chapter 15 Statistics NCERT Solution Chapter 16 Probability Free Download NCERT Solutions Class 11 Physics PDF

NCERT Solution Chapter 1 The Physical World NCERT Solution Chapter 2 Units and Measurements NCERT Solution Chapter 3 Motion in a Straight line NCERT Solution Chapter 4 Motion in a Plane NCERT Solution Chapter 5 Laws of Motion NCERT Solution Chapter 6 Work, Energy and Power NCERT Solution Chapter 7 Systems of Particles and Rotational Motions NCERT Solution Chapter 8 Gravitation NCERT Solution Chapter 9 Mechanical Properties of Solids NCERT Solution Chapter 10 Mechanical Properties of Fluids NCERT Solution Chapter 11 Thermal Properties of Matter NCERT Solution Chapter 12 Thermodynamics NCERT Solution Chapter 13 Kinetic Theory NCERT Solution Chapter 14 Oscillations NCERT Solution Chapter 15 Waves

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