#three dimensional geometry class 12

[shiva10010]

JEE Main 2025! Prep Your Math Strategy with the Latest Syllabus

The Joint Entrance Examination (JEE) Main is a critical gateway for aspiring engineers in India. While the official syllabus for JEE Main 2025 will likely be released by the National Testing Agency (NTA) in November 2024, you can get a head start on your preparation using the previous year's syllabus as a guide.

This article focuses on the Mathematics section of the JEE Main 2025 exam.

Key Elements of the JEE Main 2025 Maths Syllabus

The JEE Main Maths syllabus covers a wide range of topics from Class 11 and 12 NCERT textbooks. Here's a quick glimpse of the major areas you'll encounter:

Algebra: Sets, relations and functions, complex numbers, matrices and determinants, mathematical induction, binomial theorem, sequence and series.

Calculus: Limit, continuity and differentiability, integral calculus, differential equations.

Geometry: Coordinate geometry, three-dimensional geometry, vector algebra.

Other Quantitative Techniques: Statistics and probability, trigonometry, mathematical reasoning.

Why eSaral is Your Perfect JEE Main 2025 Maths Companion

While the syllabus provides a roadmap, in-depth preparation is essential for success. This is where eSaral steps in:

Complete Syllabus Coverage: eSaral ensures you cover all the essential JEE Main Maths topics.

Detailed Learning Material: Access a treasure trove of resources, including crisp explanations, illustrative examples, and topic-wise revision notes [refer to JEE Main 2025 Maths Revision Notes on eSaral for details].

Catered Learning Styles: Whether you prefer short and focused content or a deep dive into concepts, eSaral offers options to match your learning style.

Practice Makes Perfect: Sharpen your skills with ample practice problems available on the platform.

Additional Tips to Conquer JEE Main 2025 Maths

Focus on NCERT Textbooks: They form the foundation for the entire syllabus.

Regular Practice: Solve problems consistently to build speed, accuracy, and exam temperament.

Mock Tests: Take regular mock tests to simulate the exam environment and identify areas for improvement.

Clear Your Doubts: Don't hesitate to seek clarification from teachers or online forums.

Conclusion

JEE Main 2025 Maths can be aced with the right approach and resources. By leveraging the detailed syllabus and comprehensive learning materials offered by eSaral, you can approach the exam with confidence and a strategic plan. Remember, consistent effort and focused practice are key to achieving your engineering dreams.

[mpboardsolutions-blog]

MP Board Class 12th Maths Book Solutions in English Medium

MP Board Class 12th Maths Chapter 1 Relations and Functions

Chapter 1 Relations and Functions Ex 1.1

Chapter 1 Relations and Functions Ex 1.2

Chapter 1 Relations and Functions Ex 1.3

Chapter 1 Relations and Functions Ex 1.4

Chapter 1 Relations and Functions Miscellaneous Exercise

MP Board Class 12th Maths Chapter 2 Inverse Trigonometric Functions

Chapter 2 Inverse Trigonometric Functions Ex 2.1

Chapter 2 Inverse Trigonometric Functions Ex 2.2

Chapter 2 Inverse Trigonometric Functions Miscellaneous Exercise

MP Board Class 12th Maths Chapter 3 Matrices

Chapter 3 Matrices Ex 3.1

Chapter 3 Matrices Ex 3.2

Chapter 3 Matrices Ex 3.3

Chapter 3 Matrices Ex 3.4

Chapter 3 Matrices Miscellaneous Exercise

MP Board Class 12th Maths Chapter 4 Determinants

Chapter 4 Determinants Ex 4.1

Chapter 4 Determinants Ex 4.2

Chapter 4 Determinants Ex 4.3

Chapter 4 Determinants Ex 4.4

Chapter 4 Determinants Ex 4.5

Chapter 4 Determinants Ex 4.6

Chapter 4 Determinants Miscellaneous Exercise

MP Board Class 12th Maths Chapter 5 Continuity and Differentiability

Chapter 5 Continuity and Differentiability Ex 5.1

Chapter 5 Continuity and Differentiability Ex 5.2

Chapter 5 Continuity and Differentiability Ex 5.3

Chapter 5 Continuity and Differentiability Ex 5.4

Chapter 5 Continuity and Differentiability Ex 5.5

Chapter 5 Continuity and Differentiability Ex 5.6

Chapter 5 Continuity and Differentiability Ex 5.7

Chapter 5 Continuity and Differentiability Ex 5.8

Chapter 5 Continuity and Differentiability Miscellaneous Exercise

MP Board Class 12th Maths Chapter 6 Application of Derivatives

Chapter 6 Application of Derivatives Ex 6.1

Chapter 6 Application of Derivatives Ex 6.2

Chapter 6 Application of Derivatives Ex 6.3

Chapter 6 Application of Derivatives Ex 6.4

Chapter 6 Application of Derivatives Ex 6.5

Chapter 6 Application of Derivatives Miscellaneous Exercise

MP Board Class 12th Maths Chapter 7 Integrals

Chapter 7 Integrals Ex 7.1

Chapter 7 Integrals Ex 7.2

Chapter 7 Integrals Ex 7.3

Chapter 7 Integrals Ex 7.4

Chapter 7 Integrals Ex 7.5

Chapter 7 Integrals Ex 7.6

Chapter 7 Integrals Ex 7.7

Chapter 7 Integrals Ex 7.8

Chapter 7 Integrals Ex 7.9

Chapter 7 Integrals Ex 7.10

Chapter 7 Integrals Ex 7.11

Chapter 7 Integrals Miscellaneous Exercise

MP Board Class 12th Maths Chapter 8 Application of Integrals

Chapter 8 Application of Integrals Ex 8.1

Chapter 8 Application of Integrals Ex 8.2

Chapter 8 Application of Integrals Miscellaneous Exercise

MP Board Class 12th Maths Chapter 9 Differential Equations

Chapter 9 Differential Equations Ex 9.1

Chapter 9 Differential Equations Ex 9.2

Chapter 9 Differential Equations Ex 9.3

Chapter 9 Differential Equations Ex 9.4

Chapter 9 Differential Equations Ex 9.5

Chapter 9 Differential Equations Ex 9.6

Chapter 9 Differential Equations Miscellaneous Exercise

MP Board Class 12th Maths Chapter 10 Vector Algebra

Chapter 10 Vector Algebra Ex 10.1

Chapter 10 Vector Algebra Ex 10.2

Chapter 10 Vector Algebra Ex 10.3

Chapter 10 Vector Algebra Ex 10.4

Chapter 10 Vector Algebra Miscellaneous Exercise

MP Board Class 12th Maths Chapter 11 Three Dimensional Geometry

Chapter 11 Three Dimensional Geometry Ex 11.1

Chapter 11 Three Dimensional Geometry Ex 11.2

Chapter 11 Three Dimensional Geometry Ex 11.3

Chapter 11 Three Dimensional Geometry Miscellaneous Exercise

MP Board Class 12th Maths Chapter 12 Linear Programming

Chapter 12 Linear Programming Ex 12.1

Chapter 12 Linear Programming Ex 12.2

Chapter 12 Linear Programming Miscellaneous Exercise

MP Board Class 12th Maths Chapter 13 Probability

Chapter 13 Probability Ex 13.1

Chapter 13 Probability Ex 13.2

Chapter 13 Probability Ex 13.3

Chapter 13 Probability Ex 13.4

Chapter 13 Probability Ex 13.5

Chapter 13 Probability Miscellaneous Exercise

[studyupindia]

NCERT Class 12 Mathematics Part-II ( English Medium )

All books are 100℅ original on Studyupindia.com ( Online NCERT Book Store ) as per the latest NCERT syllabus.

This NCERT Class 12 History Books Contains  :

Mathematics (Part  2)

Chapter 7.  Integrals

Chapter 8. Application of Integrals

Chapter 9. Differential Equations

Chapter 10. Vector Algebra

Chapter 11. Three Dimensional Geometry

Chapter 12. Linear Programming

Chapter 13. Probability

As Studyupindia provides products with quick delivery, easy exchanges from trusted sellers .

[meritbatch]

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

[learnsarthaks]

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!

[ashishkumarletslearn]

#ThreeDimensionalGeometry #Class12Maths #CBSEBoard

Three Dimensional Geometry Class 12 Maths Chapter 11.

[studiestoday123]

Download MCQs for Class 12 Three Dimensional Geometry for important topics for all chapters in Class 12 Three Dimensional Geometry based on CBSE and NCERT pattern. Multiple choice questions help to develop understanding of all key points of chapter. Download latest MCQs for Class 12 Three Dimensional Geometry in pdf free

https://www.studiestoday.com/multiple-choice-questions/481/three-dimensional-geometry.html

[the-fae-folk]

your story talked about faeries being able to see stuff that humans can't (the dark fire). And you said it was similar to gamma rays. can faeries see colors we can't?

Yes indeed, many of the folk are able to see a very different range upon the electromagnetic spectrum, or even a much greater range. They may even be able to differentiate more individual shades in every hue. And of course, let us not forget that they could even be capable of seeing colors entirely unique, colors we cannot even imagine. That is... assuming that their ability to perceive such things manifests as anything remotely like our ability to see certain wavelengths of light as color. Perhaps instead they might hear it, or smell it instead. Or maybe exactly 333 tiny sense organs that are easily mistaken for the tips of antlers or some other such appendage will all send a specific signal to their brains upon being hit with an exact frequency of light wave and their brain will move the 12 bones in their left vestigial wing in such a way that the twitch tells them exactly what color they're seeing. Sort of like an internal dowsing rod. An entirely different sense altogether, with all of its own nuances and insights. All of this is speculation based upon the assumption that their senses even work like our own, with nerve ending and sense organs and signals to and from a complicated brain. If, perhaps, a Faerie were to be closer to a tree, then they might sense things in the ways of those ancient standing sentinels. Trees (and other plants) have photoreceptors all over their bodies instead of contained within eyes (though you may yet meet a tree with two or significantly more eyes) and thus are capable of seeing light in a way. They speak through their roots by sending out trace amounts of chemicals into the soil and through vast networks of tree roots and fungus roots. For all you and I know, the Dryads we see as beautiful women, and the Greenmen who guard the lonely forests, could merely be a projection, a sort of living avatar of the trees or the forest. Not true in of itself, but for your benefit, a humanoid form where the preferred tree wouldn't do. (It is proposed by some researchers that not only do plants possess all five senses commonly found in humans, after a fashion, but approximately fifteen further ones that we do not possess nor require. I'm ever so excited to see where this line of research leads.) But of course, besides grand extensions of the senses we are familiar with, as well as a series of new and unique new senses we can only guess at that come with strange sense organs or entirely different biological makeups, we still have further to dream of the Folk and what they might be able to perceive. Once, when you were in a math class, you might have been introduced to the very basics of geometry. Along with a number of formulas, symbols, and numbers which we will not be going in to, they taught you of subjects such as a point, a line, and a plane? Let me remind you some of it. A point is a little dot. It is Zero Dimensional you could say, because it does not extend for any distance in any direction, but remains confined and contained within itself. Then we have a line, stretching infinitely in two directions. This is One Dimensional. If you were a creature who lived and dwelled in this Dimension you would only be able to perceive things along that line. Not up nor down nor side to side, only forward or back. Let us add another dimension. A plane, flat like a sheet of the thinnest paper in existence, so thin that it becomes invisible if seen perfectly from the edge. A being who lived and died within this plane is Two Dimensional (2D). Forever unable to look to either side, it can only see the things which lie up or down or forward or back, or any other direction you wish to give a name to, so long as it lies upon the plane and not off of it. Then we come to three dimensions (3D). In many ways, humans are in a world of three physical dimensions (at least as far as we are able to perceive for now). Like the dimensions before, it merely adds one more vector to our flat plane, one more direction in which we are able to move. Instead of a flat surface, we can suddenly move forward, back, up,

down, and side to side. Now.... what if we went further? It is easy enough in mathematics, simply account for a fourth vector, add one more set of numbers to take into account for your calculations. But how would that translate for us? We who are trapped so happily within our own perceptions? Well... let us return to our flat plane. If we were to send a sphere through the flat plane, any living flat being would see only a circle. But to their astonishment the circle would first appear from nowhere at all, then grow to an enormous size, then inexplicably shrink before vanishing once more. You see, the flat person we've made up for this exercise is only capable of seeing things that are directly on their flat plane. It can only see one very very thin slice of the sphere at any given time, so as the sphere moves through their flat world and off to the other side it appears to be changing through some strange sorcery. Now, sadly, we must cause our fictitious flat person, whom I have arbitrarily decided to name Wendell, a certain amount of emotional stress. Let us take poor, flat Wendell and turn him so that he is facing a direction that is not normally accounted for on his 2D plane. He cannot, of course, turn back. This is because he lacks the capability to turn sideways, so for the same reason he was unable to turn in this direction to begin with is why he cannot turn away from it now that we have turned him. So what shall Wendel see? Well more of the world, parts of it that connect and work with the parts he knows so well, but that he was never able to see or interact with before, parts he didn't even know were there. Like suddenly finding a new hallway in your own house that reveals an entire wing you were unaware of, but yet you cannot seem to get back to the parts you know, despite still being able to see the faded flowered wallpaper you picked out three years ago, still see the yard from the window (it is not a part of the yard you recognize, clearly your yard, but a section where the grass hasn't been mown in some time). Perhaps, if he stands in exactly the right place, Wendell might be able to hear the television still going in the living room where he left it on, still be able to catch a glimpse of the newspaper he just sat on the countertop in the kitchen. When he is where his old plane and his new plane intersect, he might be able to catch the briefest glimpse of the place he knows he ought to be. Let us restore Wendell to his proper place and look at the problem in another way. Let's say you start with a square. A flat shape. Then lets make it 3 Dimensional, a cube. Excellent. Now it has six different sides to it. But perhaps our little cube friend is being mischievous and continues on without us, becoming an entirely 4 Dimensional shape without our knowing it. What would that be like? Well... to our eyes, it would remain very much cube shaped. We could turn it and look at each side in turn, but what's this? The cube now seems to have 24 different faces instead of the usual six. As you turn it, the object seems to shift its shape, becoming almost like a hexagonal prism or a rhombic dodecahedron, before eventually returning to the shape you're familiar with but with a side you are not. This is no longer a cube, but a Tesseract, a four dimensional shape. But where is this extra part of the Tesseract at? Why can't you see it without turning this cube? It is because you are turning it through your dimension, leaving the missing sides in a fourth spatial dimension you cannot see. A direction you cannot look in. Some might like to argue that Time is the fourth dimension, and in a way, they too are correct. But that's only for a very specific type of calculations and isn't entirely relevant when looking at spatial dimensions. You could describe our ordinary every day world as 3 Dimensions of Space, and 1 Dimension of Time. Separate, but there with the other three. Now of course, you could continue on this way in mathematics, adding further vectors, directions, to shapes. Describing with fancy numbers all the

shapes you might find in a 4th, 5th, 6th, 7th, 8th or even higher dimension. But because your average everyday human can only see in the usual 3 dimensions, it becomes very difficult to visualize what things might look like with extra dimensions added on. So some mathematicians have tried to solve the problem in various ways. They either look at a four dimensional shape in a large number of slices (or pieces) and try to understand it that way, or they unfold it until it's a flat shape and they can count all the points and edges. Not a good method for seeing it properly in its entirety, but unless we manage to develop four dimensional vision it's really all we have to work with. You're probably wondering how this deals with the Folk. I shall tell you. Imagine a faerie creature who, for all intents and purposes, appeared more or less human. Maybe they move in a slightly odd way, and seem to possess very odd abilities regarding their appearance (seeming to shift colors and shapes and details with every new angle or movement). But still, they look human. Yet... you cannot help but feel something is off. This hypothetical Faerie Creature is actually a being who lives in no less than 7 Dimensions at once. A very complicated creature with a very odd and complex form. As it not only needs to interact with its fellow 7D friends but also all the Faeries and humans who exist only in dimensions below it, it has to adapt so that what each dimension sees is something they can understand. So should you suddenly gain the ability to see in 4 Dimensions you would see more of this Faerie Creature than you would before, though not all by any means. Now that we've explored this idea somewhat, let's make some important points. Some physicists have the most annoying tendency to point out various details such as the fact that we've not discovered evidence that further spatial dimensions exist or that if they do they might be very finite and looking in that direction wouldn't show you anything because it doesn't go very far (via experiments mostly to do with gravity). And others might sit and argue about the semantics of what a dimension is defined as and why time is one or isn't one, etc etc. They also love to point out that the landscape of physics is always turning, always changing, and that new things are discovered all the time which wipe away entire categories of thinking that no longer work. Or how there are a lot of mathematical ideas that are entirely abstract and theoretical with no current basis in real life. All of this is absolutely true, and well done to them for being aware of it. But still, rushing in to point it out at every opportunity is still an incredibly annoying habit. Regardless, another important thing to consider is how very alien the way a being who can not only boast of vastly different senses but extra dimensions on top of that would be to us. While not impossible for us to vaguely conceive of and write about in a tale, you run the risk of confusing your audience and shattering their willing suspension of disbelief if you stretch it too far. As much as I would love to extend myself entirely into the mindset of my hypothetical 7th Dimensional Faerie Creature with his extra seven inhuman senses and write an epic story from such a viewpoint.... the result would be a very conceptual and avant garde piece with very little for my readers to relate to and even less that they could understand without a great deal of mental effort. While a very fun exercise and test of ability, a way to explore, challenge myself, and develop my skills... It is not a story that is likely to be appreciated. If that's not your goal, then carry on. But the point remains. For those trying to build an audience, you might need to limit how many boundaries you push in each piece, slowly work your way up to greater heights, taking care to give your audience a solid trail to follow. I hope this answers your question. You asked after colors and you received so much more. (It's also entirely possible I've constructed a possible theory for how

"The Backrooms" work now that I think about it. How funny.)

[vectoralgebraclass12]

How to Study Vector Algebra and Three Dimensional Geometry of Class 12 Maths explained by expert teacher.

Lecture -1 Vector Algebra Class 12 Maths Chapter 10

NCERT Exercise 10.1 Vector Algebra Class 12 Maths 

NCERT Exercise 10.2 Vector Algebra Class 12 Maths

How to study Vector Algebra & Three-Dimensional Geometry?

Vector Algebra Class 12 Maths

Vector Algebra Class 12 Assignments

Full Syllabus of Class 12 Maths

[vidfom-com]

Class 11 Maths Chapter 1 - English Medium

NCERT Solutions for Vidfom.com for  Class 11 Maths Chapter 1 - English Medium includes all the important topics with detailed explanation that aims to help students to understand the concepts better. Students who are preparing for their Class 11 exams must go through NCERT Solutions for Vidfom.com for  Class 11 Maths Chapter 1 - English Medium. Going through the solutions provided on this page will help you to know how to approach and [solve the problems.](https://www.vidfom.com)

Students can also find NCERT intext, exercises and back of chapter questions. Also working on Vidfom.com for  Class 11 Maths Chapter 1 - English Medium NCERT Solutions will be most helpful to the students to solve their Homeworks and Assignments on time. Students can also download NCERT Solutions for Vidfom.com for  Class 11 Maths Chapter 1 - English Medium PDF to access them even in offline mode.

NCERT Books for Class 11 Maths – English Medium

Chapter 1: [Sets](https://www.vidfom.com/2020/10/ncert-solutions-for-class-11-maths.html)

Chapter 2: [Relations and Functions](https://www.vidfom.com/2020/10/ncert-solutions-for-class-11-maths_3.html)

Chapter 3: [Trigonometric Functions](https://www.vidfom.com/2020/10/ncert-solutions-for-class-11-maths-chapter-4.html)

Chapter 4: [Principle of Mathematical Induction](https://www.vidfom.com/2020/10/ncert-solutions-for-class-11-maths-chapter-4_5.html)

Chapter 5: [Complex Numbers and Quadratic Equations](https://www.vidfom.com/2020/10/ncert-solutions-for-class-11-maths-chapter-5.html)

Chapter 6: [Linear Inequalities](https://www.vidfom.com/2020/10/Class-11-Maths-Chapter-6%20.html)

Chapter 7: [Permutations and Combinations](https://www.vidfom.com/2020/10/Class-11-Maths-Chapter-7-English-Medium.html)

Chapter 8: [Binomial Theorem](https://www.vidfom.com/2020/10/class-11-maths-chapter-8-binomial.html)

Chapter 9: [Sequences and Series](https://www.vidfom.com/2020/10/Class-11-Maths-Chapter-9-English-Medium.html)

Chapter 10: [Straight Lines](https://www.vidfom.com/2020/10/Class-11-Maths-Chapter-10-English-Medium.html)

Chapter 11: [Conic Sections](https://www.vidfom.com/2020/10/class-11-maths-chapter-11-conic.html)

Chapter 12: [Introduction to Three Dimensional Geometry](https://www.vidfom.com/2020/10/class-11-maths-chapter-12-introduction.html)

Chapter 13: [Limits and Derivatives](https://www.vidfom.com/2020/10/class-11-maths-chapter-13-limits-and.html)

Chapter 14: [Mathematical Reasoning](https://www.vidfom.com/2020/10/Class-11-Maths-Chapter-14-English-Medium.html)

Chapter 15: [Statistics](https://www.vidfom.com/2020/10/class-11-maths-chapter-15-statistics.html)

Chapter 16: [Probability](https://www.vidfom.com/2020/10/Class-11-Maths-Chapter-16-English-Medium.html)

Here we are providing the Chapter-wise NCERT Book for "Class 11 Maths Subject". Students can easily download and access the chapters of Class 11 Maths. Digital edition of "NCERT Books Class 11 Maths pdf" are always handy to use when you do not have access to a physical copy. Here you can get "Class 11 Maths" NCERT Books. The "NCERT for Class 11 Maths" Chapters wise relevant topic covered on this page.

NCERT Book for "Class 11 Maths" is a vital resource for students preparing for the 16th Class Examination. In this NCERT Books Class 11 Maths both books are provided with all chapters of the Civics Subject. Get here the complete chapters wise study material of "NCERT Book Class 11 Maths".

We suggest you go through NCERT Book for Vidfom.com for  Class 11 Maths Chapter 1 - English Medium and get the distinguished study materials. Practising these study materials will help you a lot in your school exam & board exam. All NCERT Chapters for Vidfom.com for  Class 11 Maths Chapter 1 - English Medium given here are as per the latest syllabus

Chapter 1 - English Mediumedium  help you. If you have any query regarding Vidfom.com for  Class 11 Maths Chapter 1 - English Medium  drop a comment below and we will get back to you at the earliest.

[azspot]

The revelation, which occurred on July 19, 1595, in the middle of teaching a class on planetary alignment, involved the curious geometric properties of Platonic solids. These are three-dimensional polygons, every face of which is identical: A cube is a Platonic solid. So is a tetrahedron (a pyramid with three faces and one base which are all equilateral triangles). It had been understood since Antiquity—and much discussed by Plato, hence the name—that there can only be five such polygons: The laws of geometry forbid any others. In addition to the tetrahedron and cube, which have respectively four and six faces, there are the octagon (eight), dodecahedron (12), and icosahedron (20). It became obvious to Johannes that God must have interleaved invisible Platonic solids between the orbits of the planets, such that spheres based on the radius of each orbit were contained and in turn contained by each polygon, like a series of nested Russian dolls. Since there were only five Platonic solids there could only be six planetary spheres. The beauty of this geometry was, to Johannes, further proof of the truth of Copernican astronomy.

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CBSE Class 11 Courses Module

Class 11 is the first step in the career. It is generally considered more difficult than class 12. The reason for this is, the study of class 11 is way different from that which students studied till class 10. So, several times it happens that students are unable to cope up with all the subjects together. Hereby, Edubull presents 11 different subjects for students to study according to their interests and stream. The following are the subjects available.

Maths - consist of Sequence and Series, Complex Numbers, Basic Arithmetic and Algebra, Transformation of Equations, Trigonometry, Coordinate Geometry, Circle, Hyperbola, Limits, Differentiability.

Maths Resources-I - Contains Sets, Relations and Functions, Trignometry, Mathematical Induction, Complex Numbers, Linear Inequalities, Permutation & Combination, and Binomial Theorem.

Maths Resources-II - Includes Sequence Series, Straight Lines, Conic Sections, Three Dimensional Geometry, Limits and Derivatives, Mathematical Reasoning, Statistics, and Probability.

Maths resources-III - Illustrates the concept in a very interesting manner which helps the student to understand the concept instead of mugging up formulas.

Maths resources-IV - Focus on more and more practice of sums and give easy ways to solve complicated questions.

Maths resources-V - Provides students the animated videos to learn with even more interest.

Maths resources-VI - Solves the questions in a manner that motivates the students to practice more.

Pre-Algebra - Provides more knowledge about whole number, number concepts, and integers for a better understanding of concepts.

Probability Resources - Is customized only for probability and covers the whole probability concept of class 11.

Arithmetic Maths Resources - Help the students who want to learn about Math 20 - Arithmetic Review.

Algebra Resources - Is customized for algebra lovers and provides a vast knowledge of algebra.

8 Modules to Learn

Every student either faces problems in organic or in inorganic chemistry. Edubull has divided chemistry into 8 modules to make all the branches of chemistry easy for the students.

Chemistry-I - Includes Atomic Structure Part - I, Atomic Structure Part - II, States of Matter, Chemical Bonding, Nuclear Chemistry, Electrochemistry, and Structure of atom.

Chemistry-II - Provides students with complex chemistry concepts like Classification of Elements and Periodicity in Properties, Chemical Bonding, and Molecular Structure, States of Matter in a simplified manner and provides suitable notes of the same.

Chemistry Resources-I - Explains all the concept of class 11 chemistry with several examples and make it way more interesting.

Chemistry Resources-II - Provides an explanation of concepts through animations which makes it interesting for the students to gain the knowledge as well as to learn.

Organic Chemistry Resources-I - Covers 3 chapters of organic chemistry, that are- some basic principles and techniques, hydrocarbons, and environmental chemistry.

Organic Chemistry Resources-II - Covers several topics to provide specialized knowledge for each of the topics i.e. Chirality, Newman Projections, Organic Chemistry Naming Examples, Sn Reactions, E Reactions, Comparing E2 E1 Sn2 Sn1 Reactions, Alcohols, Amine Naming Introduction, and Carboxylic Acid Introduction.

Chem Physical - Enhances the knowledge of students in physical chemistry in several topics which include Some Basic Concept of Chemistry, Atomic Structure, States of Matter, Equilibrium, Thermodynamics, and Redox Reaction.

Chemistry Inorganic Resources - Makes the inorganic chemistry easy for students by explaining Chemical Bonding and Molecular Structure, Classification of Elements and Periodicity, Hydrogen & Water, S Block Elements, and P Block Elements.

8 Modules to Explore Physics with a Wider Point of View

Physics is a weakness of many students. But the key to study physics is understanding each concept properly. Edubull teaches physics to the students in 8 modules.

Physics - Covers all the basic concepts of class 11 physics including Dimensional and Error Analysis, Introduction to Kinematics, Projectile Motion, Kinematics of Circular Motion, Particle Dynamics, Newton’s Law, Wave Motion, and Physical Properties of Waves.

Physics Resources-II - Gives various teaching aids, notes, and practice sessions of various topics which include Gravitation, General Properties of Matter, Thermal Properties of Material, Kinetic Theory of Gases, Oscillations, and Waves.

Physics Resources-III - Helps the students to build interest in physics by explaining different concepts with several examples and practical.

Physics-IV - Clarifies the concepts of topics covered in Physics of ICSE Standard with a lot of examples.

Physics Resources-V - This course is for those who want to learn the concepts of physics in an even more detailed manner.

Science - Clarifies the basic concepts of Theory and makes it more interesting for students in order to motivate students to study even more.

Thermodynamic and kinetic resources -This course is specialized for concepts of thermodynamic and kinetic physics.

Physics Animation - As the name suggests, explains the concepts through animations to make it more interesting. It includes introduction to nuclear reactor and introduction to magnetic field and magnetic field lines of force.

4 Modules to Make Biology more Interesting

However, biology is not that difficult to learn but for those who can’t just mug up and want to understand each and every concept with propper detail, edubull brings up biology in 4 modules.

Biology-I - Helps students to get an in-depth understanding of the basic concepts of topics of the biology of class 11.

Biology resources-II - Displays animated videos that grab the attention of the students who have no interest in the subject and have left it. It is also intended to help clarify the basic concepts of topics through illustrative interactive lectures and practical in a very interesting manner.

Biology resources-III - Illustrates different concepts through interactive lectures and enhance the student’s interest in the subject.

Biology resources-IV - Clarifies the most basic topics of biology.

4 Modules to get the Strategy for Accountancy

Every student gets frustrated when the entries at the last in the accounts answer does not match. Edubull provides you a platform where you can learn accounts in 4 modules and then you’ll easily be able to find your own mistake.

Accounts Resources (double entry book keeping part-1) - Explains several chapters in an easy way which include Introduction to Accounting, Basic Accounting Terms, Theory Base of Accounting, Bases of Accounting, Accounting Equation, Accounting Procedures, Origin of Transaction, Journal and Ledger, Special Purpose Books, Bank Reconciliation Statement, and Trial Balance.

Accounts Resources (double entry book keeping part-2) - Continues part-1 by including topics like Depreciation, Provisions and Reserves, Accounting for Bills of Exchange, Rectification of Errors, Adjustments in Preparation of Financial Statements, Accounts from Incomplete Records, and Computerised Accounting.

Accountancy - Explains the basic chapters of accounts of class 11 which include Accounting Equations, Journal Entries, Final Accounts, and Ledger Posting and Trial Balance.

Introduction to Financial Statement - Is specialized to learn the basic concepts of financial statements.

2 modules to Increase English Proficiency .

For English, edubull has made 2 modules, one of which explains in English and the other in Hindi.

Hornbill - Explains all the chapters of the textbook hornbill in a very interesting manner. The chapters include The Portrait of a Lady, A Photograph, We're Not Afraid to Die, The Voice of the Rain, Discovering Tut: The Saga Continues, Landscape of the Soul, The Browning Version, Childhood, and Father to Son.

Hornbill (Hindi) - Explains all of these in Hindi.

3 modules to Enhance the Skills in Informatics Practices.

For the IP lovers, edubull has made 3 modules to learn and practice.

How to build a computer - Provides students the basic knowledge of Computers and its parts, its importance, and various other basic information about computers so that the learner who is new to computers must learn about building a computer from the beginning.

SQL for beginners - Explains the basics and details of structured query language in both - Hindi and English.

Computer networks - As the name suggests, give knowledge to students about different computer networks.

8 Modules to Enhance the Skills in Computer Science

All the students you want to enrich their skills in the field of computer science have the option here to learn and practice according to their interests.

Introduction to programming - Guides the students in Hindi language about how to do programming and then the tasks are given to students for practice.

Computer science resources - Enrich the students with the basics of the computer that helps the students to start with small programming tasks.

MS Word 2016 (Hindi) - Explains the vast MS Word 2016 in Hindi by dividing it into topics like Beginning, Basic Editing, Formatting, Copying and Moving Text and Objects, Editing Features, Paragraph Formatting, Tables, Page Formatting, Graphics & Pictures, Footnote & Endnote, and Advanced Tools.

Notepad (Hindi) - Explains all the features debate in Hindi.

Windows 10 operating system (Hindi) - Explains windows 10 in detail in Hindi. It’s very useful for those who stay updated with the latest technologies.

MS PowerPoint 2016(Hindi) - This is a module in which PowerPoint is taught within the subheadings like The Fundamentals, Slides, Editing, Formatting, Images, Multimedia, and Objects, and Transitions and Animation Effects.

MS excel 2016 - This is also divided into subtopics to be specific and the topics are The Excel Window, Editing, Formatting, Formulas, Hlookup Vlookup, Pivot, Chart, Short Cuts, and Practice Sheets.

MS excel 2016 (Hindi) - Explains the same in Hindi with somewhat different topics which include The Excel Screen, Formatting, Formulas, Hlookup Vlookup, Pivot, Chart, and Practice Sheets.

3 Modules to learn Business Studies in an Interesting Manner

Business studies is beautifully divided in 3 modules by edubull according to its topics.

Business study resources (foundation of business part-1) - Explains almost all topics of textbook of business studies of class 11, which are Nature and Forms of Business, Forms of Business Organisation, Private, Public and Global Enterprises, Business Services, Emerging Modes of Business, Social Responsibility of Business and Business Ethics.

Business study resources (finance and trade part -2) - This is divided into 2 topics, that are sources of business finance and small business.

Business finance - This is personalized for those who want to startup with a new business.

7 Modules to understand the importance of Physical Education.

However, yoga is a vast practice, still, edubull has tried to collect the most of it within 7 modules.

Yoga postures by Shilpa - is a module that makes the students learn about various yoga postures and get motivated to stay healthy.

Face Yoga - is very useful for the students who stay up till late because it puts a great effect on how the face looks.

Diet and nutrition - teaches the students about how can one stay fit with a balanced diet.

Healthy eating tips - is somewhat similar to diet and nutrition, yet a lot different from it. You’ll know the difference, once you’ll attend the lectures.

Get healthy, get happy - is a module in which students are counseled to stay happy in order to be fit physically.

Yoga for Kids - brings out wonderful yoga postures specialized for kids which are highly effective on a child’s growth and development.

Yoga in office - Yoga in office’ is based on stretching which should be done while prolong sitting.

1 module to enrich your interest in Political Science

Since it just has 1 module ‘political science’, it is divided into several chapters in order to gain the most. The chapters are Constitution Why and How?, Rights in Indian Constitution, Election and Representation, Executive, Legislature, Judiciary, Federalism, Local Governments, Constitution as a Living Document, and The Philosophy of the Constitution.

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NCERT Class 11 Math [ English Medium ]

(All books are 100℅ original and as per the latest NCERT syllabus. Prices includes Rs. 32 per book mandatory binding charges.)

Chapter 1: Sets Chapter 2: Relations and Functions Chapter 3: Trigonometric Functions Chapter 4: Principle of Mathematical Induction Chapter 5: Complex Numbers and Quadratic Equations Chapter 6: Linear Inequalities Chapter 7: Permutations and Combinations Chapter 8: Binomial Theorem Chapter 9: Sequences and Series Chapter 10: Straight Lines Chapter 11: Conic Sections Chapter 12: Introduction to Three Dimensional Geometry Chapter 13: Limits and Derivatives Chapter 14: Mathematical Reasoning Chapter 15: Statistics Chapter 16: Probability

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Introduction to Three Dimensional Geometry Class 11 Notes Maths Chapter 12