#class 11 maths relations and functions

[class11maths]

NCERT Exercise 2.1 Chapter 2 Relations and Functions Class 11 Maths | MathYug

Expert Video Lecture by Ashish Sir – Relations and Functions (Class 11 Maths Chapter 1)

This video lecture provides a comprehensive explanation of the Cartesian Product, Ordered Pairs, and NCERT Exercise 2.1 from the chapter "Relations and Functions" in Class 11 Mathematics. The session is conducted by Ashish Sir, a subject expert known for in-depth and student-friendly teaching.

Lecture Timeline:

00:00:01 Introduction to this lecture 

00:00:30 Why Relations And Functions is important for Class 12 Maths 

00:02:06 Practical Example related to Cartesian Product 

00:06:16 Cartesian Product and Ordered Pairs NCERT Exercise 2.1 

00:11:46 Question 1 

00:13:36 Question 3 

00:18:46 Question 2 

00:22:16 Question 6 

00:23:16 Question 9 

00:27:06 Question 5 

00:34:26 Question 10 

00:39:06 Brief revision of Cartesian Product 

00:44:26 Question 4 

00:47:46 Question 7 

00:52:06 Question 8

This session is ideal for students looking to strengthen their conceptual understanding and master the fundamentals of Cartesian Products and relations through detailed NCERT problem-solving.

To access the complete course, including all video lectures, notes, and assignments, visit: https://mathyug.com/class-11-maths

[ashishkumarletslearn]

Sample Videos of Class 11 Maths Tutorials by Ashish Sir on MathYug

In this blog, we will explore some sample videos that showcase the quality, depth, and teaching methodology employed by Ashish Sir in his MathYug tutorials.

1. Sets

2. Relations and Functions

3. Permutations and Combinations

4. Complex Numbers

5. Straight Lines

6. Sequences and Series

7. Limits and Derivatives

8. Conic Sections

9. Principle of Mathematical Induction

Join MathYug Today!

MathYug, under the expert guidance of Ashish Sir, offers a transformative learning experience for Class 11 students. The sample videos provide a glimpse into the high-quality content and teaching methods that make MathYug a preferred choice for many. Whether you are struggling with a particular topic or looking to excel in your studies, Ashish Sir’s video tutorials are an invaluable resource.

To explore more and start your journey towards mastering Class 11 Maths, visit MathYug and dive into the world of mathematics with confidence and enthusiasm!

Explore the complete library of tutorials and start learning today!

[lipshits-continuous]

answer all the primes on the real's mathblr ask post!

Hopefully I don't miss any, here goes! I'll put it under a cut cause my answer to 2. is already long oops

2. What math classes did you do best in?

I got 93% in my differential geometry exam last year which is my best grade. It was definitely the easiest module relative to the difficulty of other third year modules.

It also helped that one of the lecturers refused a question from the past exam that we were given solutions to

I also got 91% in the analysis module I took last year which was half measure theory and half an intro to functional analysis. And I got 90% in complex analysis, multivariable calculus, and pdes. It may come as a surprise that topology wasn't my best but do to a mix of personal circumstances, the exam being at the very end of a long exam season and the exam having a more combinatorial flavour in the second half all played against me (not that I did badly, I still got 83% but was my second lowest grade last year)

3. What math classes did you like the most?

In first year linear algebra was my favourite and being able to give tutorials in it this year I still think it's one of my favourites.

Complex analysis is also still high up there and is probably what spawned my love of topology (the topological stuff was definitely more present than in real analysis).

Obviously topology is also one of my favourites, though as alluded to in the previous question there was a more combinatorial approach to some things which I wasn't as much of a fan of (they did change the course significantly for this year though and it seems much better). Differential geometry was also very enjoyable.

This year, algebraic topology has obviously been one of my favourites, even if the second term lecturer wasn't the most organised person. I enjoyed representation theory a lot more than I thought I would and was probably my second favourite module this year. Riemannian geometry was also really good, especially since the lecturer was lovely!

5. Are there areas of math that you enjoy? What are they?

Topology first and foremost! I'm quite interested in differential topology and homotopy theory at the moment. The former is what my dissertation is about and there are things I'd like to read more about relating to it! Homotopy theory is more of a curiosity since I've not had much chance to read about it yet but that's one of my summer plans!

I also enjoy group theory and homological algebra a lot!

7. What do you like about math?

It's inherent exploratory nature as well as how everything connects. One big thing in maths is we have structures and we see what happens when we play with them or alter them. Another is realising connections between different areas. Like for example, my friend who has the same advisor as me for his diss is writing his about Kähler manifolds and Dolbeault cohomology and there's a proof of the Hodge decomposition theorem (I think that's the theorem) that involves the representation theory of sl_{2,C} (as in the lie algebra). Like the fact there's a connection at all is really interesting to me. I suppose that relates to my interest in when algebraic structures sort of arise naturally when looking at certain things in topology.

11. Tell me a funny math story.

13. Do you have any stories of Mathematical failure you’d like to share?

My real analysis lecturer was giving an example of a sequence that didn't converge uniformly and I realised how to alter the example slightly to make it converge uniformly. Turns out that was his next example and he was so happy that I'd preempted it that he jokingly proposed to me.

17. Are there any great female Mathematicians (living or dead) you would give a shout-out to?

None that have come to mind, and I've been thinking a while /lh

Emmy Noether is an obvious one but she literally started homology theory as we know it! I think the story is she attended combinatorial topology lectures and realised she could reframe the language of Betti numbers etc in terms of what we know as simplicial homology.

There are a few living female mathematicians I could shout out but it I do not wish to be doxxed.

19. How did you solve it?

I'm not exactly sure what this question is referring to so I will just give one piece of advise for solving problems. Sometimes a problem is hard because you just haven't had enough experience to solve it yet. Obviously this is isn't helpful is you're trying to solve a homework/exam problem but more generally about learning mathematics. Sometimes you haven't got the tools or the experience to think about it in the right way and that's okay. And the best part about it is that one day you'll come back to the problem and realise that it's easy/easier for you to solve. I think everyone studying maths would benefit from being able to experience this once in a while because it serves as an excellent reminder that you're growing as a mathematician.

23. Will P=NP? Why or why not?

Probably not, though I'm not well-versed enough in it that I could recall well the explanations given for why people think not.

29. You’re at the club and Grigori Perlman brushes his gorgeous locks of hair to the side and then proves your girl’s conjecture. WYD?

Asking him to join the polycule obviously

31. Can you share a math pickup line?

This one is courtesy of me in first year: Are you a subset of a vector space whose elements are of the form ax+b because you're looking (af)fine

37. Have you ever used math in a novel or entertaining way?

Certainly not novel but I have dabbled in how train timetabling works a bit because I have what is essentially a model railway in (heavily modded) Minecraft!

41. What’s the silliest Mathematical mistake you’ve ever made?

I remember in secondary school we did these tests every so often that tested your "essential mathematical skills". I once made the very silly error of writing 3×8=18. Perhaps not the silliest mistake ever but it's one that's stuck with me

43. Did you ever fail a math class?

Not as of yet

47. Just how big is a big number?

As my friend would say: at least 3

53. Do you collect anything that is math-related?

Currently only textbooks, of which I have quite a few now!

59. Can you reccomend any online resources for math?

For algebraic topology I can recommend Friedl's lecture notes. It's a massive several thousand pages. I have currently only used it as a reference document/supplementary material. But from what I've used of it it's clearly written (though trying to use the search function is an uphill battle with how large the document is)

61. Does 6 really *deserve* to be called a perfect number? What the h*ck did it ever do?

It's perfect insofar as its equal to the sum of its proper divisors but it's certainly not free of sin

67. Do you have any math tatoos?

The statement "every tattoo that I have is a maths tattoo" is vacuously true.

71. 👀

👀

73. Can you program? What languages do you know?

Yes but I am very rusty. I used to know java decently well and I knew a bit of python. But I'd probably have to refresh myself a bit before being able to program again

Thanks for the ask!!

[ddaleishere45]

Exploring S.T.E.M

By Dale V. Aldea (Grade 11-Perfection)

As a senior high school student, you've probably heard the term "STEM" being talked around countless times. Maybe you have heard that this strand is for students who wants to be a Doctor, an Engineer, even a Software Genius! But what exactly is STEM? Is it just more than just a senior high school strand? In this blog, we'll dive into the fascinating world of the STEM strand.

S.T.E.M and its origins

STEM is one of many strands you can take up in Senior High School. It stands for Science, Technology, Engineering, and Mathematics. The S.T.E.M acronym was first introduced in 2001 by a a group of scientific administrators at the U.S. National Science Foundation (Hallinen, 2023). The organization previously used the acronym SMET when referring to the career fields in those disciplines or a curriculum that integrated knowledge and skills from those fields but was later changed to STEM and since then, STEM-focused curriculum has been extended to many countries like the United States, Australia, China, France, South Korea, Taiwan, United Kingdom, and was later introduced here in the Philippines by the K-12 program.

Decoding the Acronym

S.T.E.M - SCIENCE Science is all about understanding the natural world, from the smallest particles to the vastness of the space. It involves asking questions, making hypotheses, conducting experiments, and analyzing data to discover the basic principles that govern the universe. If you aim to take science related courses or medicine in college, well you're in luck because this strand offers primary education for the said courses.

S.T.E.M - TECHNOLOGY

Technology is everything from smartphones and laptops to life-saving medical devices and cutting-edge space exploration equipment. It's the practical application of scientific knowledge to create tools, systems, and solutions that make our lives more efficient, convenient, and safe. If you're interested in software development, computer engineering, or even app designs in college, this strand is for you.

S.T.E.M - ENGINEERING

Engineering is the art of using scientific and technical knowledge and using it to design and make solutions. From bridges and skyscrapers to renewable energy systems and electric cars, engineers turn ideas into real, functional realities. The field of engineering is big, with specialties like civil engineering, mechanical engineering, electrical engineering, and aerospace engineering, to name just a few. Well in this strand you can learn the basics of those courses to prepare yourselves in college.

S.T.E.M - MATHEMATICS

Mathematics serves as the language of STEM. It is the foundation upon which all the other subjects are based. Our high school math classes help us develop critical thinking skills, problem-solving abilities, and logical reasoning qualities that are highly sought after in any profession. Whether you are planning on taking a career directly related to mathematics or use it as a tool to excel in another S.T.E.M field, its importance cannot be overstated.

Is STEM important?

The S.T.E.M strand in senior high school very important for students like me. The strand prepares students who are planning on taking on courses that are related to science, technology things, engineering, architecture and many more. The strand also focuses on enhancing the students problem-solving skills, critical thinking and creativity. This is a big help, giving us students a big boost in knowledge in the fields of science and math for college.

So keep this in mind, STEM isn't just a some random acronym made for Senior High School, it is a gateway of understanding the world around us. The strand equips students with knowledge and curiosity for the fields in science, technology, engineering and mathematics, creating a path for a bright future. STEM is more than just a strand, it is a journey of discovery and learning to limitless possibilities.

References:

[inversetrigonometricfunctions]

00:00:00 Introduction for inverse trigonometry identities

00:03:34 Derivation of all inverse trigonometric identities

00:15:14 NCERT Solutions Exercise 2.2 Question 1

00:20:04 NCERT Solutions Exercise 2.2 Question 2

00:21:34 NCERT Solutions Exercise 2.2 Question 3

00:23:44 NCERT Solutions Exercise 2.2 Question 4

00:27:54 NCERT Solutions Exercise 2.2 Question 6

00:34:54 NCERT Solutions Exercise 2.2 Question 7

00:36:24 NCERT Solutions Exercise 2.2 Question 8

00:38:54 NCERT Solutions Exercise 2.2 Question 5

00:42:54 NCERT Solutions Exercise 2.2 Question 9

00:45:44 NCERT Solutions Exercise 2.2 Question 10

00:48:54 NCERT Solutions Exercise 2.2 Question 11

00:50:24 NCERT Solutions Exercise 2.2 Question 12

00:51:04 NCERT Solutions Exercise 2.2 Question 13

00:52:54 NCERT Solutions Exercise 2.2 Question 14

00:54:44 NCERT Solutions Exercise 2.2 Question 15

00:59:54 NCERT Solutions Exercise 2.2 Question 16

01:01:24 NCERT Solutions Exercise 2.2 Question 17

01:03:04 NCERT Solutions Exercise 2.2 Question 19

01:04:24 NCERT Solutions Exercise 2.2 Question 20

01:05:34 NCERT Solutions Exercise 2.2 Question 21

01:07:04 NCERT Solutions Exercise 2.2 Question 18

Detailed explanation of 'how to drive identities of Inverse Trigonometric Functions' and questions related to NCERT Solutions for Exercise 2.2 of Inverse Trigonometric Functions Class 12 Maths Chapter 2.

💎 Purchase the Class 12 Maths Membership for full access to video lectures, notes, and assignments: https://mathyug.com/class-12-maths

[sethiswiftlearn]

Class 11 Math | Relations and functions | JEE Mains, CUET Preparation

Master the topic of Relations and Functions from Class 11 Maths in this detailed session designed for JEE Mains and CUET 2025 aspirants. Understand core concepts, formulas, and shortcuts to solve questions quickly and accurately.

📌 What You’ll Learn:

Basics of Relations and Functions

Types of Relations

Domain, Co-domain, and Range

Functions and their types

Practice Questions for JEE & CUET

🎯 Perfect for Class 11 students, and anyone preparing for: ✔️ JEE Mains 2025 ✔️ CUET 2025 ✔️ Board Exams

📺 Watch now: https://youtu.be/9MhyQPL4-uU?si=ia-UBCmP08MdVPLH

🔔 Don’t forget to Like, Share & Subscribe for more Maths tutorials and exam tips!

[qwschoolca]

Are You Looking For Grade 11 Math Course In Brampton

Are you struggling to make time for a traditional Grade 11 maths class? Functions, a grade 11 math course offered online by QW School, offers flexibility and personalized learning to suit your needs. For students who plan to attend any of the university programs, including physics, engineering, social sciences, liberal arts, and education, this course is essential. Gain the skills required to excel in future maths-related courses. Sign up now!  https://www.qwschool.ca/grade-11/

[3dprintinginedushaikhsamreen]

Application of 3D Printing in STEM Education

3D printing has revolutionized various fields, and its application in STEM (Science, Technology, Engineering, and Mathematics) education is particularly significant. By providing hands-on learning experiences, 3D printing enhances students’ understanding of complex concepts and encourages creativity and innovation. Here are some examples of how 3D printing is being utilized in STEM education.

 1.Engineering Prototyping

In engineering courses, students can design and print prototypes of their projects. mechanical engineering students can create working models of machines or mechanisms, allowing them to test and examine their designs quickly. This hands-on experience solidifies theoretical knowledge and develop problem-solving skills.

2. Biology and Anatomy Models

3D printing is extensively used in biology classes to create models of cells, organs, and organisms. Students can print detailed models of the human heart or brain, which helps them understand anatomy in a easier way.

3.Mathematics Visualization

Students can create geometric shapes and complex mathematical surfaces, allowing them to explore properties such as volume and surface area. This practical application helps fill the gap between theoretical math and real-world applications.4

4. Robotics and Coding

Students can design and print custom parts for their robots, coding them to specific functions. This process integrates coding with mechanical design, providing a comprehensive learning experience that enhances both programming and engineering skills.

5.Environmental Science Projects

Students can use 3D printing to create models that simulate ecological systems or showcase the impact of human activities on environments. For instance, they might design models of habitats to study biodiversity or print pollution models to visualize and analyze data. These projects foster awareness and understanding of environmental issues.

 6.Art and Design Integration

In STEM courses, students can design artistic sculptures or functional items, . This integration encourages innovation and creative problem-solving, essential skills in both STEM and the arts.

7. Space Exploration Stimulation 

With the growing interest in space exploration, students can engage in projects that involve 3D printing to design and create models of spacecraft or Martian habitats. This not only enhances their understanding of aerospace engineering but also inspires interest in STEM fields related to space science.

8. Accessibility and Customization

3D printing also allows for the customization of educational tools and resources. For example, students with disabilities can have assistive devices tailored to their needs, fostering inclusivity in STEM education. This adaptability makes learning more accessible and engaging for all students.

9. Chemistry Molecular Models

In chemistry classes, students can use 3D printing to create models of molecules and chemical compounds. By printing these structures, students gain a better understanding of molecular geometry, bonding, and chemical reactions, which can be challenging to visualize through diagrams alone.

10. Physics Experiments

Physics students can design and print custom apparatus for experiments. For example, they might create resonance or simple machines to study forces, motion, and energy transfer. This hands-on approach helps to understand theoretical principles through practical application.

 11.Historical Artifacts in Social Studies

In social studies or history classes, students can print replicas of historical artifacts, such as ancient tools or architectural features. This experience enhance their understanding of historical contexts making learning more engaging.

 12.Renewable Energy Models

Students studying renewable energy technologies can design and print models of solar panels, wind turbines, or hydroelectric systems. These projects can be used to simulate energy production and understand the principles of sustainability, engineering, and environmental science.

13. Customized Tools and Gadgets

In technology and design courses, students can create customized tools or gadgets tailored to specific tasks or problems. For example, they could design ergonomic tools for specific user needs, promoting innovation and practical application of design thinking.

14. Architectural Models

Architecture students can use 3D printing to create detailed scale models of their designs. This allows them to visualize relationships and aesthetics, providing insights into both structural integrity and design principles.

15.Game Design and Development

In computer science and game design programs, students can print 3D models of characters or environments they create. This integration of physical and digital design fosters creativity and helps students understand the complexities of game development.

 16. Assistive Technology Projects

Students can engage in projects that focus on designing assistive technologies, such as prosthetic limbs or adaptive devices. By creating functional prototypes, students learn about engineering design, user-centered design, and the impact of technology on accessibility.

17. Personalized Learning Tools

Teachers can use 3D printing to create customized learning tools, such as tactile math manipulatives for younger students or specialized equipment for science labs. This tailored approach supports diverse learning styles and needs within the classroom.

 18. Bioengineering Simulations

In bioengineering programs, students can print models of biological systems or tissues to study concepts like tissue engineering and regenerative medicine. This application enhances understanding of complex biological processes and fosters innovation in medical technology.

 19. Virtual Reality Integration

Combining 3D printing with virtual reality (VR) allows students to create physical models that can be used alongside VR simulations. This integration provides a multidimensional learning experience, enabling students to explore concepts in both physical and digital spaces.

20.Student Competitions and Challenges

Many educational institutions host competitions that encourage students to solve real-world problems using 3D printing. For instance, challenges might involve designing and building sustainable housing models or innovative transportation solutions, fostering collaboration and creativity.

 Conclusion

These examples illustrate the diverse applications of 3D printing in STEM education, highlighting its potential to enhance learning experiences, encourage innovation, and prepare students for future careers in technology and engineering fields. As educators continue to explore and implement 3D printing in their curriculum.

[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

[studiestoday123]

Explore CBSE NCERT Class 11 Maths Relations and Functions with StudiesToday. Our comprehensive resources include detailed notes, practice questions, and solutions, designed to help students master concepts and excel in exams. Achieve academic success with expert guidance.

[studyupindia]

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

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

[ashishkumarletslearn]

Join us as we explore Exercise 2.1 of Chapter 2 on Relations and Functions for Class 11 Maths with MathYug's expert teacher Ashish Sir, affectionately known as Agam Sir. This video lecture provides an in-depth analysis of each question, including practical examples and detailed explanations. Join us as we delve into Cartesian Product, ordered pairs, and tackle NCERT questions.

Timestamps:

00:00:01 Introduction to this lecture

00:00:30 Why Relations And Functions is important for Class 12 Maths

00:02:06 Practical Example related to Cartesian Product

00:06:16 Cartesian Product and Ordered Pairs

NCERT Exercise 2.1

00:11:46 Question 1

00:13:36 Question 3

00:18:46 Question 2

00:22:16 Question 6

00:23:16 Question 9

00:27:06 Question 5

00:34:26 Question 10

00:39:06 Brief revision of Cartesian Product

00:44:26 Question 4

00:47:46 Question 7

00:52:06 Question 8

Watch now for a comprehensive understanding of Class 11 Maths!

[class11maths]

NCERT Exercise 2.1 Relations and Functions Class 11 Maths Chapter 2

[0rb0t]

Don't mind me, just talking about Shadow as being on the autistic spectrum, and how his portrayal in the games and anime (before 2010s era) reflected this even if it was never outright stated.

(TIME FOR A CHARACTER ANALYSIS ABOUT SHADOW THE HEDGEHOG)

    When I was in high school, I struggled a lot in social situations, I'd go completely stiff and just watch people. I had a "resting bitch face", I never really could have conversations and seemed to just fixate on things. I'd make observations that irritated people. I'd ask "why" a lot. (Asking why or even asking 'obvious' questions seemed to make people think I was questioning their judgment, or that I was challenging them. But no, I just didn't understand and wanted clarification. I still run into this a lot and I wish people would stop assuming I have ulterior motives. I just wanna understand stuff better cause it doesn't connect for me. Even if it seems obvious. I'm the genius that asked my mom why she was crying at her dad's funeral when I was 11. It's not that I didn't understand why Grandpa was gone, I knew he passed away, but it hadn't really landed for me, and my brain registered my mom's sadness before it registered the why.)

    I didn't like small talk (still don't) and would rather every interaction have a specific purpose. You'd never catch me at a party and I didn't think drinking or drugs looked fun or interesting. The act of rebelling didn't interest me either. The few interests I did have were something I'd always go back to, and I couldn't function without them. (For me, drawing has always been a huge part of my life and if I didn't have a pencil or pen and paper, then I couldn't hear. I know, very weird. If I were doodling or just even had my sketchbook open, I could study a lot easier. In High school, my teachers started telling me to put the sketchbook away, and my grades plummeted because my attention did, too. Trying to tell them just kind of led to the same old "well everyone else can't doodle so you can't either". I wasn't in any of the special ed stuff because I guess I masked too well.)

    Sonic 06 and Sonic X have the same characterization for Shadow, especially in Japanese, and I think that's honestly the best he'd ever been-- he's quiet, he's reserved, he observes and he doesn't like to "waste time". Not because he's edgy, not because he's a jerk or too serious, but because he struggles in social situations and he's more introverted. He doesn't want to be the centre of attention, he doesn't enjoy any of that. Shadow also behaves like an adult, and I'm sure a ton of us on the spectrum have heard that before, that we're very mature for our age. In reality, we can't relate with our peers and have very fixated interests that don't really expand to other things. Limited interests and we just wanna do stuff tied to that. We know so much about that one thing or those things, but those things won't get you ahead in school. Unless you're LUCKY and your fixation is math, oy vey! (My fixation was etymology. I loved learning and knowing where words came from. Useful for 2 seconds in English class, quickly loses its usefulness in a skill-oriented world.)

    I don't even think he's naturally boastful, at least he wasn't since SA2 (when he was an antagonist), but Sonic brings out a competitive side in him. Sonic brings out the childhood-self that he lost to trauma and being sealed away. Shadow never got to be a normal kid/adult. He has always had expectations placed on him. I think Sonic really brings out a side of him that even surprises himself. It's why he will even say very often "What am I doing?" or "This is such a waste of time!" but he won't STOP… Because he's having fun and doesn't know how to describe his own feelings. Shadow's the type who'll say "I'm fine" no matter what state he's in when you ask if he's okay. My spouse is like this actually-- I can often tell when he's feeling down, but he doesn't know how to describe emotions beyond functional things like "i'm healthy" or "i'm unhealthy", so he'll say he's fine even if he's having a melancholy day. I struggle with understanding my emotional responses, but not necessarily identifying them. A lot of people on the spectrum do struggle with identifying their emotions beyond empirical things. "Do I feel sick? No? then I'm fine" Shadow is exactly like this. And because his expression is so neutral, sometimes intense, he gets mistaken as being angry or too serious. In reality, he's just standing there. He's not gonna expend energy smiling when he's got nothing to smile about. Why force yourself to emote for people? Especially if it feels unnatural.

    Another thing about Shadow being autistic is if he's got nothing to say, then he won't say it. If he wants to leave, he'll leave. Good luck stopping him! But for many actual people it's not an option to leave. We can't just teleport out or skate at lightning speeds like he can, so we have to just sit there and do little coping or self soothing methods to keep ourselves in the moment and calm. We don't often see Shadow stimming in traditionally understood ways, like lip biting or rubbing his arms or fidgeting with his fingers-- but he often stands with his arms crossed. This CAN BE a stim. Feeling the weight of your arms on top of each other, it allows for you to be aware of your own body. I fold my arms a lot in public, because I'm usually playing with the hem of my sleeves, or I'm rubbing my arms or squeezing them. Shadow doesn't seem to do any of that but he's rarely seen without his arms folded.

    When his arms aren't folded, he stands so still and just stares at people. He looks completely out of his element. He doesn't seem to have a relaxed stance--until the anime, where he's shown standing with his hand on his hip. Rouge also does this, leading to the popular headcanons that Shadow is unintentionally imitating Rouge-- his masking leads him to identify the most 'normal' person in the room and copy their behavior in order to blend in better. Unfortunately it rarely, in my experience, leads to people NOT thinking I'm weird. Sometimes I'll even start imitating speech patterns or accents and BOY. I don't even realize I'm doing it until it HAPPENS. So embarrassing. But Shadow absolutely imitates everyone around him. We can see him do this even as far back as Sonic Heroes--that scene where he's nodding or shaking his head to whatever Rouge is saying. The scene where Sonic starts getting competitive and Shadow starts kind of imitating his posture and his way of speaking to become competitive with them-- I don't even think he realizes he's doing it. But it also makes sense with his NAME.

    His name is Shadow. I think of Peter Pan, where Peter's Shadow can sometimes get away from him. Usually it does everything he does, but sometimes it gets away and does its own things, and Peter has to catch it. Wendy sews the shadow back on in Hook. I think Shadow's name is referencing that as well, that just like a shadow, he mimics those around him. He's watching over them, but also copying them. Learning to blend in.

    Another moment I adore is in SA2 (and Sonic X) when Amy Rose hugs him from behind. According to the 2010s era and early IDW, you'd have expected Shadow to push her away or yell DONT TOUCH ME or whatever. But no, he actually just goes REALLY RIGID and doesn't even say anything. It isn't until Amy realizes her mistake that Shadow turns around to look at her, smiling like 'What are you doing???' But in Sonic X, they changed this scene further into autistic territory--

    Shadow doesn't even TURN to her. He goes rigid, yes, and his eyes widen and he just stands there looking towards the audience like 8| He's completely OUT OF HIS ELEMENT. He prepared for the mission, NOT to deal with random people HUGGING HIM. He's probably not been hugged since Maria over 50 years ago. We don't even know if Maria hugged him much because Shadow has always seemed pretty touch-averse. I love GIVING hugs and I love receiving hugs but only from people I'm REALLY close to. I don't even like getting hugs from extended family. My spouse? VERY touch averse. He'll get hugs from me but hugging and touch are just not his thing. Shadow is not a huggy person, but he does tend to hold hands.

    We know he grabbed and held Maria's hand, running with her-- but we never actually saw that until Sonic X (2003) he can be seen running with her away from the military, and he's holding her hand as he leads her. In Shadow the Hedgehog, Maria often grabs Shadow's hand when telling him things. This is also a grounding method to bring the person into the moment. For me, I feel like I can focus better on what my spouse is saying to me when he holds my hand and it's crowded or busy. Even in our home, if he wants to tell me something, I recommend that he hold my hand or touch my arm so I can focus on him better. This happens with Shadow.

    Sonic doesn't tend to hold peoples' hands. In Sonic X he usually just picks people up, but we do see him grab Elise's arm in 06 and run with her. But holding hands? Not really his thing! Shadow does do it more often though. In Sonic X S3, in the episode, Molly's Dream, Shadow's immediate way of leading Molly away from danger is to grab and hold her hand. He even keeps holding her hand until she lets go. It speaks to me the sort of childlike behavior he may still be exhibiting, but not that I'm trying to say that autistic people are more like children. From my experience on the spectrum, I am more childish than my peers. I still react like a kid might to things, and I don't really think like an adult is expected to. I am mentally behind my peers as well, I think my emotional maturity is lower? But it's hard to measure that without a doctor. It's not just about laughing at fart jokes or knowing to pay bills, it's like, how I problem solve is more creatively aligned with kids than it is adults. This is both great and terrible, depending on the situation. A situation that requires math and stuff cannot be solved my way. A situation that involves encouraging kids to try again or be nice to each other, well it's very useful because I can communicate with them on their level (I was a teacher in South Korea for over half a decade, my brain was great for being a teacher but not great for other things).

    I think Shadow really gets misread as a mean guy a lot, but he really isn't. I also don't really enjoy the headcanons that imagine him as very outgoing and whimsical when he was on the ARK, and I especially don't like headcanons that infantilize him-- I really don't like headcanons where people infantilize autistic people. We've seen Shadow when he loses his memories a few times. In Heroes, but also in S3 of Sonic X-- his personality is still the same. He's still reserved, he's still quiet, he still struggles in social situations and prefers getting to the point rather than dilly-dallying. I'd argue that he was exactly like that before the incident on the ARK, too. It's just that the incident caused his inner peace to be destroyed. His precious person, Maria, was no longer around and he lost everything all at once. He doubled down on the one thing that made sense: Revenge. But even after all of that was sorted out, he's not gonna just magically be a different person. He's still reserved, he's still serious, he's still "get to the point". If he played FFXIV, he'd only focus on main quests, and never do side quests. He'd never spend money on cosmetics, probably. He's likely a person who values gameplay over story. If the game is broken or the mechanics aren't utilized well, that's probably more what he'd be fixated on than whether the story was good or not. He'd skip through dialogue because he reads fast, even if the dialogue is voiced (my spouse does this and it drives me nuts. SHADOW I BEG OF YOU PLEASE DO IT FOR ME, DISABLE THE VOICE ACTING IN OPTIONS SO I STOP HEARING THE FIRST UTTERANCE OF A WORD EVERY TIME U MASH THROUGH THE DIALOGUE)

    Trauma affects people in all kinds of ways. I don't think all autistic people are like Shadow, because autism is a spectrum and no two people present exactly the same, although there will be similarities. Shadow's trauma happened at a time where he barely knew himself already, so that's why it was so easy for him to fixate on revenge, and then he'd be content with dying afterwards because he figured he had nothing left to live for. Finding out he was wrong was the best thing that could have happened to him.

    I was really saddened when SEGA decided he was an edgelord who hated everything and had no friends because that's such a horrible read of this nuanced character. In my personal headcanons for Shadow, he's actually very into plants and flowers, because Maria loved the planet so much. And eventually he learns to love the planet because of nature. Shadow's never going to be a people person, in fact he probably still doesn't care much for people as a whole, but that doesn't mean he won't step up when they need his help. Which is why his line in Sonic 06 is still so poignant. "If the world chooses to become my enemy, then I'll fight like I always have." Basically, it really doesn't matter, I've made my choice, I know who I am now and I get to make those decisions. No one else will shake the foundations of who I am.

    And because he knows who he is, he doesn't feel the need to repeat it and boast about himself. He's confident, not arrogant. He can be smug and competitive, but that's playfulness, not cruelty. He's quiet and may just straight up walk away while someone is mid-sentence, but that's not because he's evil or intentionally being a jerk-- it's just how he is. He needs to work on it if he wants to have friends, but his friends already understand him very well. They know that he's like that, and from what we saw in The Murder of Sonic the Hedgehog, occasionally they forget it's not personal. I'm happy to see them admitting "oh no, I completely misjudged you, I'm so sorry!" because it's been way too long since we've heard the main cast apologize to Shadow for assuming he was a big jerk on purpose.

    Knowing the restrictions on how Shadow is written have been lifted, I'm really hoping we can get more of how he's meant to be, the reserved, socially awkward but well-meaning hedgehog we love. Autistic Shadow FTW!

    

(our experiences and headcanons

may differ, that's okay.)

[theetangerine]

What it’s real like being a Dyslexic

Today's  post shall be about Dyslexia from  "Dyslexia the Gift". Well I didn't know that I was blessed with such an omnipotent power. Thank you Dyslexia the Gift for Awakening my abilities. Anyways this post is just my rebuttal to this list as an Anthropomorphic Tangerine with severe dyslexia. Here we go: General:

1. Appears bright, highly intelligent, and articulate but unable to read, write, or spell at grade level.

Ahhhhh.......... so I am all those big words that I can't spell or pronounce.

BTW who ever came up with the word Dyslexia is a troll cause you knew damn well I can't spell that.

2. Labelled lazy, dumb, careless, immature, “not trying hard enough,” or “behavior problem.”

Hey I am not lazy just because Suzie spends her the night figuring out Algebra questions and I on the other hand will look at her formula, "Copy and Paste" for myself and even then at the end of the day I stilled will have learned it. Einstein did say there are different types of genius.

3.Isn’t “behind enough” or “bad enough” to be helped in the school setting.

Let's just pretend it didn't take me 3 times to read this inorder to understand it. Anywhose.

The school suggested to my parents to take me to get tested. Although I think it was because they wanted justify their discrimination against me.

 4.   High in IQ, yet may not test well academically; tests well orally, but not written.

Lies. I failed in both.

5.Feels dumb; has poor self-esteem; hides or covers up weaknesses with ingenious compensatory strategies; easily frustrated and emotional about school reading or testing.

*clear throat* In best Beyonce voice "I'm survivor................"

6.Talented in art, drama, music, sports, mechanics, story-telling, sales, business, designing, building, or engineering.

 Ohh.......come on I suppose to be talented in these fields why didn't Dyslexia tell me this.

7.Seems to “Zone out” or daydream often; gets lost easily or loses track of time.

They were in the Zone like in Soul

woahh..... that was a bar.

8.Difficulty sustaining attention; seems “hyper” or “daydreamer.”

 As I type this I peer out through the window wondering if clouds really are made of precipitation or that is what the Illuminati wants you to think.

 9. Learns best through hands-on experience, demonstrations, experimentation, observation, and visual aids.

Crash Course history is my religion.

Vision, Reading, and Spelling:

10.Complains of dizziness, headaches or stomach aches while reading.

 Starts going in the 4th dimension if I pick up a book.  

11.Confused by letters, numbers, words, sequences, or verbal explanations.

Algebra is not for dyslexics. You mix letters and numbers together. Mathematicians were not thinking of dyslexics when Algebra was created.

 12. Reading or writing shows repetitions, additions, transpositions, omissions, substitutions, and reversals in letters, numbers and/or words.

Yes Yes . Truly feal for all of of my teacher who read my essays.

13.Complains of feeling or seeing non-existent movement while reading, writing, or copying.

I am Percy Jackson so I am a god.

 14.Seems to have difficulty with vision, yet eye exams don’t reveal a problem.

 I actually had glasses.

15.Extremely keen sighted and observant, or lacks depth perception and peripheral vision.

Yet another sentence I can't understand. Hold up let me go and look up “depth perception” so I can understand this sentence, real quick.........................This is true.  

 16.Reads and rereads with little comprehension.

Reading number fifteen (15) proves this.

 17.Spells phonetically and inconsistently.

 Hooked on Phonics told me otherwise.

Hearing and Speech:

18.Has extended hearing; hears things not said or apparent to others; easily distracted by sounds.

Being an only child while being home alone this ability doesn't have any benefits.

 19.Difficulty putting thoughts into words; speaks in halting phrases; leaves sentences incomplete; stutters under stress; mispronounces long words, or transposes phrases, words, and syllables when speaking.

 I feel called out.

Writing and Motor Skills:

20.Trouble with writing or copying; pencil grip is unusual; handwriting varies or is illegible.

 I may have changed my writing style multiple times. Some legible, some not.

 21.Clumsy, uncoordinated, poor at ball or team sports; difficulties with fine and/or gross motor skills and tasks; prone to motion-sickness.

But if I am supposed to be talented at sports in the afro-mention point why can't I catch a ball.

Dyslexia being confused since 1877.

 22.Can be ambidextrous, and often confuses left/right, over/under.

Yip...A 20 something that doesn't know their left from their right.

 Math and Time Management:

23.Has difficulty telling time, managing time, learning sequenced information or tasks, or being on time.

Well if I can't tell time I can't manage my time thus I don't have enough time to do tasks so that is why I am never on time.

 24.Computing math shows dependence on finger counting and other tricks; knows answers, but can’t do it on paper.

 Only if Math exam were oral I would have accolades in Math.

 25.Can count, but has difficulty counting objects and dealing with money.

 Y'all I have nightmares about being a cashier.  

 26.Can do arithmetic, but fails word problems; cannot grasp algebra or higher math.

As I said before Algebra not, for dyslexics.

Memory and Cognition:

27:Excellent long-term memory for experiences, locations, and faces.

I wish could forget about that time I fell down in front the entire school. And yes this is not an exaggeration. The ENTIRE school saw this.  

28.Poor memory for sequences, facts and information that has not been experienced.

Subjects dyslexics shouldn't do:

Science: too many big words you can't spell.

History or Literature: reading is detrimental to your health.

Math:  A-L-G-E-B-R-A

 29.Thinks primarily with images and feeling, not sounds or words (little internal dialogue).

Sad truth I wear my heart on my sleeves. It's fricking annoying cause I want to be mad in peace without anyone knowing Goddamn it .

 Behavior, Health, Development, and Personality: 

30.Extremely disorderly or compulsively orderly.

I am Death the Kid.

(If you don't get that reference you are uncultured)

 31.Can be class clown, trouble-maker, or too quiet.

Like I was disliked in school for being too quiet. You would think that it was students oh no no no Patricia it was teachers.

Sorry Mrs. Emily for not giving you grey hairs, so you have the opportunity to go home to your loving husband to complain about how much you hate your job and kids. While you thinking about your affair with the young nextdoor neighbour, who you would end up marrying only to then leave them for a hot 20 yea.............................Ummmm that got a bit personal there lets continue shall we  

32.Had unusually early or late developmental stages (talking, crawling, walking, tying shoes).

 It took a while to learn how to tie my laces.

 33.Prone to ear infections; sensitive to foods, additives, and chemical products.

So wait not only did Dyslexia inhibit my ability to read, comprehend and to tell my right from my left to function normally in society but it caused my ear infections too. That is it I'm done

Moving to Siberia.

 34.Can be an extra deep or light sleeper; bedwetting beyond appropriate age.

 I was a very well trained tangerine.

 35.Unusually high or low tolerance for pain.

Everytime I stub my pinky toes it feels like an aeroplane wheel rolled over it.

36.Strong sense of justice; emotionally sensitive; strives for perfection.

 Facts!

37.Mistakes and symptoms increase dramatically with confusion, time pressure, emotional stress, or poor     health.

2 second Rant

Examiners don't think of dyslexic people, even with extra time. The sheer amount of times it takes just to understand the question then to answer with the best possible Grammar is straight cruelty.

You automatically want me to fail and not finish don't you.

You Demon.

  Mini sidestory:

While writing this I asked my significant other to spell "Exaggerate", dude looked at me and told me to sound it out. Past me knew he was going to say this and I did sound it out  before he asked me to sound it out. I told him that I did and that I don't know what letter comes after "Ex", he was like babe sound it out..................................

Tangerine internal thoughts: (Exsqueeze me) Every time try that a ""H" is coming up in my head. I thought this through ya know.

In conclusion I sound it out to my phone.

 To anyone who don't understand Dyslexia fully I do suggest researching.  

My commentary is completely subjective but if you relate that is good :)

 That's all my Fruits until next time

- TheeTangerine

Proof read by TheeApple<3

https://www.dyslexia.com/about-dyslexia/signs-of-dyslexia/test-for-dyslexia-37-signs/