#ncert 11 maths solutions

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Mastering Permutations and Combinations - A Key Part of NCERT Class 11 Maths

Permutations and combinations form an important part of the NCERT syllabus for Class 11 Maths. This topic is covered in Chapter 7 - Permutations & Combinations, under the Algebra section. Having a strong grasp of permutations and combinations is essential for competitive exams like JEE, CBSE 12th boards, and more. In this blog, we will explore this topic in-depth.

Understanding Basic Definitions and Principles

Permutations refer to arranging objects in a definite order. For example, the permutations of ABC are ABC, ACB, BAC, BCA, CAB, CBA.

Combinations refer to selecting objects without regard to order. For instance, combinations of ABC are ABC, AB, AC, BC.

The fundamental principles include factorial notation, permutation and combination formulas, and the fundamental principle of counting.

NCERT solutions provide step-by-step techniques for applying these basic definitions and formulas to solve questions.

Using Permutations and Combinations Formulas

Some key formulas students should remember include:

Permutations of n objects taken r at a time: nPr = n!/(n-r)!

Combinations of n objects taken r at a time: nCr = n!/r!(n-r)!

Permutations with repetitions like AAAABC: n^r

Combinations with repetitions like ABCABC: (n+r-1)Cr

Solving a variety of examples from NCERT textbooks will help students master these formulas.

Understanding Properties and Applications

Some important properties and applications covered in this chapter are:

Circular permutations

Combinations of multi-stage selections

Applications in probability

Occupancy problems

Arrangements of letters to form words

Practicing questions on these applications is vital for gaining comprehensive understanding.

Tips for Solving Permutation and Combination Problems

Some useful tips for solving these problems include:

Write down all key information given in the question

Figure out if it involves permutations or combinations

Determine the objects being arranged/selected

Identify which formula applies and substitute the values

Preparing Well for Permutations/Combinations Questions

To summarize, students should thoroughly study the NCERT 11 maths solutions for this chapter. Solving examples, intext questions, chapter exercises and NCERT book class 11 exercises will ensure full preparation. Permutations and combinations serve as a foundation for competitive exams, so dedicate ample time to master this topic.

FAQs about Permutations and Combinations

Q1. What is the permutation formula for n objects taken r at a time?

A1. The permutation formula is nPr = n! / (n-r)! where n is total objects and r is objects being permuted.

Q2. How is a combination different from a permutation?

A2. A combination only considers which objects are selected, while a permutation considers their ordered arrangement.

Q3. What are some real-world applications of permutations and combinations?

A3. Applications include finding probabilities, forming words, combinations of passwords, committees selection, etc.

Q4. How do you solve problems involving permutations/combinations with repetitions?

A4. Use formulas like n^r for permutations with repetition and (n+r-1)Cr for combinations with repetition.

Q5. What are some common mistakes students make with these concepts?

A5. Common mistakes include confusing permutations and combinations, choosing wrong formula, incorrectly substituting values in formula.

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To give you a taste of what MathYug has to offer, we are sharing a selection of sample videos from our Class 11 Maths tutorials. These videos exemplify the high-quality, in-depth teaching style that Ashish Sir is known for.

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MathYug is thrilled to announce the reactivation of memberships for Class 10 Maths, Class 11 Maths, and Class 12 Maths. Responding to the overwhelming requests from our dedicated learners, we're reintroducing these exclusive memberships to provide an unparalleled academic experience.

Our memberships are designed to empower students with comprehensive resources, expert guidance, and a supportive learning community. Whether you're navigating the challenges of Class 10 board exams, diving into advanced concepts in Class 11, or preparing for the competitive exams in Class 12, MathYug's reactivated memberships cater to diverse educational needs.

Members will gain access to a wealth of study materials, interactive tutorials, and personalized assistance from our experienced educators. The platform's user-friendly interface ensures a seamless learning experience, allowing students to progress at their own pace.

At MathYug, we understand the importance of continuous improvement and staying ahead in the academic journey. By bringing back these memberships, we aim to further enrich the educational experience for students, helping them achieve excellence in mathematics.

Seize the opportunity to reignite your passion for learning and excel in Class 10, 11, and 12 Maths. Join MathYug's reactivated memberships and embark on a journey towards academic success and mathematical mastery.

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Class-8 Maths Ncert Solution Chapter-11 Mensuration Q4 & Q5 | #aaetclasses #narendrasir #maths

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Class-8 Mathematics NCERT Solution Exercise 3.1 Q:- 1, 2, 3 & 4 #maths with narendra sir #maths

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NCERT Solutions For Class 11 Maths 2024-25

Access comprehensive NCERT Solutions for Class 11 Maths 2024-25. Master complex topics with step-by-step solutions to all chapters, designed to boost understanding and exam preparation. Perfect for students seeking clarity and success.

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How to Study for JEE: A Complete Guide for Aspiring Engineers

Preparing for the Joint Entrance Examination (JEE) can feel like a massive challenge. But with the right strategy and mindset, it’s absolutely possible to conquer this exam and get into your dream engineering college. Whether you're preparing for JEE Main or JEE Advanced, here’s a step-by-step guide to help you study effectively.

1. Understand the Syllabus and Exam Pattern

Before diving into preparation, it's important to know what you're preparing for. The JEE syllabus is based on the NCERT curriculum for Classes 11 and 12, covering Physics, Chemistry, and Mathematics. You should:

Download the latest syllabus from the official JEE website.

Break down the topics subject-wise and categorize them into easy, moderate, and difficult based on your understanding.

Familiarize yourself with the exam pattern: JEE Main has multiple-choice questions (MCQs) and numerical-based questions, while JEE Advanced has a mix of MCQs, numerical, and match-the-columns types.

2. Create a Realistic Study Plan

A well-structured plan is crucial for JEE preparation. Here's how to make one:

Time management: Set a timetable allocating specific time for each subject daily. Focus on balancing all three subjects—Physics, Chemistry, and Math.

Set daily and weekly goals: Break the syllabus into smaller portions and set achievable goals. Prioritize understanding the concepts over just memorizing formulas.

Revision time: Dedicate at least an hour every day to revising what you've learned.

3. Focus on Concepts

JEE isn’t just about mugging up formulas; it tests your conceptual clarity and problem-solving abilities. Here’s what you can do:

Start with NCERT textbooks: For JEE Main, NCERT textbooks for Physics, Chemistry, and Mathematics are your foundation. They explain concepts in a clear and easy way.

Reference books: For more in-depth understanding and practice, use additional books like:

Physics: "Concepts of Physics" by H.C. Verma

Chemistry: "Organic Chemistry" by O.P. Tandon

Mathematics: "IIT Mathematics" by M.L. Khanna

Avoid skipping topics: Even if some topics seem hard, try to cover them since every mark counts in JEE.

4. Practice, Practice, Practice

The key to success in JEE is regular practice.

Solve previous years’ question papers: This helps you understand the type of questions asked and gives insight into the exam pattern.

Mock tests: Take timed mock tests regularly to simulate the exam environment and improve speed and accuracy. It also helps in identifying your weak areas.

Solve sample papers: The more problems you solve, the better your problem-solving speed and accuracy become.

5. Strengthen Your Problem-Solving Skills

JEE is all about smart problem-solving. Here’s how you can boost these skills:

Work on understanding the problem rather than jumping to a solution.

Use shortcut methods only when you have mastered the basics. Shortcut formulas can save time, but only if you have a solid understanding of the concepts.

Don’t spend too much time on one question during practice. If you’re stuck, move on to the next and revisit it later.

6. Time Management During the Exam

While solving questions during JEE, time management is critical.

Attempt easier questions first: This boosts your confidence and ensures that you get marks in areas you are comfortable with.

Divide your time effectively: Allocate time to each section (Physics, Chemistry, Math) and avoid spending too much time on one subject.

Don’t panic if you get stuck: Stay calm and move on to the next question if a particular one is taking too long.

7. Stay Healthy and Take Breaks

Studying for long hours without rest can lead to burnout. Here’s how to maintain balance:

Take short breaks: After studying for 1-2 hours, take a 10-15 minute break to refresh your mind.

Get enough sleep: Sleep for 7-8 hours every night to keep your brain sharp.

Eat healthy food: Avoid junk food and maintain a balanced diet to stay energetic and focused.

8. Seek Help When Needed

If you’re struggling with certain topics, don’t hesitate to ask for help. You can:

Join coaching classes for expert guidance and additional study materials.

Watch online lectures on YouTube or educational platforms like Unacademy or Byju’s.

Form a study group with friends to discuss difficult problems and explain concepts to each other.

9. Stay Positive and Motivated

JEE preparation can be stressful, but staying motivated is key to success.

Celebrate small achievements: When you complete a topic or solve a tricky problem, reward yourself.

Stay consistent: Even if progress seems slow at times, trust the process. Consistency is more important than cramming at the last moment.

Stay away from distractions like social media, games, or TV during your study hours.

Looking for the best JEE Main coaching in Siliguri? Career & Courses offers expert guidance, personalized study plans, and comprehensive resources to help you excel in JEE Main. With experienced faculty, regular mock tests, and a focused approach, we ensure your path to success in the competitive JEE examination.

Final Thoughts

Preparing for JEE is a marathon, not a sprint. With determination, hard work, and smart preparation strategies, you can crack the exam. Focus on understanding concepts, practicing regularly, and maintaining a healthy balance between studies and relaxation. Stay positive, and remember—every small step you take brings you closer to your dream of becoming an engineer.

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NCERT Solutions for Class 11 - All Subjects PDF Download

Access comprehensive NCERT Solutions for Class 11. Download free PDFs for all subjects including Math, Physics, Chemistry, and more to excel in your exams.

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Get comprehensive access to Class 10, 11, and 12 Maths with MathYug's all-inclusive membership.

For the comprehensive access membership, we bring together an extensive range of resources spanning all three tiers of mathematics education. This package provides an all-inclusive learning experience, combining the offerings of Class 10, Class 11, and Class 12 mathematics memberships.

Here's what you can expect:

A total of 60 individual courses, covering all 52 NCERT chapters across Classes 10, 11, and 12.

Access to recorded videos elucidating NCERT exercise solutions, fundamental concepts, and illustrative examples for each chapter. Recorded video sessions dedicated to assignments sourced from NCERT Exemplar problems, RD Sharma, Board question banks, and more.

Supplementary PDFs of assignments to aid your practice and comprehension.

Complete Access Membership for Class 10, 11 & 12 Maths | MathYug

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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.

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Get Free NCERT Solutions for Class 11 Subjects - PDF Download

Get free NCERT Solutions for Class 11 subjects. Download PDFs for Maths, Physics, Chemistry, Biology, English, and more to ace your exams.

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Explore Complex Numbers: Video Tutorials on MathYug for Class 11 Maths

In the realm of Class 11 Mathematics, complex numbers often stand out as a topic that both intrigues and challenges students. With its unique algebraic and geometric properties, mastering complex numbers not only enhances mathematical prowess but also lays a solid foundation for future studies in calculus, physics, and engineering. To aid in this journey of understanding, Ashish Kumar, through MathYug, offers an invaluable resource: video tutorials, comprehensive PDF notes, and challenging assignments designed to illuminate the intricacies of complex numbers.

Video Tutorials: Visual Learning at Its Best

Ashish Kumar’s video tutorials on complex numbers are a beacon for students seeking clarity and deeper understanding. These tutorials are meticulously crafted to simplify complex concepts, using intuitive explanations and step-by-step breakdowns of problems. Whether you’re grappling with the basics of imaginary numbers or diving into the geometric interpretation of complex plane operations, Ashish Kumar’s approach ensures that every student can grasp the material at their own pace.

The benefits of video tutorials extend beyond mere explanation. They provide a dynamic learning experience where students can rewind, pause, and revisit explanations until they achieve mastery. Visual learners find these tutorials particularly effective as they can see concepts unfold in real-time, aiding in retention and comprehension.

To give you a glimpse into the comprehensive learning experience offered by MathYug, we’ve included a sample video tutorial on complex numbers by Ashish Kumar. This video exemplifies Ashish Kumar’s pedagogical approach, combining clarity with depth to unravel the intricacies of complex numbers. From foundational concepts to practical applications, Ashish Kumar adeptly guides viewers through each step, ensuring a thorough understanding. Whether you’re new to complex numbers or looking to reinforce your knowledge, this sample video provides a valuable insight into the quality of education available on MathYug.

Comprehensive PDF Notes: Your Go-To Study Companion

Accompanying the video tutorials are comprehensive PDF notes, meticulously prepared to encapsulate every aspect of complex numbers covered in the tutorials. These notes serve as a handy reference, allowing students to reinforce their understanding of key concepts and formulas outside of the video lessons.

Ashish Kumar’s PDF notes are structured to align with the video tutorials, ensuring a seamless learning experience. They include detailed derivations, solved examples, and practical tips for tackling complex number problems. Whether preparing for exams or aiming to deepen conceptual understanding, these notes provide a structured framework that consolidates learning and promotes academic success.

Challenging Assignments: Testing Your Limits

Understanding complex numbers isn’t just about passive learning — it’s about active engagement and application. Ashish Kumar’s challenging assignments for complex numbers are designed to push students beyond their comfort zones, encouraging them to apply theoretical knowledge to solve complex problems.

These assignments cover a spectrum of difficulty levels, from foundational exercises to advanced problems that stimulate critical thinking. By grappling with these assignments, students not only reinforce their understanding but also develop problem-solving skills essential for academic and real-world challenges.

Why Choose MathYug?

MathYug, under the guidance of Ashish Kumar, stands out as a beacon of quality education in the digital era. With a commitment to clarity, depth, and accessibility, MathYug’s resources on complex numbers empower students to excel in their mathematical journey. Whether you’re struggling to grasp the basics or aiming for mastery, MathYug’s comprehensive approach ensures that every student finds the support they need to succeed.

Empowering Students Through Knowledge

In conclusion, Ashish Kumar’s video tutorials, complemented by comprehensive PDF notes and challenging assignments on MathYug, offer a transformative learning experience for students tackling complex numbers in Class 11 Mathematics. By leveraging these resources, students not only gain mastery over complex concepts but also cultivate a deeper appreciation for the beauty and utility of mathematics in everyday life.

If you’re ready to embark on a journey of mathematical discovery and excellence, MathYug is your gateway to success. Explore the world of complex numbers with Ashish Kumar and pave the way for a future rich in mathematical understanding and academic achievement.

Remember, the power to master complex numbers lies within your grasp — unlock it with Ashish Kumar and MathYug today!

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NCERT Solutions for Class 11 - GET Free 2023-24 PDFs

Looking for the best NCERT Solutions for Class 11 to help you excel in your CBSE board exams 2023-24? Look no further! We provide free PDF downloads of detailed NCERT Solutions for Class 11 Maths, Physics, Chemistry, Biology, Accountancy, Economics, Business Studies, History, Geography, Political Science, Sociology, and more subjects.

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NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry