#Integrals Class 12 NCERT Solutions

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NDA Syllabus 2025 PDF download – Maths and GAT Syllabus

NDA Syllabus 2025 PDF download – Maths and GAT Syllabus

Are you dreaming of joining the Indian Armed Forces through NDA in 2025? Then buckle up, because understanding the NDA syllabus 2025 is the first step toward success. Whether you’re aiming for the Army, Navy, or Air Force wings, the syllabus is your ultimate guide to cracking the NDA written exam.

Let’s break it all down for you — subject by subject, topic by topic. Ready? Let’s dive in.

Introduction

What is the NDA Exam?

The National Defence Academy (NDA) entrance exam is conducted by the Union Public Service Commission (UPSC) twice a year. It’s your gateway to a life of honor, discipline, and adventure in the Indian Armed Forces.

Why Knowing the NDA Syllabus Matters?

You wouldn’t go into battle without knowing the terrain, right? Similarly, you can’t ace NDA without knowing the NDA syllabus 2025 inside-out. It helps you plan, prepare, and perform better.

Overview of NDA Syllabus 2025

Structure of the NDA Exam

The exam consists of two papers:

Mathematics – 300 Marks

General Ability Test (GAT) – 600 Marks

Each paper is of 2.5 hours duration and both are conducted on the same day.

Subjects Covered

The NDA syllabus 2025 focuses on:

Mathematics: Designed to test your problem-solving and logical abilities.

GAT: Evaluates your command over English and General Knowledge.

NDA Mathematics Syllabus 2025

Here’s what you need to conquer:

Algebra

Sets, Venn diagrams

Complex numbers

Quadratic equations

Arithmetic and geometric progression

Logarithms and their applications

Matrices and Determinants

Types of matrices

Operations on matrices

Determinants and their properties

Inverse of a matrix

Solution of simultaneous equations

Trigonometry

Trigonometric ratios

Identities and equations

Heights and distances

Inverse trigonometric functions

Analytical Geometry of Two and Three Dimensions

Cartesian coordinates

Distance formula

Equation of a line and circle

Direction cosines and direction ratios

Plane and line in 3D space

Differential Calculus

Functions and limits

Continuity and differentiability

Derivatives and applications

Integral Calculus and Differential Equations

Indefinite and definite integrals

Area under curves

First-order differential equations

Vector Algebra

Addition and multiplication of vectors

Scalar and vector products

Applications in geometry

Statistics and Probability

Mean, median, mode

Variance and standard deviation

Probability theories and distributions

NDA GAT Syllabus 2025 (General Ability Test)

Let’s break this 600-mark section down further.

English Section (200 Marks)

Your command over English will be tested through:

Grammar and usage

Spotting errors

Synonyms and antonyms

Vocabulary usage

Comprehension passages

Sentence improvement

General Knowledge Section (400 Marks)

Covers a wide range of topics:

Physics

Motion and laws

Heat and Thermodynamics

Light, Sound, Electricity

Nuclear physics

Chemistry

Physical and chemical changes

Atomic structure

Acids, bases, and salts

Carbon compounds

General Science

Human body and nutrition

Biotechnology

Environmental science

History, Freedom Movement, etc.

Ancient, Medieval, and Modern History

Indian National Movement

Constitution of India

Geography

Earth structure and atmosphere

Climate and vegetation

Rivers and mountains

Demography

Current Affairs

National and international events

Awards, sports, and culture

Marking Scheme for NDA 2025

Mathematics: 300 marks (Each question = 2.5 marks, -0.83 for wrong answers)

GAT: 600 marks (Each question = 4 marks, -1.33 for wrong answers)

You need to be accurate — guesswork can cost you.

Best Tips to Cover NDA Syllabus Efficiently

Make a Study Plan

Break the syllabus into daily goals. Focus on weak areas but don’t ignore your strengths.

Practice Mock Tests

Time-bound mock tests simulate real exam pressure. Analyze mistakes and improve.

Refer to NCERT Books

NCERT books from class 9 to 12 are the holy grail, especially for Maths and Science.

Focus on Time Management

Don’t spend too much time on a single question. Practice makes perfect!

Recommended Books and Resources

For Maths

NDA Pathfinder by Arihant

NCERT Maths (Class 11 & 12)

R.S. Aggarwal for basics

For GAT

Wren & Martin (English Grammar)

Lucent’s GK

Current affairs magazines like Pratiyogita Darpan

Importance of NDA Syllabus for SSB Preparation

While the SSB is a different stage, your understanding of current events, logical reasoning, and communication—covered in the NDA syllabus—plays a vital role in your SSB interview.

Changes in NDA Syllabus Over the Years

While the core structure remains the same, the paper pattern and emphasis areas evolve. For instance, recent papers are heavier on applied mathematics and current affairs.

Mistakes to Avoid While Preparing

Ignoring English or GAT

Relying solely on coaching

Not analyzing previous year papers

Poor time management

Final Thoughts

If you’re serious about NDA 2025, your first mission is to decode the NDA syllabus 2025. It’s your blueprint to success. From solving matrices to mastering military history, every topic brings you closer to that dream uniform. Stay consistent, stay curious — and victory will follow.

Conclusion

Cracking NDA isn’t just about hard work, it’s about smart work. And smart work begins with mastering the NDA syllabus 2025. Whether it’s complex numbers or the history of the Indian freedom struggle, every topic holds the key to your dream career in the armed forces.

So grab that syllabus, make your plan, and start today. The parade ground awaits you!

FAQs

Q1. What are the main subjects in the NDA syllabus 2025? A1. The main subjects are Mathematics and General Ability Test (GAT), which includes English, General Knowledge, Science, and Current Affairs.

Q2. Is there any change in the NDA Maths syllabus for 2025? A2. No major changes are expected. However, UPSC may increase the complexity or pattern of some topics.

Q3. How to prepare for the NDA GAT paper? A3. Read newspapers daily, revise NCERT Science & History, and practice English grammar regularly.

Q4. Are NCERT books enough for NDA Maths? A4. Yes, they form the base. You can complement them with practice books like Arihant or Pathfinder.

Q5. What is the level of difficulty for NDA Maths? A5. It’s moderate to high. Basic concepts from Class 11 and 12 are tested in a tricky manner, so conceptual clarity is vital.

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UPSC Weekend Batches for 2025–2026 | IAS Weekend Batches | Hyderabad – La Excellence IAS Academy

Looking to prepare for the Civil Services Exam while managing your job or college schedule? La Excellence IAS Academy presents UPSC Weekend Batches for 2025–2026, specially designed for working professionals, college students, and anyone seeking a flexible learning model without compromising quality.

As one of the most trusted names in civil services preparation, La Excellence offers the most comprehensive and result-oriented IAS Weekend Batches in Hyderabad.

Why Choose Weekend Batches for UPSC Preparation?

Preparing for the UPSC Civil Services Exam requires consistency, guidance, and a clear roadmap. However, full-time aspirants aren't the only ones with dreams of cracking the IAS exam. For many, balancing college, jobs, or personal responsibilities with preparation is the reality.

That’s where UPSC Weekend Batches for 2025–2026 at La Excellence become the perfect solution.

Key Features of La Excellence’s UPSC Weekend Batches for 2025–2026

✅ Structured Learning – Just on Weekends

Our weekend classes are conducted every Saturday and Sunday, offering a well-paced curriculum that ensures you don’t fall behind. The program covers both Prelims and Mains preparation, including GS papers, CSAT, and essay writing.

✅ Expert Faculty Sessions

Our experienced faculty includes retired bureaucrats, senior UPSC mentors, and subject specialists who understand the unique challenges of weekend students and help them stay on track.

✅ Complete Study Material & Current Affairs

Students receive:

Comprehensive study notes

NCERT-based and advanced materials

Monthly current affairs compilations

Practice questions for Prelims and Mains

Everything is customized for weekend learners who may have less time during the weekdays.

Why La Excellence is the Best for IAS Weekend Batches

1. Tailored Schedule

Unlike crash courses, our IAS Weekend Batches offer year-long, structured preparation aligned with the UPSC 2025–2026 calendar. Each session is focused, intensive, and revision-friendly.

2. Integrated Prelims + Mains Curriculum

This is not just a test series or a note-sharing program. Our weekend batch includes:

GS Papers I–IV

CSAT preparation

Essay & Ethics

Optional subject guidance

Daily answer writing (through weekly assignments)

3. Personal Mentorship

Weekend batches also receive dedicated mentors who guide students individually. You can book mentorship slots to review your progress and get help with your preparation strategy.

4. Hybrid Learning

You can attend classes offline at our Hyderabad centers or online in real time. Missed a class? No worries – get access to high-quality recorded lectures for revision.

Batch Details

Batch Name: UPSC Weekend Batch 2025–2026

Mode: Offline (Hyderabad) + Live Online + Recorded Backup

Duration: 12–15 months

Start Date: [Insert Start Date]

Fee Structure: [Insert Fee Information or link to fee page]

Testimonials

“La Excellence’s weekend batch helped me manage my full-time job and UPSC prep seamlessly. The structured classes and mentorship were game changers.” — Rohit, UPSC 2022 Aspirant

“The balance of Prelims and Mains in the weekend program is perfect. If you're in Hyderabad and want to crack UPSC while working, this is the best option.” — Anjali, Student, CSE 2023

FAQs – UPSC Weekend Batches for 2025–2026

Q1. Who should join the weekend batches? A: Working professionals, college students, or those needing flexibility.

Q2. Are optional subjects covered in the weekend batch? A: Yes, we provide mentorship and optional subject support.

Q3. Is this a crash course? A: No. It is a full-length, year-long foundation program.

Q4. Are tests and answer writing included? A: Yes. Regular MCQs, Mains tests, and evaluation are part of the program.

Q5. Can I switch between offline and online classes? A: Yes, hybrid flexibility is available.

Q6. Are recorded sessions provided? A: All sessions are recorded and accessible for revision.

Q7. Does it cover both Prelims and Mains? A: Yes. It's an integrated Prelims-cum-Mains course.

Q8. What is the batch size? A: We keep batches limited for personalized attention.

Q9. Will I get mentorship if I’m in the online batch? A: Yes. Online students receive the same mentorship support.

Q10. How do I register? A: Visit www.laex.in or call [Your Number] to enroll.

Enroll Today – Secure Your UPSC Future

If you're committed to clearing the UPSC but need a schedule that works for you, La Excellence’s UPSC Weekend Batches for 2025–2026 are your best bet. Whether online or offline, our IAS Weekend Batches in Hyderabad deliver results.

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Mastering the General Studies (GS) Papers: A Comprehensive Guide

The General Studies (GS) papers form the backbone of the UPSC Civil Services Examination (CSE). Covering a wide array of topics, they test an aspirant’s knowledge, analytical skills, and ability to present ideas clearly. Mastering the GS papers is crucial for securing a high rank in the exam. This blog outlines strategies, resources, and tips to help you excel in these papers.

Overview of GS Papers

The Mains examination has four GS papers, each carrying 250 marks, covering diverse topics:

GS Paper I: Indian Heritage and Culture, History, Geography of the World and Society.

GS Paper II: Governance, Constitution, Polity, Social Justice, and International Relations.

GS Paper III: Technology, Economic Development, Biodiversity, Environment, Security, and Disaster Management.

GS Paper IV: Ethics, Integrity, and Aptitude.

Each paper requires a unique approach and preparation strategy. Let’s dive deeper into how to tackle them effectively.

How to Master Each GS Paper

1. GS Paper I: History, Culture, Society, and Geography

Topics to Focus On

Indian Art and Culture: Focus on architecture, dance forms, music, and crafts.

Modern Indian History: Key events, freedom struggle, and contributions of leaders.

World History: Revolutions, world wars, and significant international movements.

Indian Society: Social issues, diversity, and population-related topics.

Geography: Physical, human, and economic geography.

Resources

Indian Art and Culture by Nitin Singhania

A Brief History of Modern India by Spectrum

NCERTs (History and Geography)

Certificate Physical and Human Geography by G.C. Leong

Tips

Use diagrams and maps to enhance answers in Geography.

For society-related questions, link them to current issues.

Memorize historical timelines and practice integrating them into your answers.

2. GS Paper II: Polity, Governance, and International Relations

Topics to Focus On

Constitution and Polity: Amendments, judiciary, and governance policies.

Social Justice: Welfare schemes, NGOs, and vulnerable sections.

International Relations: India’s foreign policy and relations with neighboring countries.

Resources

Indian Polity by M. Laxmikanth

Introduction to the Constitution of India by D.D. Basu

Current affairs from The Hindu or Indian Express.

Rajya Sabha TV debates on international relations.

Tips

Link static topics to recent developments (e.g., constitutional amendments or international summits).

Use Supreme Court judgments and committee recommendations in your answers.

Focus on concise, structured answers with relevant examples.

3. GS Paper III: Economy, Environment, Science, and Security

Topics to Focus On

Indian Economy: Budget, economic policies, and agriculture.

Science and Technology: Space, IT, biotech, and AI.

Environment: Biodiversity, climate change, and conservation efforts.

Internal Security: Cybersecurity, terrorism, and border management.

Resources

Indian Economy by Ramesh Singh

Economic Survey and Union Budget documents

NCERT Science books (Class 6–12)

Environment and Ecology by Shankar IAS Academy

Tips

Incorporate data from reports like NITI Aayog and IPCC.

Use diagrams to explain concepts like climate change or economic trends.

Relate technological advancements to real-world applications in India.

4. GS Paper IV: Ethics, Integrity, and Aptitude

Topics to Focus On

Ethics and Human Interface: Morality, values, and ethical dilemmas.

Case Studies: Real-life application of ethical principles.

Integrity and Probity: Governance, accountability, and corruption.

Resources

Lexicon for Ethics, Integrity, and Aptitude by Chronicle Publications

Second ARC Report (Ethics in Governance)

Daily practice of case studies from mock tests.

Tips

Keep answers practical and solution-oriented in case studies.

Use examples of real-life ethical leaders (e.g., Mahatma Gandhi, A.P.J. Abdul Kalam).

Define terms clearly and provide examples in theoretical questions.

General Strategies for GS Papers

1. Understand the Question Pattern

Analyze previous year question papers to identify trends and frequently asked topics.

Understand the directive words like "critically analyze," "discuss," and "evaluate."

2. Answer Writing Practice

Write answers regularly to improve speed and structure.

Stick to the word limit (150–250 words).

Use the "Introduction-Body-Conclusion" format.

3. Use Diagrams and Flowcharts

Visual aids enhance presentation and save word count.

Practice creating maps, charts, and flow diagrams for various topics.

4. Stay Updated with Current Affairs

Relate static topics to current issues for a balanced approach.

Make notes from newspapers, magazines like Yojana and Kurukshetra, and government reports.

5. Time Management

Allocate time wisely for each question during the exam.

Attempt all questions to maximize marks, even if some answers are incomplete.

Common Mistakes to Avoid

Overloading Answers with Data: Avoid excessive statistics; use data selectively.

Ignoring Diagrams: Maps and illustrations can make your answers stand out.

Skipping Revision: Regular revision ensures better retention and confidence.

Lack of Balance: Don’t focus on one GS paper while neglecting others.

Mastering the GS papers is not just about memorizing facts but developing a well-rounded perspective on various issues. With consistent efforts, smart strategies, and effective answer writing, you can excel in these papers and significantly boost your overall UPSC score.

Remember, UPSC preparation is a journey of learning and growth. Embrace the process, stay disciplined, and success will follow. Good luck!

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How to Approach Indian Society Topics for IAS Exams

Preparing for the Indian Administrative Service (IAS) exams requires a deep understanding of various subjects, and Indian Society is one of the critical areas of focus. This topic encompasses a wide range of issues, including social structures, cultural practices, and contemporary challenges. Here’s a structured approach to mastering Indian Society topics, which will be beneficial for your IAS preparation.

Understanding the Syllabus

Before diving into the intricacies of Indian Society, it is essential to have a clear understanding of the syllabus outlined by the UPSC. The syllabus often includes themes related to:

Social Issues: Poverty, gender inequality, and caste discrimination.

Cultural Diversity: Understanding the pluralism of Indian culture.

Social Movements: Significant movements and their impact on society.

Policies and Programmes: Government initiatives aimed at improving societal conditions.

By thoroughly understanding the syllabus, you can strategically plan your study sessions and focus on the most relevant topics.

Building a Strong Foundation

To effectively approach Indian Society topics, it is vital to build a strong foundation through various resources. Reading NCERT textbooks, government reports, and authentic journals can provide you with a comprehensive view of societal issues in India. Additionally, attending sessions at a TNPSC coaching centre in Coimbatore can provide valuable insights into complex topics and clarify any doubts you may have.

Suggested Resources:

NCERT Books: Start with Class 11 and 12 Sociology textbooks.

Government Reports: Look for reports from the Ministry of Social Justice and Empowerment.

Journals and Articles: Academic journals often provide contemporary analysis of social issues.

Developing Analytical Skills

Merely memorizing facts will not suffice; developing analytical skills is crucial. Here’s how you can enhance your analytical abilities:

Critical Thinking: Analyze different perspectives on social issues. For instance, when studying caste discrimination, examine the historical context and current developments.

Comparative Analysis: Compare and contrast various social movements to understand their impact on society. This could involve looking at the women's rights movement versus the farmers' protests.

Case Studies: Utilize real-life case studies to illustrate social issues. This can help you contextualize theoretical knowledge and apply it in practical scenarios.

Group Discussions

Engaging in group discussions at a TNPSC coaching centre in Coimbatore can significantly enhance your understanding. These discussions not only allow you to articulate your thoughts but also expose you to different viewpoints that you might not have considered.

Current Affairs and Its Relevance

Staying updated with current affairs is crucial for tackling Indian Society topics effectively. Newspapers, magazines, and online portals are excellent sources for the latest developments in social issues. Focus on:

Government Initiatives: Be aware of new policies and programs aimed at addressing social issues, such as the National Rural Livelihoods Mission or the Beti Bachao Beti Padhao scheme.

Social Issues: Keep track of ongoing discussions surrounding gender inequality, caste-based politics, and communal harmony.

Answer Writing Techniques

When it comes to the exam, your ability to articulate your understanding of Indian Society topics in your answers is paramount. Here are some tips to enhance your answer writing:

Structure Your Answers: Use a clear structure—introduction, body, and conclusion. Begin with a brief introduction to the topic, followed by detailed analysis, and conclude with a solution or personal opinion.

Use Examples: Integrate relevant examples to substantiate your points. Whether it’s a government initiative or a recent social movement, examples will add credibility to your answers.

Stay Objective: Maintain a neutral tone and present balanced arguments, especially when discussing sensitive topics. This reflects maturity and depth of understanding.

Conclusion

Approaching Indian Society topics for the IAS exam requires a well-rounded strategy, involving in-depth study, analytical thinking, and current awareness. By leveraging resources like a TNPSC coaching centre in Coimbatore, you can strengthen your foundation and enhance your preparation. Remember, consistent effort and a structured approach will set you on the path to success in your IAS journey.

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‘Together with’ CBSE Phygital Question Banks: Witness the Powerful Integration of Technology & Academics

Rachna Sagar has released the latest edition of ‘Together with’ PHYGITAL CBSE Question Banks Class 12 to master the subjects and ace the exams. A perfect blend of learning via book and digital facilities makes it a complete package for getting excellent results in CBSE Board exams 2024–25.

With Emergent Hybrid Learning Tech, Stepping into an Enticing Experience with ‘Together with’ e-Edition of CBSE Question Banks for Class 12 2025 is the wisest choice. Let’s walk through the academic journey where our dear learners can access the World-Of-Digital-Learning via exclusively designed QR CODES.

First-time ever any reference book for CBSE Class 12, Under NCERT Textbooks has been released in Phygital format. Practice the Best Study Material to achieve 100% success in exams. Chapter-wise Mind Maps, Ample Questions to Practice, Self-Evaluation Tests to Gauge your Readiness, 2 levels of Questions: Knowledge-based and Comprehension/Analytical Skills questions have been provided in the e-Edition of best Question Banks 2024–25.

Detailed Inclusions of ‘Together with’ Phygital Question Bank Class 12 comprises a Physical book with Digital resources, to provide Solved Practice Questions to the students in both online & offline modes. Chapter-wise solved Reference book focuses on core conceptual development.

Detailed chapter-wise analysis with solutions and an array of questions are given by the latest board exam pattern and marking scheme for the Class 12 CBSE Board 2025 Examination. Best reference books proffer Technology-assisted Academic journey by compiling Question-Answers in both online & offline modes.

Read More: https://medium.com/@rachna-sagar/together-with-cbse-phygital-question-banks-witness-the-powerful-integration-of-technology-22a0dee82668

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"Explore CBSE NCERT Class 12 Indefinite and Definite Integrals on StudiesToday. Master calculus concepts with comprehensive resources, practice questions, and solutions. Ace your exams with in-depth coverage tailored to the CBSE curriculum."

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Tackle all class 12 maths complex questions with NCERT solutions for 12 class maths. Memorysclub provides each question solutions for integrals exercise 7.3 class 12 maths and increases deep understanding of your mathematical foundation and conquering the intricacies of integrals by engaging with this carefully crafted exercise tailored to Class 12 curriculum requirements. Download class 12 ex 7.3 pdf.

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NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

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Integrals NCERT Chapter 7 Exercise 7.4 | Integration Class 12 - MathYug

Detailed explanation of questions related to NCERT Solutions for Exercise 7.4 (Q1 & Q9) of Integrals Class 12 Maths Chapter 7.  

Main Website: https://mathyug.com 

Mathyug is an online education platform focussed to strengthen your mathematical skills and allows you to deepen your knowledge by studying independently. 

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Detailed explanation of Direct & Simplification Method and questions based on NCERT Solutions of Chapter 7 Integrals Class 12 Maths IIT JEE Mains explained by expert teacher.

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How To Solve Class 12 Hard Chapters Easily

How To Solve Class 12 Hard Chapters Easily

Out of 13 sections in class 12 maths there are 3 hardest parts. They are complex and tedious. Simultaneously they are exceptionally scoring examples as well. Subsequently, this blog has been arranged that will allow 12th standard students like you to be aware, which is the hardest section in NCERT Solutions for Class 12 Maths? Three Toughest Chapter Of Class 12 Maths Applications of Integrals,…

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NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Ex 8.2

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Ex 8.2

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

Get Free NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Ex 8.2 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Application of Integrals Exercise 8.2 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers.…

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Integrals Class 12 Ncert Solutions

Extramarks offers NCERT solutions for Integrals of CBSE Class 12. Study notes & practice Integrals sample question paper to score high in school board exams. see more: https://www.extramarks.com/ncert-solutions/cbse-class-12/mathematics-integrals

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Explore comprehensive solutions and detailed explanations for CBSE NCERT Class 12 Applications of Integrals at StudiesToday. Enhance your understanding with our expertly crafted materials, practice problems, and step-by-step guides to excel in your mathematics exams.

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NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Ex 8.2

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Ex 8.2

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

Get Free NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals Ex 8.2 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Application of Integrals Exercise 8.2 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers.…