#NCERT Solutions for Determinants Class 12 Maths

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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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NCERT Solutions for Class 12 Maths Chapter 4 Determinants

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We provide an expanding number of detailed high-quality video lectures and study material for Determinants Class 12 Maths Chapter 4.

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#Class12Maths #CBSEBoard #PropertiesOfDeterminants

Detailed explanation for Properties of Determinants and NCERT Exercise 4.2 Determinants Class 12 Maths explained by expert teacher as per CBSE (NCERT) book guidelines.

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ncert ex 4.2 class 12 Questions 1,2,3,4,5 | Determinants Properties |#MathsbyMukeshSir

ncert exercise 4.2 class 12 maths Q1,Q2,Q3,Q4,Q5,Q6 Solution Maths by mukesh sir exercise 4.2 class 12 maths ncert solutions | ncert math class 12 exercise 4.2 in hindi, exercise 4.2 ncert class 12th | exercise 4.2 class 12 ncert solutions |determinants class 12 ncert exercise 4.2 | ncert exercise 4.2 class 12 maths |ncert solution exercise 4.2 class 12 ncert ex 4.2 class 12 Questions 1 - ncert ex 4.2 class 12 Questions 2 - ncert ex 4.2 class 12 Questions 3 - ncert ex 4.2 class 12 Questions 4 - ncert ex 4.2 class 12 Questions 5 - ncert solutions of exercise 4.2 class 12 maths ncert solution class 12th exercise 4.2 ncert math solution class 12th exercise 4.2 class 12th maths ncert exercise 4.2 ncert solutions for class 12th mathematics exercise 4.2 ncert exercise 4.2 ncert solution of exercise 4.2 class 12 ncert ex 4.2 class 12 ncert exercise 4.2 class 12th exercise 4.2 class 12 ncert solutions ncert solutions ex 4.2 class 12 class 12 ncert exercise 4.2 exercise 4.2 class 12 ncert ex 4.2 class 12 ncert exercise 4.2 class 12 solutions exercise 4.2 class 12 solution of exercise 4.2 class 12 exercise 4.2class 12 ex 4.2 class 12 ncert solutions exercise 4.2 class 12th ex-4.2 class 12 exercise 4.2 class 12 maths ncert solutions ex 4.2class 12 ex.4.2 class 12 ex 4.2 class 12 ex. 4.2 class 12 exercise 4.2 class 8 ncert solutions

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3

Get Free NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.3 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Determinants Exercise 4.3 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the…

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CBSE Class 12 Maths Revision Notes

Class 12 Maths Notes: Class 12 Maths Notes is designed to help for the students who are going to appear final exams, students can read this CBSE Class 12 Maths Revision Notes before going to exam to cover all chapters and topics in last minute and can easily revise all chapters of class 12 Maths. Important topics like Trigonometry, integrals, equations and three-dimensional geometry has been included in Class 12 Maths Notes. For CBSE Students board exams will be conducted by NCERT. Class 12 Maths Notes has been designed on the basis of the latest NCERT syllabus textbooks. So students can check CBSE Class 12 Maths Quick Revision Notes and can download the solutions in PDF’s format as well. Students can practice the Class 12 Maths Revision Notes to gain more knowledge.

Class 12 Maths consists of 13 Chapter below is the list of chapter Names.

Chapter 1: Relations and Functions Chapter 2: Inverse Trigonometric Functions Chapter 3: Matrices Chapter 4: Determinants Chapter 5: Continuity and Differentiability Chapter 6: Application of Derivatives Chapter 7; Integrals Chapter 8: Application of Integrals Chapter 9: Differential Equations Chapter 10: Vector Algebra Chapter 11: Three Dimensional Geometry Chapter 12: Linear Programming Chapter 13: Probability

Students can download the PDF’s of Class 12 Maths Revision Notes. The Class 12 Maths Notes will also help in understanding the chapters properly as it will contain the important points for revision purpose in short times

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Life is now lived with more significant direction and purpose. And once those goals are achieved, trust builds, and not only do we feel a sense of achievement, but we want to reach even more. 

If you want to succeed in your life, you have to set a goal. Without goals, you lack focus and direction. The goal allows you to take control of your life's direction. It also provides you with a benchmark for determining whether you are succeeding. However, if you're waiting until everything's perfect before you begin, you'll be waiting for a very long time! The best time to start working on your goals is now.

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Tags: Free online courses for CBSE,  NCERT Solutions,  CBSE Class 10, CBSE Class 12,  NCERT Solutions For Class 10 Maths,  NCERT Solutions For Class 10 Science,  NCERT Solutions For Class 10,  CBSE Syllabus,  ICSE Class 10,  ISC Class 12

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ncert solutions for class 8 maths

NCERT Solutions for class 8 Maths

in case if you are looking for accurate, comprehensive and free ncert solutions for class 8 maths then you are at very right place. These ncert solutions for class 8 maths are available in the PDF format, which can be easily shared and accessed among friends. The diligent efforts of faculties at Entrancei have made sure the best of all solutions are available for students.

In order to make the learning process very easy, the students need to just go throw the study material. These ncert solutions for class 8 maths are the best tool for a quick revision of your concepts. The complete syllabus has been broke down into various parts in the manner of chapters. Students need to just sign up at Entracei. The categorization of chapters is made below

Ø  Chapter 1: Rational Number

This chapter of ncert solutions for class 8 maths helps the students with giving them a deep understanding of number system and rational numbers.

Ø  Chapter2: Linear Equations in One Variable

This chapter of ncert solutions for class 8 maths helps the students in getting acquainted with the method of solving contextual problems based upon linear equations

Ø  Chapter 3: Understanding Quadrilaterals

This chapter of ncert solutions for class 8 maths helps the students with knowledge of angles and their sum. This chapter helps the students with convex, concave and parallelograms.

Ø  Chapter 4: Practical Geometry

This chapter of ncert solutions for class 8 maths helps the students with enhancing their knowledge regarding rhombus, parallelograms, squares, and rectangles.

Ø  Chapter 5: Data Handling

This chapter enhances students’ knowledge with the method of representing data in the form of bar graphs and charts.

Ø  Chapter 6: Square and Square roots

This chapter of ncert solutions for class 8 maths teaches the students in solving critical square roots through factor method and division method

Ø  Chapter 7: Cube and Cube roots

This method presents a stepwise representation of methods to determine cube roots.

Ø  Chapter 8: Comparing Quantities

This chapter of ncert solutions for class 8 maths helps the students with unit quantities like percentage, ratio, sales tax, and compound interests.

Ø  Chapter 9: Algebraic expressions and Identities

This chapter of ncert solutions for class 8 maths helps the students in solving algebraic expression with addition, subtraction, division, and multiplication.

Ø  Chapter 10: Visualising solid shapes

This chapter of ncert solutions for class 8 maths helps the students regarding 3D objects and their plotting on map.

Ø  Chapter 11: Mensuration

This chapter of ncert solutions for class 8 maths helps the students in determining areas of polygon and trapezium.

Ø  Chapter 12: Exponents and powers

This chapter of ncert solutions for class 8 maths helps the students regarding the integers in the number system.

Ø  Chapter 13: Direct and Inverse Proportions

This chapter of ncert solutions for class 8 maths helps the students regarding the variation which is direct and in-direct quantities in NCERT book.

Ø  Chapter 14: Factorization

This chapter helps the students in enhancing their concepts associated with algebraic identities and factorization.

Ø  Chapter 15: Introduction to Graphs

This chapter of ncert solutions for class 8 maths helps the students reading numbers, perimeters, and length of square graphs.

Ø  Chapter 16: Playing with numbers

This chapter of ncert solutions for class 8 maths is more of like a fun game where students need to plot 2 digits and 3 digit number from the puzzles.

 Why ncert solutions for class 8 maths at Entancei

Ø  Since maths has been crucial in building strong foundation, we make sure you get the best of all.

Ø  The ncert solutions for class 8 maths are up-to-date and as per the latest NCERT regulations

Ø  The expert provided ncert solutions for class 8 maths is sufficient to score great marks in Examination

Ø  While solving the NCERT class 8 maths the most important think you required is maths formula. Check out all maths formula in one page

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Q1 Exercise1.1 I Class 12 Maths NCERT Chapter 1 Relations and Functions | NCERT solutions

NCERT Class 12Chapter: Relations and FunctionsExercise 1.1Question 1: Determine whether each of the following relations are reflexive, symmetric and transitive:(i) Relation R in the set A = {1, 2, 3, …, 13, 14} defined as R = {(x, y) : 3x – y = 0}(ii) Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x less than 4}(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6}…

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NCERT Exercise 4.6 Determinants Class 12 Maths Chapter 4

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Detailed explanation of Determinants using Cofactors and questions based on NCERT Solutions of Exercise 4.4 and 4.5 of Chapter 4 Determinants Class 12 Maths explained by expert teacher.

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#DeterminantsClass12Maths #Class12Maths

Live video lecture explaining NCERT Solutions for Exercise 4.4 and 4.5 of Chapter 4 Determinants Class 12 Maths explained by expert teacher.

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JEE MAIN 2022: IMPORTANT TOPICS FOR MATHEMATICS

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

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

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

Mathematics chapters and their weightage-

Chapters

Total Questions

Weightage

Sets

1

3.3%

Permutations & Combinations

1

3.3%

Probability

1

3.3%

Complex Numbers

1

3.3%

Binominal Theorem

1

3.3%

Limits

1

3.3%

Differentiability

1

3.3%

Indefinite Integration

1

3.3%

Definite Integration

1

3.3%

Differential Equations

1

3.3%

Height & Distance

1

3.3%

Trigonometric Equations

1

3.3%

The Area under the Curve

1

3.3%

Quadratic Equations

1

3.3%

Vectors

1

3.3%

Tangents and Normals

1

3.3%

Maxima and Minima

1

3.3%

Statistics

1

3.3%

Parabola

1

3.3%

Ellipse

1

3.3%

Hyperbola

1

3.3%

Mathematical Reasoning

1

3.3%

Sequences & Series

2

6.6%

Straight Lines

2

6.6%

3-D Geometry

2

6.6%

Determinants

2

6.6%

Important topics-

Quadratic Equations & Expressions

Complex Numbers, Probability

Vectors & 3D Geometry

Matrices in Algebra

Circle, Parabola, Hyperbola in Coordinate Geometry

Functions

Limits

Continuity and Differentiability

Application of Derivatives

Definite Integral in Calculus

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

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

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2

Get Free NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Determinants Exercise 4.2 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the…

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How much does it cost to develop an e-learning app like Extra marks?

How much does it cost to develop an e-learning app like Extra marks?

E-Learning has evolved as a savior of life for students and teachers, especially during the Coronavirus Pandemic addict. This e-learning mobile application has changed the traditional method of educational processes throughout the world. When the spread of the Covid-19 pandemic has significantly affected the education segment. When there is no remaining option, people can continue their education outside the regular class settings only by efficient ways to induce results through e-learning applications.

About Extra marks:

Extra marks, an app with an enjoyable, thrilling, and collaborative way of eLearning with advanced features. It is unique in its way of precise via appealing visuals and amazing graphics, that resolve the queries within no time. Students can find innovative and accurate solutions for diverse topics on the app, via various graphics and collaborative learning segments, comprising projects, homework, tests, or assignments. Extra marks, is the only app that has solutions for all topics for all classes (KG to 12), for CBSE and ICSE Boards.

It has introduced an AI-supported study bot named Alex, which will aid students in learning the topics effectively at all times of need. You can easily click a picture of the queries of your choice and post it to get the answer.

Tailored Learning process This advanced bot crafts an innovative learning journey as it analyses the precise learning requirements and educational motives. It may employ surprise tests to understand the level of understanding, and adjust to the outcomes to meet the specific goals of the personalised learning process.

Another service called “Achieve” offers practical clearing of doubts with comprehensive supervision. It is a special feature that lets teachers use SNAAP (Student Needs Analysis and Academic Profile) to guarantee success in every student's journey.

The complete process of learning at Extra marks is supported by an innovative Reports and Analytics platform. This is crucial in understanding individual and relative student performance. By recognizing the gaps and strengths in your learning process. The student will have access to view complete figures on key metrics such as average time consumed for every query, accuracy, understanding capacity, etc. You will get total understanding via comparative ranking and breakdown. Be guaranteed to utilize an innovative process at all your future subjects via suggestions and alterations as per learning curve necessities.

The app covers complete topics from KG to grade 12 with the same level of zeal and competitiveness. It is popular among several educational apps in the country, as it is the one-stop solution for diverse subjects such as Maths, Science, Social Science, English, English Core, English Elective, Sanskrit, Hindi, Economics, Geography, History, Political Science, Business Studies, Accountancy, Physics, Biology, Computer Science (C++ and Python), Chemistry, Informatics Practices, Multimedia Web and Technology, etc. All the learning methodologies and topics are affiliated with NCERT books and cover all subjects comprising NCERT Solutions.

How much does it cost to develop an e-learning app like Extra marks?

Developing an innovative learning app like Extra marks requires detailed research on various key features for determining the overall cost. The development cost of developing an eLearning app like Extra marks is generally reliant on the below key points:

Operating Platforms:

Building the app on diverse platforms involves the usage of diverse technological aspects. The development cost of building on the Android platform would need consideration of testing on multiple devices that will increase the overall cost of the iOS platform. Few business owners will opt for cross-platform development to reach users across multiple platforms.

Design:

It is key to offer an intuitive and user-friendly design to engage any kind of app user. With students interacting with the app for prolonged periods, a design with simple, smooth yet exciting navigations will engage them for longer. Also, the impactful design will reach the maximum number of users to get maximum profits.

App Features:

The size of the app is dependent on the type, amount, and complexity of features and functionalities in the app. Few of the included features will be basic and a few may be extra premium elements that will highly impact the overall development costs. These advanced features might require the with 3rd party integration to provide error-free service to the users. To ensure a safe move in the initial periods, it is suggested to include only basic features in the MVP versions.

Technologies:

The type of technology utilized in the app has a straight impact on the overall cost of development. Further few libraries and tools will have open-source components while others may require extra charges. Therefore, the selection of technologies will influence the overall cost of development hugely. This needs you to strategize much earlier for avoiding surprises at the last minute.

App Size: The overall cost of building an app such as Extra marks increases with the increase in the app size. App size increases exponentially with the inclusion of complex features and functionalities. Hence, with the increase in these elements, there will be a guaranteed increase in the app size. It is suggested only to select appropriate features that are relevant to the users.

Maintenance works:

It is key for any successful E Learning app development company to offer reliable coverage of app development services including maintenance service after the release of the app. Maintenance is key in the long-term success of the app as it runs without any flaws.

Selection of app Development Company:

The location, expertise, and guidance of the mobile app development company are highly important. A knowledgeable team will produce an excellent app at the expected interval but a slightly higher price.

Final Thoughts:

If you have understood the importance of an eLearning app such as Extra marks, then choose a reliable E Learning app development company in New Delhi like Brillmindz. The skilled team possesses unmatched experience and knowledge in creating profitable mobile apps across multiple industries. There will be a guaranteed success due to the right reach of the target audience and the use of accurate technologies.