#determinants class 12 ncert solutions

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NCERT Solutions for Moving Charges and Magnetism Class 12

Class 12 Physics typically covers the topic of moving charges and magnetism, which is an essential part of electromagnetism. Here's a brief overview of the key concepts:

1. Magnetic Field (B):

A magnetic field is a region around a magnet or a moving electric charge where magnetic forces are experienced.

The SI unit of magnetic field is the tesla (T).

2. Magnetic Force on a Moving Charge:

When a charged particle moves through a magnetic field, it experiences a magnetic force perpendicular to both its velocity and the magnetic field direction.

The magnitude of the force is given by the formula: F = qvBsinθ, where q is the charge of the particle, v is its velocity, B is the magnetic field strength, and θ is the angle between v and B.

3. Lorentz Force:

The total force experienced by a charged particle moving in an electric field (E) and a magnetic field (B) simultaneously is called the Lorentz force.

The formula for the Lorentz force is given by: F = q(E + v x B), where x represents the cross product.

4. Magnetic Field due to a Current-Carrying Conductor:

Ampere's law states that the magnetic field produced by a current-carrying conductor is directly proportional to the current and inversely proportional to the distance from the conductor.

The direction of the magnetic field can be determined using the right-hand rule.

5. Magnetic Force between Two Parallel Current-Carrying Conductors:

When two parallel current-carrying conductors are placed close to each other, they experience a magnetic force due to the interaction of their magnetic fields.

6. Magnetic Field due to a Circular Loop:

A circular loop carrying a current produces a magnetic field similar to that of a bar magnet. The field is stronger inside the loop and weaker outside.

7. Torque on a Current Loop in a Magnetic Field:

When a current-carrying loop is placed in a magnetic field, it experiences a torque, which tends to align the loop with the magnetic field.

These are some of the fundamental concepts covered in the topic of moving charges and magnetism in Class 12 Physics. Understanding these concepts is crucial for various applications, including the functioning of electric motors, generators, transformers, and many more.

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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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The Way AI and Machine Learning Are Changing the Field

The increasing use of artificial intelligence (AI) and machine learning (ML) is causing a major shift in the education sector. The way we interact with educational content, teach, and learn is being completely transformed by these new technologies. We'll study the advantages, difficulties, and possible effects of AI and ML in education in this article.

Adapted Educational Opportunities

Adaptive learning systems powered by AI are changing the old universal method of teaching. These systems change the learning process according to every student's needs, skills, and learning preferences by utilizing data and analytics. Students can learn at their own speed with this specialized method, which speeds up their progress and enhances results in school.

Smart Training Programs

Intelligent tutoring systems (ITS) with artificial intelligence (AI) features help students one-by-one by following human responses. These tools help students stay motivated and motivate them by providing  real-time feedback, direction, and motivation. Additionally, teachers may look on high-value activities like coaching and teaching instead of managing paperwork and analysis thanks to ITS.Feedback and Grading Are Automated Although grading and feedback are crucial parts of the learning process, they can take a lot of time and effort from teachers. ML algorithms are used by AI-powered grading solutions to determine student work and provide clear, instant feedback. In order to carry out focused operations, teachers are able to pinpoint the areas in which students require additional help.

Better Access

Education may become more inclusive and accessible with the use of AI and ML. Students with disabilities or language problems, for example, can benefit from AI-powered solutions such as language translation platforms and speech-to-text software. In addition to removing language barriers and increasing cultural diversity, these tools can give students access to learning resources in their mother tongue.

Conclusion Finally, AI and ML are changing education by offering intelligent tutoring systems, automated grading and feedback, personal learning experiences, and easier access. Unquestionably, AI and ML have the potential to improve education, even though there are issues and problems that must be resolved. Better learning outcomes and more efficient teaching methods are going to come from even more creative applications of these technologies in education as they develop further.https://pioneercommerceacademy.com/

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Explore CBSE NCERT Class 12 Matrices and Determinants with StudiesToday. Access comprehensive notes, practice questions, and solutions to master key concepts and excel in your exams. Enhance your understanding and performance with our expert-curated resources.

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How to Prepare for Boards and NEET Exams Concurrently

Preparing for both the NEET exam and the class 12 board exams can be a challenging task. Both exams require a different approach, and striking the right balance is crucial for success. Fortunately, at Pradeep Agarwal Academy, renowned as one of the best coaching institute for NEET, we offer expert guidance to help students excel in both exams simultaneously. In this blog, we will explore 12 powerful tips, including insights on finding the best physics teacher for NEET and building a strong NEET/IIT foundation. These tips will assist students in managing their time effectively and performing exceptionally well in both the NEET and board exams.

1. Focus on Similar Topics

Identifying common topics between the NEET and board exams is the first step. We help the students identify these subjects early on, allowing them to allocate their study time more efficiently. By focusing on overlapping topics, students can streamline their preparation and reduce the risk of redundancy.

2. Prioritize NEET Syllabus

While it's essential to perform well in board exams, the competitive nature of the NEET exam demands a robust foundation in its syllabus. Coaching centres prioritize this syllabus to ensure students are well-prepared for the medical entrance exam. This approach not only helps in NEET but also strengthens the base for board exams, as NEET encompasses a more extensive and in-depth understanding of the subjects.

3. Refer to NCERT Textbooks

NCERT textbooks are highly recommended for NEET preparation. These books provide clarity and a comprehensive understanding of the fundamental concepts in physics, chemistry, and biology. For class 12 students, relying on NCERT textbooks is advantageous as they cover the entire curriculum in an easily understandable language.

4. Doubt Resolution

In the journey of NEET preparation, doubts often arise, particularly in subjects like physics and chemistry. Our coaching centers feature expert doubt resolution sessions, ensuring that students can confidently master complex problems. Meet the best physics teacher for NEET success."

5. Take Notes

Taking meticulous notes during coaching classes is an excellent habit. These notes not only aid in understanding the topics thoroughly but also serve as valuable resources during revisions. Highlighting key points and marking them as important from both the board and NEET perspectives can help students focus on the most crucial aspects of each subject.

6. Use Question Banks and Expert Solutions

Regular practice through question banks and expert solutions is essential. Solving previous years' NEET and board exam papers improves problem-solving skills and provides insight into the exam pattern. Expert solutions offer shortcuts and strategies for efficient question-solving, saving valuable time during the exams.

7. Determine Strengths and Weaknesses

Participating in weekly test series and mock tests is a cornerstone of NEET and board exam preparation. These tests not only assess your knowledge but also help identify areas where you excel and areas that need improvement. Coaching centers provide detailed performance analysis, enabling students to focus on their weaknesses.

8. Review Class 11 Topics

Class 11 forms the basis for many advanced concepts in the NEET syllabus. Regularly revisiting these topics is essential to strengthening your foundation. Creating comprehensive notes containing essential formulas and principles from class 11 can aid in quick recall during the NEET and board exams.

9. Use Recorded Lectures for Revision

Recorded video lectures offered by Pradeep Agrawal allow students to revisit previously learned topics during self-study. These lectures, conducted by subject experts, provide a thorough understanding of the concepts. Combined with practice using previous years' question papers and revision notes, this approach maximizes efficiency during the revision phase.

10. Create an Effective Study Schedule

An effectively organized study schedule forms the foundation of prosperous exam readiness. Allocating specific time slots for self-study, especially for challenging chapters, enables students to systematically cover the syllabus. Consistency in following the schedule is key to mastering both NEET and board exam subjects.

11. Set Realistic Study Goals

Setting achievable daily goals is vital. Unrealistic deadlines can lead to stress and demotivation if not met. Students should consider referring to recommended textbooks and avoid overloading themselves with too many study materials, which can lead to confusion.

12. Keep Study Plan Flexible

Flexibility in your study plan allows you to adapt to unforeseen circumstances. If you face difficulties or fall behind in a particular area, a flexible study plan lets you reschedule and prioritize accordingly. This adaptability ensures that your preparation remains on track, even during challenging times.

Incorporating these valuable tips from the best NEET coaching institutes and IIT foundation into your study routine can significantly enhance your ability to excel in both the NEET and Class 12 board exams. Remember that success is the result of consistent effort, effective time management, and utilizing expert guidance. With dedication and smart planning, you can confidently tackle these crucial exams and achieve your academic goals.

To learn more, you can contact them at

Mobile no: +91–8448084352 , +91–8448084353

Email id: contactus(@)iitcoachings.in

Website: www.iitcoachings.in

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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 Solutions- Structure of Atom: Discovery of Sub-Atomic Particles Class 11

In class 11 chemistry, students typically delve into the fascinating world of subatomic particles, the fundamental building blocks of matter. These particles, namely protons, neutrons, and electrons, constitute atoms, which are the smallest units of an element. Protons carry a positive charge, neutrons are neutral, and electrons bear a negative charge. They interact via electromagnetic forces and reside within the atom's nucleus (protons and neutrons) or in electron shells surrounding the nucleus (electrons). Understanding these subatomic particles and their arrangement within atoms is crucial for comprehending the behavior and properties of elements, paving the way for a deeper exploration of chemistry's intricacies.

1. Introduction to Atoms: Atoms are the basic building blocks of matter. They consist of subatomic particles: protons, neutrons, and electrons.

2. Protons: Positively charged particles found in the nucleus of an atom. Protons have a relative charge of +1 and a mass of approximately 1 atomic mass unit (amu).

3. Neutrons: Neutral particles found in the nucleus of an atom. Neutrons have no charge (neutral) and a mass of approximately 1 amu.

4. Electrons: Negatively charged particles that orbit the nucleus of an atom in electron shells or energy levels. Electrons have a relative charge of -1 and a negligible mass compared to protons and neutrons.

5. Atomic Number (Z): The number of protons in the nucleus of an atom. It determines the identity of the element and its place in the periodic table.

6. Mass Number (A): The sum of the number of protons and neutrons in the nucleus of an atom. It represents the mass of the atom.

7. Isotopes: Atoms of the same element with different numbers of neutrons. Isotopes have the same atomic number but different mass numbers.

8. Atomic Mass Unit (amu): A unit of mass used to express atomic and molecular weights. 1 amu is approximately equal to the mass of a proton or neutron.

9. Relative Atomic Mass: The weighted average of the masses of the isotopes of an element, taking into account their relative abundances in nature.

10. Fundamental Forces: Subatomic particles interact through fundamental forces such as electromagnetic force, strong nuclear force, weak nuclear force, and gravitational force.

11. Subatomic Particle Arrangement: Electrons are arranged in electron shells or energy levels around the nucleus. The distribution of electrons follows specific rules such as the Aufbau principle, Pauli exclusion principle, and Hund's rule.

12. Quantum Numbers: Parameters that describe the properties of electrons in an atom including principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (s).

In conclusion, the study of subatomic particles in class 11 chemistry provides a foundational understanding of the basic constituents of matter. Through the exploration of protons, neutrons, and electrons, students gain insight into the structure of atoms and the principles that govern their behavior. By comprehending the roles and interactions of these subatomic particles, learners lay the groundwork for more advanced topics in chemistry, enabling them to appreciate the complexity and diversity of the elements in the periodic table. Ultimately, the knowledge acquired about subatomic particles serves as a cornerstone for further exploration into the realms of chemical bonding, reactions, and the broader field of chemistry.

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NCERT Class 12 History Chapter 2 Kings, Farmers and Towns Early States and Economies

NCERT Class 12 History Solutions

Chapter 2 Kings, Farmers and Towns Early States and Economies

NCERT TEXTBOOK QUESTIONS SOLVED : Q 1. Discuss the evidence of craft production in Early Historic cities. In what ways is this different from the evidence from Harappan cities?

Ans. Widespread and deep excavations in the early historic towns have not been possible due to the fact that these towns are still inhabited. In Harappan Civilisation, we have been fortunate enough that excavations have taken place widespread. Despite this shortcoming, we have found many artefacts in the historic towns. These throw light on the craftsmanship of those days. There are other evidences too, that throw light on the craftsmanship of those days. The salient features of such evidences are as follows:

1. From the sights the fine pottery bowls and dishes have been found. They are glossy too and we call them Northern Black Polished Ware. It looks they were used by the rich people.

2. There have also been evidence of ornaments, tools, weapons, vessels and figurines. There are a wide range of items made of gold, silver, copper, bronze, ivory, glass, shell and terracotta.

3. The donor inscription tells who all lived in towns in terms of professionals and craftsmen. It included washer men, weaver, scribes, carpenters, goldsmith, ironsmith, etc. It is notable in Harappan towns there are no evidences of iron use.

4. The craftsmen and artisans built their guilds too. They collectively bought raw materials, produced and marketed their products.

Q 2. Describe the salient features of Mahajanapadas.

Ans. Mahajanapadas were states that existed between 6th and 4th BC centuries. Buddhist and Jain texts mention sixteen Mahajanapadas. The name of all these are not uniform in all texts but some names are common and uniform which means they were the powerful ones. These Mahajanapadas are Vajji, Magadha, Kaushal, Kuru, Panchal, and Gandhar.

The important features of the Mahajanapadas are as follows.

1. Most of the Mahajanapadas were ruled by powerful kings. However, there were some Mahajanapadas where rule was in the hands of people, we call them republics. In some states the king and the subject had collective control on the economic resources of the state.

2. Every Mahajanapadas had its own capital. The capital normally would be surrounded by fort. The fortification of the capital was needed for protection and economic resources.

3. It was around 6th Qentury BC, Brahmins began to compile scripture called “Dharmshastra” which states rules of morality including that of monarch. Herein it was mentioned that the king should be Kshatriya.

4. The main job of the king was collection of taxes from farmers, traders, craftsmen. They also accepted donations.

5. It was considered fair to plunder neighbouring countries for riches.

6. Gradually Mahajanapadas began to have full time army and officials. Soldiers were from the ranks of farmers. Q 3. How do historians reconstruct the lives of ordinary people?

Ans. Ordinary people could not leave behind any historical evidence about their life. Hence, the historians use a variety of sources to reconstruct the lives of the common people during the ancient times. The important sources are:

1. Remains of houses and pottery give an idea of the life of common men.

2. Some inscriptions and scriptures talk about the relation between monarchs and the subject. It talks about taxes and happiness and unhappiness of the common men.

3. Changing tools of craftsmen and farmers talk about the lifestyle of the people.

4. Historians also depend upon folklores to reconstruct the lives of the people during the ancient times. Q 4. Compare and contrast the list of things given to the Pandyan chief (Source 3) with those produced in the village of Danguna (source 8). Do you notice any similarities and differences? 

Ans. The gifts given to Pandya chief included things like ivory, fragrant wood, honey, sandal¬wood, pepper, flowers, etc. in additions to many birds and animals were also given as gifts. On the contrary, items produced in the village of Danguda included grass, skin of animals, flower salt and other minerals, etc. In both the lists the only common item is flower. Q 5. List some of the problems faced by the epigraphists.

Ans. The specialists who study inscriptions are called Epigraphists. Some of the important problems they encounter when they try to decipher inscriptions are as follows:

1. Many of the inscriptions are not found in proper shape, they are partly damaged, hence deciphering them becomes a knotty problem.

2. The inscriptions are written from the point of view of those who have created it. Hence, in order to get an impartial understanding, we need to go beyond the written words, get into its interpretations.

3. Many of the inscriptions have descriptions in symbolic words. Hence deciphering them have become difficult.

4. Sometimes the inscriptions are engrafted in very light colors. Hence, deciphering them becomes difficult. Q 6. Discuss the main features of the Mauryan administration. Which of these elements are evident in the Asokan inscriptions that you have studied ?

Ans. Asokan inscriptions mention all the main features of the administration of the Mauryan Empire. Thus, the features of the administration are evident in the inscriptions of the Asokan age. The important features of the same are as follow:

1. The capital of the Mauryan Empire was Pataliputra. Apart from the capital there ‘ were four other centres of political power in the empire. They were Taxila, Ujjaini, Tosali and Suvamagiri.

2. Committee and subcommittees were formed to run the administration and safety of boundaries. Megasthenes has mentioned that there were one committee and six sub-committees. The six subcommittees and their areas of activities are as follows:

(i) The first sub committee looked after navy. (ii) The second sub committee looked after transport and communications. (iii) The third sub committee looked after infantry. (iv) The fourth sub committee had the responsibility of horses. (v) The fifth had the responsibility of chariots. (vi) The sixth had the responsibility of elephants.

3. Strong network of roads and communications were established. It is notable that no large empire can be maintained in the absence of the same.

4. Asoka made an attempt to keep the empire united by the philosophy of Dhamma. Dhamma are nothing but moral principles that actuated people towards good conducts. Special officers called Dhamma Mahamtras were appointed to propagate Dhamma. In fact Romila Thapar has made it the most important element of the Asokan state’s governing principle. Q 7. This is a statement made by one of the best-known epigraphists of the twentieth century, D.C. Sircar: “There is no aspect of life, culture, activities of the Indians that is not reflected in inscriptions.” Discuss. 

Ans. The statement of eminent epigraphist D.C. Sirkar has highlighted the importance of inscription as single source of information that touch upon all areas of our life. Following are the main areas we get information about from the inscriptions;

1. Determination of state’s boundaries: the inscriptions were carved in the territories of the kings and even more important is not often close to the borders. This help us find out boundaries of kingdoms and their expansions thereto.

2. Names of Kings: The names of the kings are mentioned in the inscriptions. The names and titles used by Asoka the Great got revealed through inscriptions only.

3. Historic events: The important historical events are mentioned in the inscriptions. The best example is how the event of the Kalinga war is mentioned in the inscription and how Asoka takes to Dhamma.

4. Information about conduct of Kings: Inscriptions describe the conduct and character of the kings quite well. It is through the inscriptions only that we know Asoka worked for the welfare of the masses.

5. Information about administration: Inscriptions gave information about administration. It is through the inscription. We know that Asoka appointed his son as a Viceroy.

6. Land settlement and Taxes: inscriptions mention how land were granted or gifted. It also talks about various taxes imposed by the ruler.

There is hardly any area of governance of our life that is not mentioned in the inscriptions. Hence, we are inclined to agree with D.C. Sirkar who says, “There is no aspect of life, culture, activities of Indians that is not reflected in the inscriptions.” Q 8. Discuss the notions of kingship that developed in the post-Mauryan period.

Ans. In the post-Mauryan age, the idea of kingship got associated with divine theory of state. Now, the monarchs began to talk about divine sanction to rule the people. Kushan rulers propagated the idea of the same at the unprecented scale. They ruled from central Asia to western India. We can discuss the kingship based on the dynasties.

1. Kushan Kings: Kushan Kings called themselves Devputra and hence, godly status. They built great statues of themselves in temples.

2. Gupta Rulers: Second development of kingship is found during Gupta dynasty. It was a period of large-sized states. Such states were dependent on Samantas who sometimes became powerful enough to usurp the power of kings too.

3. Literature, coins and inscriptions helped us in creating history of those days. Very often poets would describe the monarch often to praise them but giving insight into the history and kingship too. A good example is of Harisena who praised Samudragupta, the great Gupta ruler. Q 9. To what extent were agricultural practices transformed in the period under consideration? 

Ans. The demand for taxes increased in the post 600 BC. In order to meet the demand of excessive taxes, without taking lesser produce, forced the farmers to increase productivity. This resulted in the use of new tools and practices of agriculture. The important ones are as follows:

1. Use of plough: Ploughs became commonplace. They were hardly heard of in the past. The use of ploughs began in the Ganga and Cauvery basins. In places where rain was abundant, the plough was used with iron tip. This increased the paddy production manifold.

2. Use of spade: Another tool that changed the system of agriculture is spade. Those farmers who lived in the areas of harsh land used spade.

3.  Artificial Irrigation: Apart from rainfall, the farmers now began to look at artificial form of irrigation. This prompted farmers to build wells, ponds, and – canals often collectively. This increased the agricultural production.

The production increased due to new technology and tools. This created a new strata in the society. In the Buddhist literature, there is a description of small and big farmers. They were called Grihpatis. Similar description is given in the Tamil literature too. The position of village head was often hereditary. In such a situation the ownership of land became very important.

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

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NCERT Exercise 4.6 Determinants Class 12 Maths Chapter 4

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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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