Important Questions for Class 12 Maths

Mathematics is an important subject for the students of class 12. It develops creative and logical thinking of students to think diversely. As you know, class 12 is considered to be the most crucial year and the marks obtained in class 12 are responsible for admission in higher education. Thus, the concepts and the topics are perfectly formulated to create a strong base of maths for all the students of class 12. To make your learning more intense, eSaral provides  important questions for class 12 maths with answers. All the most important questions of maths class 12 are included chapter-wise so that you can practice them easily.

Our academic team of mathematics at eSaral have not only provided the important questions for class 12 maths with answer PDF but also explained the concepts, properties, terms, important theorems and definitions mentioned in various chapters of maths in easy to understand manner that helps you to revise the syllabus effectively even just before the main exam.

Class 12 maths important questions with answers pdf are provided on eSaral website that can be downloaded for free. This will help you to enhance your preparation and score good marks in class 12 board exams. By practicing important questions and class 12 maths extra questions, students can find their weakness and the reason where they are lacking to master the concepts. This helps them to boost their confidence. In class 12th Maths important questions, each question is curated by experts of eSaral with step-wise process and concepts that assist you to solve questions without any confusion. 

Benefits of Solving CBSE Class 12 Maths Important Questions

Incorporating with class 12 important questions maths provides a strategic approach to exam preparation. These questions empower you with comprehensive understanding of the subject. To score good marks in exams, You must integrate the benefits of solving important questions. Explore the benefits of solving CBSE class 12 maths important questions provided by subject experts of eSaral. 

1. Comprehensive Understanding: Solving important questions class 12 maths helps you develop a profound understanding of concepts and topics. All the questions included in important questions are carefully explained which cover a wide range of topics to ensure you are well-versed with each aspect of the curriculum. 

2. Enhance Problem-Solving Skills: Class 12 maths important questions designed by experts of eSaral have involved easy to complex questions. Regularly solving these questions helps you to sharpen your analytical and problem-solving skills.

3. Conceptual Clarity: Important questions for class 12 maths with answers target fundamental concepts of chapters that form the basis of more complex topics so that you can have a conceptual clarity for solving questions in the final exam. Also, by practicing important questions students are able to reinforce their knowledge of various advanced concepts.     

4. Time Management: As you know, the class 12 maths exam is time-bound. Thus, it is necessary to solve questions in a given time. Constantly solving class 12th maths important questions with answers pdf will improve your speed and accuracy and also help you to complete the exam within a given time frame. 

5. Self-Assessment and Improvement: Practicing important questions for class 12 maths with answers allows you to assess your own performance. You can identify your strengths and weaknesses if you practice important questions which helps you to focus on the concepts that require additional attention. 

6. Revision and Reinforcement: Class 12 maths important questions are an excellent revision tool to prepare for board exams. By revising the core concepts through class 12 maths extra questions and important questions, students reinforce their learning to achieve desired marks in class 12 board exams. 

How to Solve Class 12th Maths Questions to score more marks?

Class 12th mathematics seems difficult to many students but with the right approaches and strategies, it becomes easy to achieve this goal. To score well in the subject maths, it requires a combination of conceptual understanding, question practice and effective time management. Ultimately, this will help you to excel in class 12 board examination. eSaral’s subject matter experts have provided important questions for maths class 12. These important questions have included problems by analyzing the syllabus of class 12 maths and previous years question papers.

Students must practice these important questions for class 12 maths with answers PDF to solve questions in board exams. Students should finish their syllabus before the time so that they can revise the essential topics of chapters to master the concepts. There are numerous exercises in chapters of mathematics which you must solve to grasp all the concepts. Some of the chapters such as matrices, determinants, continuity and differentiability, vector algebra etc. includes theorems, properties and significant terms that need proper understanding to solve questions step by step in exams. You must learn these concepts and properties so that you don’t get confused while solving questions in board examinations. You can also download the PDF of important questions to practice questions and score full marks in class 12 maths board exams.

Overview of CBSE Class 12 Maths Chapter Details

CBSE class 12 maths has a vast syllabus with 13 chapters. Thus, the subject of mathematics becomes pretty scary for some students. But with proper practice of questions and complete knowledge of concepts will help you to strengthen the fundamentals of topics to achieve great results in exams. The syllabus of mathematics is structured in such a manner to help students develop logical and problem-solving skills. Here, our expert faculties of mathematics have provided an overview of chapters for class 12 maths. 

Chapter 1: Relations and Functions - In class 12 maths chapter 1 Relations and Functions, you will learn and study the introduction of relations and functions, types of relations such as empty relation, universal relation, reflexive relation, symmetric relation,transitive relation, equivalence relation. You will learn the types of functions such as one-one or injective function, onto or surjective function, one-one and onto (or bijective) function. Composition of functions and invertible function is also provided there which you must learn for better preparation for exams. There are a total of two exercises along with one miscellaneous exercise to practice questions for proper understanding of all significant topics and concepts.  

Chapter 2: Inverse Trigonometric Functions - CBSE class 12 maths chapter 2 Inverse Trigonometric Functions has included introduction of inverse trigonometric functions, basic concepts of inverse trigonometric functions such as range, domain, finding the value of inverse trigonometric functions at a particular point etc. and properties of inverse trigonometric functions. This chapter has two main exercises as well as miscellaneous exercise.You must solve all the questions included in these exercises to score good marks in exams.

Chapter 3: Matrices - Chapter 3 Matrices is one of the important chapters of maths curriculum. This chapter has many essential topics and concepts which you must learn for better comprehension of questions. You will study introduction to matrices, definition of matrix and order of matrix, types of matrices. You will also learn the order of matrices, transpose of a matrix and its properties and definitions, concepts of symmetric and skew symmetric matrices, various important theorems related to matrices and invertible matrices and its definitions. 

Chapter 4: Determinants - Class 12 maths chapter 4 Determinants has a lot of significant topics and concepts that are explained by the experts of eSaral. Students will be introduced to determinants and determinant of a matrix of order one, determinant of a matrix of order two, determinant of a matrix of order 3 × 3, area of triangle, minors and cofactors, adjoint and inverse of a matrix and some important theorems. This chapter also has involved five exercises and one miscellaneous exercise with important questions that you should solve to get a clear understanding of concepts.

Chapter 5: Continuity and Differentiability - CBSE class 12 maths chapter 5 Continuity and Differentiability helps you score full marks in this chapter if you have conceptual understanding of all the topics included in it. You will study here the introduction of continuity and differentiability, Basics of Continuity, its definition and some theorems based on them. You can also learn the theorems of differentiability and its properties. The theorem of exponential and logarithmic functions is explained. Logarithmic differentiation, derivatives of functions in parametric forms, second order derivative are also explained with easy to understand language for you to prepare well for board exams. There are 7 exercises as well as one miscellaneous exercise for you to practice the questions. 

Chapter 6: Applications of Derivatives - Class 12 maths chapter 6 Applications of derivatives is an important part of calculus. Chapter 6 includes introduction of applications of derivatives, rate of change of quantities, increasing and decreasing functions which involves its definition and theorem, definition of maxima and minima and some important theorems related with maxima and minima, maximum and minimum values of a function in a closed interval. In chapter 6, there are a total of 3 exercises along with one miscellaneous exercise for practicing questions to strengthen the concepts of applications of derivatives. 

Chapter 7: Integrals - In chapter 7 Integrals, you will study some significant topics and concepts like introduction of integrals, integration as an inverse process of differentiation, some properties of indefinite integral, methods of Integration, integrals of some particular functions, integration by partial fractions, integration by parts, definite Integral and fundamental theorem of calculus. Also, you will find 10 exercises and one miscellaneous exercise that included questions based on these topics. You must practice all the questions as well as examples provided before each exercise to build a strong foundation of concepts. 

Chapter 8: Application of Integrals - Class 12 maths chapter 8 Application of Integrals covers introduction of application of integrals. There is one important topic of area under simple curves which you must be well versed for solving questions under this topic. Chapter 8 has one main exercise and one miscellaneous exercise including problems based on area under simple curves which you should solve before the exams for clear understanding of concepts. 

Chapter 9: Differential Equations - CBSE class 12 maths chapter 9 Differential Equations is one of the important chapters of mathematics. In chapter 9, you will study introduction of differential equations, some basic concepts of differential equations such as order of a differential equation and degree of a differential equation. There are some other essential topics like general and particular solutions of a differential equation, methods of solving first order, first degree differential equations such as differential equations with variables separable, homogeneous differential equations and linear differential equations. Also, this chapter includes 5 exercises as well as one miscellaneous exercise. Students must solve these exercises to grasp all the concepts of differential equations. 

Chapter 10: Vector Algebra - Class 12 maths chapter 10 Vector Algebra plays an important role in class 12 maths board exams. Students have to master all the vital topics and concepts of vector algebra to score full marks in this chapter. This chapter includes topics like introduction of vector algebra, some basic concepts of vector algebra, type of vector like zero vector, unit vector, coinitial vectors, collinear vectors, equal vectors,negative of a vector. Addition of vectors and its properties, multiplication of a vector by a scalar, components of a vector, vector joining two points and section formula are some methods which must be learnt for proper understanding of concepts. Product of two vectors like scalar (or dot) product of two vectors, projection of a vector on a line and vector (or cross) product of two vectors. You must be well versed with all these topics and concepts to solve questions without being confused. Chapter 10 Vector Algebra has a total of 4 main exercises along with one miscellaneous exercise. Practice all the questions of exercises to score good marks in class 12th board exams. 

Chapter 11: Three Dimensional Geometry - In class 12 maths chapter 11 Three Dimensional Geometry, we use vector algebra to solve 3D geometry. The topics elaborated in this chapter are as follows- Introduction of three dimensional geometry, direction cosines and direction ratios of a line, direction cosines of a line passing through two points, equation of a line in space, equation of a line through a given point and parallel to $\vec{a}$ given vector $\vec{b}$ , angle between two lines, shortest distance between two lines, distance between two skew lines, distance between parallel lines. All the topics are essential for students to prepare for exams. In chapter 11 class 12 maths, you will also find two main exercises and one miscellaneous which include questions based on the topics mentioned above. To achieve the desired result, you have to practice all the questions and examples of chapter 11. 

Chapter 12: Linear Programming - CBSE class 12 maths Linear Programming has some methods and topics to find the value of linear equations. Chapter 12 talks about introduction of linear programming, linear programming problem and its mathematical formulation, mathematical formulation of the problem, graphical method of solving linear programming problems and some significant theorems based on linear programming. There is one main exercise and one miscellaneous exercise that you must solve to have a clear understanding of concepts and theorems related to linear programming. 

Chapter 13: Probability - Class 12 maths chapter 13 Probability is a scoring chapter for board exam point of view. Thus, students should master all the concepts associated with probability to score desired marks in exams. In chapter 13, students will learn topics such as introduction of probability, conditional probability and its properties, multiplication theorem on probability, independent events and its definition, Bayes' Theorem, partition of a sample space, theorem of total probability. There are 3 exercises and one miscellaneous exercise including questions based on probability which you must practice to achieve good marks in final exams. 

Why is eSaral the best platform for Class 12 Maths online classes?

eSaral has an ideally designed education system and perfectly developed online classes for students. We have also conducted different formats of online study classes to provide students one-on-one basis to cover topics and sub-topics of class 12 maths syllabus. Here, we have included some specific criteria that makes eSaral the best platform for class 12 maths online classes. 

1. Quality of Content - We are providing class 12 maths students a quality content that is comprehensive, well-structured, and aligned with CBSE class 12th maths syllabus.

2. Interactive Learning - eSaral offers interactive experiences during live classes such as quizzes, practice questions and simulations which can enhance the understanding and retention of concepts.

3. Experienced Educators - On eSaral platform, you will be learning with experienced and qualified teachers and faculties who can effectively elaborate complex mathematical concepts and provide support to students.

4. Availability of Resources - Students will be able to use a variety of resources such as video lectures, study materials, hand written notes, and important practice problems. 

5. Doubt Solutions - eSaral also provides a doubt solving tool (DOST) for students where they can get solutions for their doubts regarding any topic or concepts.  

6. Personal Academic Mentor - Every student of eSaral will get a personal academic mentor who will track their progress and assist and guide students during their study to achieve desired result in final exams.

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