Chapter 1 Relations and Functions
Relationships and functions, relation types, function types, function composition, invertible functions, binary operations, and other examples are covered in Chapter 1 of the NCERT textbook. The links to the exercise solutions for the subjects discussed in this chapter are provided here.
Chapter 2 Inverse Trigonometric Functions
Chapter 2, Inverse Trigonometric Functions of NCERT Class 12 Maths, provides an overview of a number of subjects, including properties of inverse trigonometric functions, remarks based on fundamental ideas of inverse trigonometric functions, and different examples. The examples used to illustrate these ideas are excellent. You may find the answers to the chapter's exercises here.
Chapter 3 Matrices
The definition of a matrix, matrix types, matrix equality, operations on matrices, including matrix addition and matrix multiplication by a scalar, matrix addition properties, scalar multiplication properties, matrix multiplication properties, matrix transpose properties, symmetric and skew-symmetric matrices, elementary operation or transformation of a matrix, the inverse of a matrix by elementary operations, and various examples are all covered in Chapter 3 of the NCERT textbook. The links to the exercise solutions for the subjects discussed in this chapter are provided here.
Chapter 4 Determinants
Determinants are covered in Chapter 4 of the 12 Class NCERT Maths Solution. The definition and meaning of determinants, remarks based on their order, properties, finding the area of a triangle using determinants, determining determinants' minors and cofactors, adjoint of a matrix, inverse of a matrix, applications of determinants and matrices, and various examples will all be covered for the students. Links to all of the exercise solutions discussed in this chapter are included below.
Chapter 5 Continuity and Differentiability
The definition of continuity opens Chapter 5 of the NCERT textbook. Through a variety of examples, students learn about the following topics: continuity, algebra of continuous functions, concept and meaning of differentiability, derivatives of composite functions, derivatives of implicit functions, derivatives of inverse trigonometric functions, exponential and logarithmic functions, logarithmic differentiation, derivatives of parametric functions, second order derivatives, and mean value theorem. Students can find tasks that adequately explain these ideas along with solutions below.
Chapter 6 Applications of Derivatives
Derivatives, rate of change of quantities, increasing and decreasing functions, tangents and normals, approximations, maxima and minima, first derivative test, maximum and minimum values of a function in a closed interval, and other examples are all covered in Chapter 6 of the NCERT textbook. Students can find tasks that adequately explain these ideas here.
Chapter 7 Integrals
The definition and meaning of definite integrals, definite integral as the limit of a sum, fundamental theorem of calculus, evaluation of definite integrals by substitution, properties of definite integrals, geometrical interpretation of indefinite integrals, geometrical interpretation of indefinite integrals, comparison between differentiation and integration, and methods of integration such as integration by substitution, integration using partial fractions, integration by parts, integration using trigonometric identities, integration of some integral functions are all covered in Chapter 7, Integrals. Based on these chapter topics, we have provided exercises and solutions here.
Chapter 8 Applications of Integrals
We continue the topic of integrals in Chapter 8 of the NCERT textbook, covering definition, area under simple curves, area of the region enclosed by a curve and a line, area between two curves, and other examples. Students can access the exercises with solutions that explain the concepts from this chapter by clicking on the links provided below.
Chapter 9 Differential Equations
Chapter 9,
Differential Equations
, focuses on solving equations involving derivatives, fundamental to understanding change and motion. It covers formation, order, degree, and methods of solving differential equations, including variable separable, homogeneous, and linear types. This chapter builds essential skills for calculus and its applications in physics, engineering, and real-world problems.
Chapter 10 Vector Algebra
Chapter 10,
Vector Algebra
, explores the mathematical study of vectors, essential for physics and engineering. It covers vector operations like addition, subtraction, scalar multiplication, and dot and cross products. These concepts simplify spatial problems and provide tools for understanding geometry, motion, and forces in three-dimensional space effectively.
Chapter 11 Three Dimensional Geometry
Chapter 11,
Three-Dimensional Geometry
, delves into the spatial representation of points, lines, and planes. It covers direction cosines, direction ratios, the equation of lines and planes, and their intersections. This chapter equips students with tools to analyze and solve complex spatial problems, crucial for engineering, physics, and architecture applications.
Chapter 12 Linear Programming
Students learn about linear programming in this chapter. This chapter covers the following topics: the mathematical formulation of linear programming problems, the mathematical formulation of the problem, the graphical way of addressing linear programming problems, and many forms of linear programming problems with various examples. Students can locate exercises that provide solutions and a proper explanation of these ideas.
Chapter 13 Probability
Chapter 13,
Probability
, explores the mathematical study of uncertainty. It covers key concepts like conditional probability, Bayes’ theorem, random variables, and probability distributions, including Binomial and Poisson. This chapter builds a foundation for analyzing data, making predictions, and solving problems in fields like statistics, finance, and machine learning.
Key Features of NCERT Solutions for Class 12 Maths
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Comprehensive Coverage
: Detailed solutions for all chapters, adhering to the NCERT syllabus and CBSE guidelines.
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Step-by-Step Approach
: Easy-to-understand explanations for every problem, ensuring conceptual clarity.
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Prepared by Experts
: Solutions crafted by subject matter experts with accuracy and reliability.
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Board Exam Focused
: Emphasis on topics and methods essential for scoring well in board exams.
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Competitive Exam Preparation
: Supports foundational understanding for exams like JEE and other entrance tests.
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Clarity in Concepts
: Simplifies complex topics such as calculus, probability, and 3D geometry.
