Differential Equations

Chapter 1: Relations and Functions

The Chapter Relation and Functions discusses the introduction of relations and functions, types of relation, types of functions, the composition of functions and invertible function, binary operations, inverse function, and miscellaneous examples....

Chapter 2: Inverse Trigonometric Functions

Inverse Trigonometric Functions of NCERT Class 12 Maths, gives an account of various topics such as the remarks based on basic concepts of inverse trigonometric functions, properties of inverse trigonometric functions, and miscellaneous examples. Inverse Trigonometric Functions are quite useful in Calculus to define different integrals. You can also check the Trigonometric Formulas here....

Chapter 3: Matrices

In Chapter 3 of NCERT textbook, we shall see the definition of a matrix, types of matrices, equality of matrices, operations on matrices such as the addition of matrices and multiplication of a matrix by a scalar, properties of matrix addition, properties of scalar multiplication, multiplication of matrices, properties of multiplication of matrices, transpose of a matrix, properties of the transpose of the matrix, symmetric and skew-symmetric matrices, elementary operation or transformation of a matrix, the inverse of a matrix by elementary operations and miscellaneous examples....

Chapter 4: Determinants

Chapter 4 of 12 Class NCERT Maths Solution discusses the topic of determinants. Students will get to learn about the definition and meaning of determinants, remarks based on the order of determinants, properties of determinants, finding the area of a triangle using determinants, minors and cofactors of determinants, adjoint of a matrix, the inverse of a matrix, applications of determinants, and matrices and miscellaneous examples. Below we have links provided to each exercise solution covered in this chapter. The determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, co-factors, and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency, and the number of solutions of a system of linear equations by examples, solving a system of linear equations in two or three variables (having unique solution) using the inverse of a matrix....

Chapter 5: Continuity and Differentiability

Chapter 5 of the NCERT textbook starts with the definition of continuity. Students go on to learn about continuity, the algebra of continuous functions, the definition and meaning of differentiability, derivatives of composite functions, the derivative of implicit functions, the derivative of inverse trigonometric functions, derivative of exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivatives, mean value theorem via miscellaneous examples. Here, students can find the exercises explaining these concepts properly with solutions. Continuity and differentiability, the derivative of composite functions, chain rule, the derivative of inverse trigonometric functions, and the derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation is the derivative of functions expressed in parametric forms. Second-order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation....

Chapter 6: Applications of Derivatives

Chapter 6 of the NCERT textbook, provides a definition of 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 miscellaneous examples. Here, students can find the exercises explaining these concepts properly. Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima, and minima (the first derivative test is motivated geometrically, and the second derivative test is given as a provable tool)....

Chapter 7: Integrals

In this chapter, the methods to determine the function when its derivative is given and the area under a graph of a function are discussed. The basic properties of integrals and the fundamental theorem of calculus are also included in this chapter....

Chapter 8: Applications of Integrals

This chapter included topics like how to find the area of different geometrical figures such as circles, parabolas, and ellipses.  The area enclosed by the curve y = f (x); x-axis and the lines x = a and x = b (b > a) is given by the formula,...

Chapter 9: Differential Equations

In this chapter, the concepts of differential equations and how to find solutions to differential equations are discussed. This topic holds various applications in Physics, Economics, Chemistry, and Biology....

Chapter 10: Vector Algebra

In this chapter, the concepts of vector quantities, how to find the position vector of a point, geometrical interpretation of vectors, and dot and cross product of vectors are discussed. These concepts have great importance in higher education (engineering and technology). The important formulas used in vector algebras are,...

Chapter 11: Three-Dimensional Geometry

Based on the vector algebra discussed in the previous chapter, here are the concepts like, how it can be applied to three-dimensional geometry. Also, the introduction to topics like direction cosines and direction ratios, cartesian and vector equations of a line, and how to find the shortest distance between two lines using these concepts are discussed in this part. Various formulas used in 3-D geometry are,...

Chapter 12: Linear Programming

This chapter is a continuation of the concepts of linear inequalities and the system of linear equations in two variables studied in the previous class. This chapter helps to learn how these concepts can be applied to solve real-world problems and how to optimize the problems of linear programming so that one can maximize resource utilization, minimize profits, etc....

Chapter 13: Probability

This chapter deals with probability, the concept of probability is also studied in earlier classes. This chapter in the present class helps to learn about conditional probability. Further, topics like Bayes’ theorem, independence of events, the probability distribution of random variables, mean and variance of a probability distribution, and Binomial distribution are discussed in this chapter....

Class 12 Maths Formulas Examples

Example 1: A circular disc of radius 7 cm is being heated. Due to expansion, its radius increases at a rate of 0.04 cm per second. Find the rate at which its area is increasing if the increased radius at any point is 8.4 cm....

FAQs on Class 12 Maths Formulas

1. What are the Basic Maths Formulas for Class 12th?...