Functions are defined as the relations which give a particular output for a particular input value. A function has a …
Composite Functions Let f : A->B and g : B->C be two functions. Then the composition of f and g, …
As the name suggests Invertible means “inverse“, and Invertible function means the inverse of the function. Invertible functions, in the …
Composition of Function is the process or operation which combines two or more functions together into a single function. We …
Inverse Functions are an important concept in mathematics. An inverse function basically reverses the effect of the original function. If you …
Inverse trigonometric functions are the inverse functions of basic trigonometric functions. In mathematics, inverse trigonometric functions are also known as …
Inverse trigonometric functions are the inverse functions of the trigonometric ratios i.e. sin, cos, tan, cot, sec, cosec. These functions …
Inverse trigonometric functions, also known as arc functions, are used to find the angle that corresponds to a given trigonometric …
Inverse Trigonometric Identities: In mathematics, inverse trigonometric functions are also known as arcus functions or anti-trigonometric functions. The inverse trigonometric functions are the inverse …
Relation and Function are two ways of establishing links between two sets in mathematics. Relation and Function in maths are …
In Class 12 Mathematics, Chapter 1, “Relations and Functions” students delve into the foundational concepts of relations and functions. Exercise …
Exercise 1.3 delves into the advanced concepts of function composition and invertible functions, building upon the foundational knowledge of relations …
Class 12 NCERT Solutions- Mathematics Chapter 1 Relations And Functions -Miscellaneous Exercise on Chapter 1 Question 1. Let f : R …
Matrices are one of the important chapters of NCERT Solutions for Class 12 Maths. It is also a powerful and essential …
Matrices are a fundamental concept in linear algebra, used extensively in mathematics, physics, engineering, computer science, and various other fields. …
Chapter 3 of the Class 12 NCERT Mathematics textbook, titled “Matrices,” delves into the fundamental concepts of matrices, including their …
Chapter 3 of the Class 12 NCERT Mathematics textbook, titled “Matrices,” covers fundamental concepts related to matrices, including operations such …
A rectangular array of m × n numbers (real or complex) in the form of m horizontal lines (called rows) …
There are different types of matrices, and they are basically categorised on the basis of the value of their elements, …
Algebra of Matrices is the branch of mathematics, which deals with the vector spaces between different dimensions. The innovation of …
Transpose of a matrix is one of the most commonly used methods in matrix transformation. For a given matrix, the …
A symmetric matrix and skew-symmetric matrix both are square matrices. But the difference between them is, the symmetric matrix is …
A matrix is an array of numbers arranged in the form of rows and columns. The number of rows and …
A matrix is an array of numbers arranged in the form of rows and columns. The number of rows and …
In linear algebra, a determinant is a special number that can be determined from a square matrix. The determinant of …
We know what a determinant is, let us know how to use Determinant to find Area of a Triangle Suppose …
Minors and cofactors are two of the most important concepts in matrices, as they are crucial in finding the adjoint …
The adjoint of a matrix, also called the adjugate of a matrix, is defined as the transpose of the cofactor …
Continuity and Differentiability is one of the most important topics which help students to understand the concepts like, continuity at a …
An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find …
Logarithmic differentiation is a method to find the derivatives of some complicated functions, using logarithms. There are cases in which …
Derivatives of a function in parametric form: There are instances when rather than defining a function explicitly or implicitly we …
For understanding the second-order derivative, let us step back a bit and understand what a first derivative is. The first …
In mathematics, the mean value theorem states, roughly, that given a planar arc between two endpoints, there is at least …
Before explaining the increasing and decreasing function along with monotonicity, let us understand what functions are. A function is basically a …
The applications of derivatives are: In this article, we will learn to use differentiation to find the equation of the tangent …
In mathematics, differential calculus is a branch of mathematics that deals with the process of finding the derivative of a …
Integral Calculus is the branch of calculus where we study integrals and their properties. Integration is an essential concept which …
Integration is the calculation of an integral. Integrals in maths are used to find many useful quantities such as areas, …
An integral in mathematics is a continuous analog of a sum that is used to determine areas, volumes, and their generalizations. …
Integration by substitution or u-substitution is a highly used method of finding the integration of a complex function by reducing it to a …
Integration by Partial Fractions is one of the methods of integration, which is used to find the integral of the …
Integration by Parts or Partial Integration, is a technique used in calculus to evaluate the integral of a product of two functions. The formula …
The process of finding the anti-derivative of a function is the inverse process of differentiation i.e. finding integral is the …
The process of finding the anti-derivative of a function is the inverse process of differentiation i.e. finding integral is the …
The process of finding the anti-derivative of a function is the inverse process of differentiation i.e. finding integral is the …
The process of finding the anti-derivative of a function is the inverse process of differentiation i.e. finding integral is the …
The process of finding the anti-derivative of a function is the inverse process of differentiation i.e. finding integral is the …
Integral is the method to sum the functions on a large scale. Hence, here we have discussed integrals of some …
Partial fractions are the fractions used for the decomposition of a rational expression. When an algebraic expression is split into …
Integration by parts is a special technique of integration of two functions when they are multiplied. This method is also …
An integral assigns numbers to functions in mathematics to define displacement, area, volume, and other notions that arise by connecting …
In Calculus, we have seen definite integral as a limit of a sum and we know how to evaluate it …
Important Concepts on Area under the Curves If the area under one curve and another curve can be found, then …
MCQs on Class 12 Maths Chapter Application of Integrals Check out the Class 12 Maths Chapter 8 Application of Integrals …
MCQs on Class 12 Maths Chapter 7 Integrals Check out the MCQs for Class 12 Maths Chapter 7 Integrals. Each …
Integration questions with answers are available here for students of Class 11 and Class 12. Integration is an important topic …
As we all know, integration means calculating the area by dividing the region into many elementary strips and then adding …
Differential Equation Definition A differential equation is an equation which contains one or more terms and the derivatives of one …
An equation with one or more terms that involve derivatives of the dependent variable with respect to an independent variable …
Solving Differential Equations The solution of a differential equation – General and particular will use integration in some steps to …
A differential equation is an equation of the form \(\begin{array}{l}\frac{\mathrm{d} y}{\mathrm{d} x} = g(x),\;\;\;\; where\;\; y = f(x)\end{array} \). General …
Vectors, in Maths, are objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented …
What is a vector? Vector is a physical quantity that has both direction and magnitude. In other words, the vectors …
Laws of Vector Addition A vector is a physical quantity which is represented both in direction and magnitude. In the …
A vector relates two given points. It is a mathematical quantity having both the Magnitude and the direction. Multiplication of …
Vector is a quantity that has both magnitude and direction. Some mathematical operations can be performed on vectors such as …
Direction Cosines When a directed line OP passing through the origin makes \(\begin{array}{l}\alpha \end{array} \) , \(\begin{array}{l}\beta\end{array} \) and \(\begin{array}{l} …
Equation of a line is defined as y= mx+c, where c is the y-intercept and m is the slope. Vectors …
A line in mathematics and geometry is a fundamental concept representing a straight, one-dimensional figure that extends infinitely in both …
The shortest distance between two lines in three-dimensional space is the length of the perpendicular segment drawn from a point …
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is …
Imagine a student who takes leave from school twice a week excluding Sunday. If it is known that he will …
The multiplication rule of probability explains the condition between two events. For two events A and B associated with a …
Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a …
Bayes’ theorem describes the probability of occurrence of an event related to any condition. It is also considered for the …
In Statistics, the probability distribution gives the possibility of each outcome of a random experiment or event. It provides the …
Bernoulli Trials and Binomial Distribution are explained here in a brief manner. Bernoulli’s trial is also said to be a …
Linear programming is a method of optimising operations with some constraints. The main objective of linear programming is to maximize …
Linear Programming Problems (LPP): Linear programming or linear optimization is a process which takes into consideration certain linear relationships to …
Linear programming or linear optimization is a process that takes into consideration certain linear relationships to obtain the best possible …
