Onto Function is one of the many types of functions defined based on the relationship between its domain and codomain. For any function to be onto, it needs to relate two sets with a very specific mapping between elements, meaning that each element of the codomain has at least one element in the domain as its pre-image. In simple words, for any function, if all the elements of the codomain are mapped to some element of the domain, then the function is said to be an onto function....
HCF (Highest Common Factor) and LCM (Least Common Multiple) are fundamental concepts in mathematics, particularly in number theory. HCF is the highest common number which can exactly divide the two given numbers. LCM or Lowest Common Multiple is the common number that is divisible by both the given numbers. These concepts are essential tools for solving a wide range of mathematical problems....
NCERT Solutions for Class 12 are based on the latest syllabus prescribed by the CBSE (Central Board of Secondary Education) to help the student score well in their board examination. The solutions for Class 12 NCERT, are provided by experts to help students prepare for their Class 12 board exams for session 2024-25....
Scalar matrix is a type of diagonal matrix that has all the elements the same or equal. The elements that are present other than in the diagonal are zero....
Combination is a way of selecting items from a collection of items in combination we do not look at the order of selecting items, but our main attention is on the total number of selected items from a given set of items. For example- suppose that we have three numbers say, a, b, and c. Then in how many ways we can select two numbers is known as a combination....
The circumcenter of Triangle is a specific point where the perpendicular bisectors of the sides of the triangle intersect. This point is significant because it is equidistant from all three vertices of the triangle. It makes it the center of circle that can be circumscribed around the triangle which is known as circumcircle....
Chain Rule is a way to find the derivative of composite functions. It is one of the basic rules used in mathematics for solving differential problems. It helps us to find the derivative of composite functions such as (3x2 + 1)4, (sin 4x), e3x, (ln x)2, and others. Only the derivatives of composite functions are found using the chain rule. The famous German scientist, Gottfried Leibniz gave the chain rule in the early 17th century....
The area of a Parallelogram is the space or the region enclosed by the boundary of the parallelogram in a two-dimensional space. It is calculated by multiplying the base of the parallelogram by its height. In this article, we will learn more about the Area of Parallelogram Formulas, and how to use them with the help of examples....
Complex numbers are the representation of numerical expressions in the form of a+ib where a and b are real integers and i stands for imaginary numbers. Consider a complex number 2 + 3i, in this expression 2 and 3 are the integers or real numbers whereas, ‘i’ represents the imaginary number....
Arithmetic Operations are the basic mathematical operations used for calculation. Arithmetic Operations are the backbone of Mathematics. There are four basic arithmetic operations, namely, Addition, Subtraction, Multiplication, and Division. These four basic arithmetic operations are very helpful in solving daily life calculations such as sharing biscuits among your friend and sibling, counting the total bill you have to pay at a shop, complex calculations such as problems of time and work, data interpretations, etc....
Before proceeding with the given question one must know what are rational numbers. Hence a brief definition of rational number is added below....
