## Important Mathematics Short Tricks Notes

**Hello Aspirants,**

Mathematics is a field of study that deals with numbers, quantities, structures, patterns, and relationships. It is a systematic and logical discipline that uses deductive reasoning to analyze and understand abstract concepts and solve problems.

Here are some key branches and concepts within mathematics:

Arithmetic: Arithmetic is the branch of mathematics that deals with basic operations such as addition, subtraction, multiplication, and division. It also includes concepts like fractions, decimals, percentages, and ratios.

Algebra: Algebra involves the study of mathematical symbols and the rules for manipulating these symbols to solve equations and analyze mathematical relationships. It includes topics like equations, inequalities, polynomials, functions, and graphs.

Geometry: Geometry focuses on the study of shapes, sizes, properties, and relationships of figures and spaces. It includes concepts such as points, lines, angles, polygons, circles, and three-dimensional objects.

Calculus: Calculus deals with the study of change and motion. It is divided into differential calculus, which focuses on rates of change and slopes, and integral calculus, which deals with the accumulation of quantities and areas under curves. Calculus is widely used in physics, engineering, economics, and other fields.

Probability and Statistics: Probability deals with the study of uncertainty and the likelihood of events occurring. Statistics involves the collection, analysis, interpretation, presentation, and organization of data. These fields are used to make predictions, draw inferences, and make informed decisions based on data.

Number Theory: Number theory is the study of properties and relationships of numbers, particularly integers. It explores concepts like prime numbers, divisibility, modular arithmetic, and number patterns.

Discrete Mathematics: Discrete mathematics focuses on mathematical structures that are fundamentally discrete rather than continuous. It includes topics like combinatorics, graph theory, and logic.

Linear Algebra: Linear algebra studies vectors, vector spaces, matrices, and linear transformations. It has applications in areas like computer graphics, cryptography, and quantum mechanics.

Mathematical Logic: Mathematical logic deals with formal systems, proofs, and the study of mathematical reasoning. It includes topics like propositional logic, predicate logic, and set theory.

Mathematical Modeling: Mathematical modeling involves using mathematics to represent real-world phenomena, systems, or processes. It helps in analyzing and predicting the behavior of these systems.

These are just some of the major branches of mathematics, and there are many more specialized fields and interdisciplinary applications. Mathematics is a powerful tool that plays a crucial role in various scientific, technological, and practical domains.

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**Important Question & Answer Mathematics Formula **

- प्राकृतिक संख्या (Natural Numbers) – an – bn = (a – b)(an-1 + an-2 +…+ bn-2a + bn-1)
- सम संख्या (Even) – (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
- विषम संख्या (Odd) – (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
- (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
- घातांक के नियम (Low Of Formula Exponents)
- 1. (am)(an) = am+n
- 2. (ab)m = ambm
- 3. (am)n = amn
- a2 – b2 = (a – b)(a + b)
- (a+b)2 = a2 + 2ab + b2
- a2 + b2 = (a – b)2 + 2ab
- (a – b)2 = a2 – 2ab + b2
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
- (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
- (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – 3a2b + 3ab2 – b3
- a3 – b3 = (a – b)(a2 + ab + b2)
- a3 + b3 = (a + b)(a2 – ab + b2)
- (a + b)3 = a3 + 3a2b + 3ab2 + b3
- (a – b)3 = a3 – 3a2b + 3ab2 – b3
- (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
- (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
- a4 – b4 = (a – b)(a + b)(a2 + b2)
- a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)

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