# Important Formulas of NDA Mathematics for NDA Exam 2023

The National Defence Academy (NDA) examination is a prestigious entrance test conducted by the Union Public Service Commission (UPSC) of India. Mathematics is a crucial subject in the NDA exam, and a strong grasp of fundamental concepts and formulas is essential for success. In this article, we will explore some of the important formulas of NDA Mathematics that candidates should focus on while preparing for the NDA Exam 2023.

**Trigonometry Formulas:**Trigonometry plays a significant role in the NDA mathematics paper. Some essential trigonometric formulas to remember include:- Pythagorean identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ
- Sum and difference formulas: sin(A ± B), cos(A ± B), tan(A ± B)
- Double angle formulas: sin(2θ), cos(2θ), tan(2θ)
- Half-angle formulas: sin(θ/2), cos(θ/2), tan(θ/2)

**Algebraic Formulas:**Algebraic formulas are fundamental for solving equations, simplifying expressions, and solving quadratic equations. Some crucial algebraic formulas to remember are:- Quadratic formula: x = (-b ± √(b² – 4ac)) / (2a)
- Arithmetic progression (AP): nth term (Tn) = a + (n – 1)d, Sum (Sn) = n/2 [2a + (n – 1)d]
- Geometric progression (GP): nth term (Tn) = ar^(n-1), Sum (Sn) = a(r^n – 1) / (r – 1)

- Geometry Formulas: Geometry is another vital topic in the NDA mathematics syllabus. Some essential geometry formulas include:
- Area of a triangle: 1/2 * base * height
- Area of a circle: πr², Circumference: 2πr
- Volume of a cube: side³, Volume of a cylinder: πr²h
- Perimeter of a rectangle: 2(length + breadth)

**Calculus Formulas:**Calculus involves concepts of differentiation and integration. While the NDA mathematics syllabus does not cover advanced calculus, knowing the basics is crucial. Some key calculus formulas include:- Derivative formulas: d/dx [sin(x)] = cos(x), d/dx [cos(x)] = -sin(x), d/dx [tan(x)] = sec²(x)
- Integration formulas: ∫sin(x)dx = -cos(x) + C, ∫cos(x)dx = sin(x) + C, ∫sec²(x)dx = tan(x) + C

**Probability and Statistics Formulas:**Probability and statistics questions are also part of the NDA mathematics paper. Familiarize yourself with these important formulas:- Probability of an event: P(E) = Number of favorable outcomes / Total number of possible outcomes
- Mean (Average): Sum of all values / Total number of values
- Median: Middle value in a sorted list of values
- Mode: Most frequently occurring value(s) in a set of values

**Logarithmic Formulas:**Logarithms are integral to solving complex equations. Some essential logarithmic formulas include:- Logarithmic identities: log(ab) = log(a) + log(b), log(a/b) = log(a) – log(b), log(a^n) = n*log(a)
- Change of base formula: logₐ(b) = log(b) / log(a)
- Natural logarithm: ln(x), where e is the base of the natural logarithm

**Matrices and Determinants Formulas:**Matrices and determinants are topics covered in the NDA mathematics syllabus. Some key formulas include:- Matrix multiplication: (AB)ₘₓₚ = Aₘₓₙ * Bₙₓₚ
- Determinant of a matrix: |A| or det(A)
- Properties of determinants: determinant of the transpose, determinant of the inverse

**Sets, Relations, and Functions Formulas:**Sets, relations, and functions form an integral part of the NDA mathematics syllabus. Important formulas in this area include:- Set operations: Union (A ∪ B), Intersection (A ∩ B), Complement (A’), Difference (A – B)
- Domain and range of a function
- Types of relations: reflexive, symmetric, transitive

**Complex Numbers Formulas:**Complex numbers involve real and imaginary components. Key formulas in this area include:- Imaginary unit: i = √(-1)
- Complex number representation: z = a + bi, where a is the real part and bi is the imaginary part
- Euler’s formula: e^(iθ) = cos(θ) + i*sin(θ)

**Coordinate Geometry Formulas:**Coordinate geometry deals with points, lines, and shapes on a coordinate plane. Important formulas include:

- Distance formula: d = √((x₂ – x₁)² + (y₂ – y₁)²)
- Slope of a line: m = (y₂ – y₁) / (x₂ – x₁)
- Equation of a line: y = mx + c, where m is the slope and c is the y-intercept

Remember, this is not an exhaustive list, but it covers some of the key formulas that are often asked in the NDA mathematics paper. Practice regularly, revise these formulas, and solve ample practice questions to strengthen your understanding and application of these concepts.

Mastering the important formulas of NDA Mathematics is crucial for success in the NDA Exam 2023. By understanding and practicing these formulas, candidates can enhance their problem-solving abilities and improve their overall performance in the mathematics section. Remember to practice regularly, solve previous year question papers, and seek guidance from experts or mentors to excel in the NDA mathematics paper. You can join MKC for complete preparation of NDA 2023 Exam. Best of luck with your preparations!