The NDA exam demands strong mathematical skills, quick problem-solving ability, and a solid grasp of essential formulas. Below, we provide the key mathematical formulas categorized by topics to help you excel in the NDA 2025 Mathematics section.
List of Important Mathematics Formulae for NDA 2025
The NDA exam demands strong mathematical skills, quick problem-solving ability, and a solid grasp of essential formulas. Below, we provide the key mathematical formulas categorized by topics to help you excel in the NDA 2025 Mathematics section.
1. Algebra
Quadratic Formula: x = (-b ± √(b2 − 4ac)) / 2a
Sum of Roots: α + β = -b/a
Product of Roots: αβ = c/a
Linear Equation: ax + by + c = 0
Cubic Equation: ax3 + bx2 + cx + d = 0
Binomial Theorem: (x + y)n = Σ[C(n, k) * xn-k * yk]
Arithmetic Progression (AP): an = a + (n-1)d
Geometric Progression (GP): an = arn-1
Sum of AP: Sn = (n/2)(2a + (n-1)d)
Sum of GP: Sn = a(1 − rn) / (1 − r) (for |r| < 1)
2. Trigonometry
Pythagorean Identity: sin2(θ) + cos2(θ) = 1
Sum of Angles: sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
Difference of Angles: cos(A − B) = cos(A)cos(B) + sin(A)sin(B)
Double Angle Formula: sin(2A) = 2sin(A)cos(A)
Half Angle Formula: sin(A/2) = ±√((1 − cos(A)) / 2)
Law of Sines: (a / sin(A)) = (b / sin(B)) = (c / sin(C))
Law of Cosines: c2 = a2 + b2 − 2ab cos(C)
Area of Triangle: Area = (1/2)ab sin(C)
Cotangent Rule: cot(C) = (a2 + b2 − c2) / (4 * Area)
3. Geometry
Distance Formula: d = √((x2 − x1)2 + (y2 − y1)2)
Midpoint Formula: M = ((x1 + x2)/2, (y1 + y2)/2)
Equation of Circle: (x − h)2 + (y − k)2 = r2
Area of Circle: A = πr2
Perimeter of Circle: C = 2πr
Area of Triangle (Heron's Formula): A = √(s(s − a)(s − b)(s − c)), where s = (a + b + c) / 2
Volume of Sphere: V = (4/3)πr3
Surface Area of Sphere: A = 4πr2
Volume of Cylinder: V = πr2h
Volume of Cone: V = (1/3)πr2h
4. Calculus
Derivative: f'(x) = lim(h → 0) [f(x + h) − f(x)] / h
Power Rule: d/dx [xn] = nxn-1
Product Rule: (uv)' = u'v + uv'
Quotient Rule: (u/v)' = (u'v − uv') / v2
Chain Rule: (f(g(x)))' = f'(g(x))g'(x)
Indefinite Integral: ∫xn dx = (xn+1)/(n+1) + C
Definite Integral: ∫ab f(x) dx = F(b) − F(a)
Area under a Curve: A = ∫ab f(x) dx
Volume of Solid of Revolution: V = π∫ab [f(x)]2 dx
Taylor Series: f(x) = f(a) + f'(a)(x−a) + (f''(a)/2!)(x−a)2 + ...
5. Probability and Statistics
Probability: P(E) = (Number of Favorable Outcomes) / (Total Outcomes)
Mean: μ = (Σx) / n
Variance: σ2 = (Σ(x − μ)2) / n
Standard Deviation: σ = √(σ2)
Binomial Probability: P(X = k) = C(n, k)pk(1−p)n−k
Poisson Distribution: P(X = k) = (e−λλk) / k!
Normal Distribution: P(X ≤ x) = ∫−∞x f(t) dt
Correlation Coefficient: r = (Σ(x−μ)(y−ν)) / (σxσy)
Conditional Probability: P(A|B) = P(A ∩ B) / P(B)
Bayes' Theorem: P(A|B) = P(B|A)P(A) / P(B)
6. Matrices and Determinants
Matrix Addition: (A + B)ij = Aij + Bij
Matrix Multiplication: (AB)ij = ΣAikBkj
Transpose: (AT)ij = Aji
Determinant of 2x2 Matrix: |A| = ad − bc
Adjoint: adj(A) = cofactor matrix(A)T
Inverse: A−1 = adj(A) / |A|
Cramer's Rule: x = |Dx| / |D|
Eigenvalues: Ax = λx
Eigenvectors: (A − λI)x = 0
Tips for Effective Formula Revision
- Categorize and Prioritize: Focus on high-weightage topics like Trigonometry, Algebra, and Calculus.
- Create Flashcards: Write formulas on flashcards for quick revision.
- Practice Daily: Apply these formulas to solve previous years' questions.
- Use Visual Aids: Sketch graphs and diagrams to better understand geometric and trigonometric concepts.
Mastering these formulas and incorporating consistent practice can boost your confidence and score well in the NDA Mathematics section. Remember, revision is key!
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