List of Important Mathematics Formulas for NDA Exam 2025

Topic

Formula

Quadratic Equations

x = (-b ± √(b² – 4ac)) / 2a

Sum of Roots

α + β = -b/a

Product of Roots

αβ = c/a

Linear Equation

ax + by+ c=0

Matrix Multiplication

 AB = [Σa_ij * b_jk]

Inverse of Matrix

A^-1 = adj(A) / |A|

Category

Formula

Basic Ratios

Sine: sin(A) = opposite side / hypotenuse

Cosine: cos(A) = adjacent side / hypotenuse
etc

Pythagorean Identity

sin²(A) + cos²(A) = 1

Sum and Difference Formulas

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

cos(A + B) = cos(A)cos(B) – sin(A)sin(B)

Double Angle Formulas

sin(2A) = 2sin(A)cos(A)

cos(2A) = cos²(A) – sin²(A)

Formula Type

Formula

Distance Formula

d = √((x2 – x1)² + (y2 – y1)²)

Midpoint Formula

((x1 + x2)/2, (y1 + y2)/2)

Circle Equation

(x – h)² + (y – k)² = r²

Topic

Formula

Derivative Rules

f'(x) = lim(h → 0) [f(x + h) – f(x)]/h

Product Rule

If f(x) = u(x)v(x), then f'(x) = u'(x)v(x) + u(x)v'(x)

Indefinite Integral

∫f(x) dx = F(x) + C

Area Under Curve

A = ∫[f(x) dx] from a to b

Measure

Formula

Mean

μ = (Σx) / n

Variance

σ² = Σ(x – μ)² / n

Standard Deviation

σ = √(Σ(x – μ)² / n)

Concept

Formula

Probability

P(E) = Number of favorable outcomes / Total number of outcomes

Binomial Distribution

P(X = k) = nCk * p^k * q^(n-k)

Poisson Distribution

P(X = k) = (e^-λ) * (λ^k) / k!