In the NDA entrance test, mastering mathematical formulae is crucial for success. The NDA exam, known for its rigorous standards, demands not only a deep understanding of mathematical concepts but also the ability to quickly apply them under pressure. In this Article, We are providing you with all the important formulas a candidate appearing for the NDA Exam 2024 Must know to score good marks in the NDA Mathematics section.
Important Formulas for NDA Maths 2024
The formulae used in this exam form the backbone of problem-solving strategies, enabling candidates to tackle a wide range of questions efficiently. Whether for revision, practice, or during the actual exam, having a firm grasp on these mathematical formulas can significantly enhance performance. This article delves into the key formulae essential for the NDA maths section, emphasizing their importance in achieving a high score and providing tips for effective revision and application.
Important Formula for NDA Algebra
The Questions from given Formula are seen more than often in the Previous year NDA Maths Examinations.
Equation and Inequality
- Quadratic Formula: x = (-b ± √(b² – 4ac)) / 2a
- Sum of roots: α + β = -b/a
- Product of roots: αβ = c/a
- Linear equations: ax + by + c = 0
- Quadratic inequalities: ax² + bx + c > 0 or < 0
Linear Algebra
- Matrix multiplication: AB = [Σa_ij * b_jk]
- Inverse of a matrix: A^-1 = adj(A) / |A|
- Determinant of a matrix: |A| = a(ei – fh) – b(di – fg) + c(dh – eg)
- Cramer’s rule: x = Δ_x / Δ
- Eigenvalues and eigenvectors: Ax = λx
Vector Algebra
- Dot product: a · b = |a| |b| cosθ
- Cross product: a × b = |a| |b| sinθ
- Magnitude of a vector: |a| = √(a · a)
- Unit vector: â = a / |a|
- Vector triple product: a × (b × c) = b(a · c) – c(a · b)
Complex Numbers
- Complex number: z = a + ib, where a and b are real numbers
- Conjugate of a complex number: z̄ = a – ib
- Modulus of a complex number: |z| = √(a² + b²)
- Argument of a complex number: arg(z) = tan⁻¹(b/a)
- De Moivre’s theorem: (cosθ + isinθ)^n = cos(nθ) + isin(nθ)
Important formulas for NDA Trigonometry
Trigonometry is the most important topic to cover for the NDA Maths.
Triangle and Trigonometric Ratios
- Sine: sin(A) = opposite side / hypotenuse
- Cosine: cos(A) = adjacent side / hypotenuse
- Tangent: tan(A) = opposite side / adjacent side
- Cotangent: cot(A) = adjacent side / opposite side
- Secant: sec(A) = hypotenuse / adjacent side
- Cosecant: csc(A) = hypotenuse / opposite side
Trigonometric identities and equations
- 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)
- Half angle formulas:
sin(A/2) = ±√((1 – cos(A))/2)
cos(A/2) = ±√((1 + cos(A))/2)
Height and Distance
- Angle of elevation: tan(θ) = height / distance
- Angle of depression: tan(θ) = height / distance
- Height of an object: h = d * tan(θ)
- Distance of an object: d = h / tan(θ)
- Height and distance problems involving right triangles and trigonometric ratios.
Important Formulae for Geometry
Geometry hold the weightage of maximum marks in the NDA Mathematics, Here are the Important formulas to excel in the NDA Geometry.
Coordinate Geometry
- Distance formula: d = √((x2 – x1)² + (y2 – y1)²)
- Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2)
- Slope of a line: m = (y2 – y1) / (x2 – x1)
- Equation of a line: y = mx + c
- Equation of a circle: (x – h)² + (y – k)² = r²
Lines and planes
- Equation of a line in slope-intercept form: y = mx + c
- Equation of a line in general form: ax + by + c = 0
- Equation of a plane: ax + by + cz + d = 0
- Distance from a point to a line: d = |ax + by + c| / √(a² + b²)
- Distance from a point to a plane: d = |ax + by + cz + d| / √(a² + b² + c²)
Circle and Conic Sections
- Equation of a circle: (x – h)² + (y – k)² = r²
- Equation of a parabola: y² = 4ax
- Equation of an ellipse: (x²/a²) + (y²/b²) = 1
- Equation of a hyperbola: (x²/a²) – (y²/b²) = 1
- Focal distance for a parabola: F = a
- Focal distance for an ellipse: F = √(a² – b²)
- Focal distance for a hyperbola: F = √(a² + b²)
Important Formulae for Calculus
The Importance of Calculus is known to every NDA Aspirant. Here are the Most Asked Formulas in the NDA Maths from Calculus section.
Differential Calculus
- Derivative of a function: f'(x) = lim(h → 0) [f(x + h) – f(x)]/h
- Power rule: If f(x) = x^n, then f'(x) = nx^(n-1)
- Product rule: If f(x) = u(x)v(x), then f'(x) = u'(x)v(x) + u(x)v'(x)
- Quotient rule: If f(x) = u(x)/v(x), then f'(x) = (u'(x)v(x) – u(x)v'(x)) / v(x)^2
- Chain rule: If f(x) = g(h(x)), then f'(x) = g'(h(x)) * h'(x)
Integral Calculus
- Indefinite integral: ∫f(x) dx = F(x) + C
- Definite integral: ∫[f(x) dx] from a to b = F(b) – F(a)
- Fundamental theorem of calculus: ∫[f(x) dx] from a to b = F(b) – F(a)
- Integration by substitution: ∫f(g(x))g'(x) dx = ∫f(u) du
- Integration by parts: ∫u(x)v'(x) dx = u(x)v(x) – ∫v(x)u'(x) dx
Application of Calculus
- Area under a curve: A = ∫[f(x) dx] from a to b
- Volume of a solid: V = ∫[πf(x)^2 dx] from a to b
- Surface area of a solid: S = ∫[2πf(x)√(1 + f'(x)^2) dx] from a to b
- Center of mass: x̄ = (1/M) ∫x dm
- Moment of inertia: I = ∫r^2 dm
Important Formulae for Statistics
It is most important to remember the Statistics formulas for NDA Math. Here are the Must remember statistics formulas.
- Mean: μ = (Σx) / n
- Median: M = (n+1)/2 th term (for odd n)
- Mode: M = most frequently occurring value
- Variance: σ² = Σ(x – μ)² / n
- Standard Deviation: σ = √(Σ(x – μ)² / n)
- Coefficient of Variation: CV = (σ / μ) * 100
- Correlation Coefficient: r = Σ[(x – μ)(y – ν)] / (σ_x * σ_y)
Probability
- Probability: P(E) = Number of favorable outcomes / Total number of outcomes
- Conditional Probability: P(E|F) = P(E ∩ F) / P(F)
- Bayes’ Theorem: P(A|B) = P(B|A) * P(A) / P(B)
- Independent Events: P(E ∩ F) = P(E) * P(F)
- Mutually Exclusive Events: P(E ∩ F) = 0
Important formulae for Random Variables and Distribution
Here is the list of most important formula for NDA Variables and Distribution in the NDA maths section.
- Discrete Random Variable: P(X = x) = f(x)
- Continuous Random Variable: P(a < X < b) = ∫[f(x) dx] from a to b
- Binomial Distribution: P(X = k) = nCk * p^k * q^(n-k)
- Poisson Distribution: P(X = k) = (e^-λ) * (λ^k) / k!
- Normal Distribution: P(X < x) = ∫[f(t) dt] from -∞ to x
Matrices
- Matrix addition: A + B = [a_ij + b_ij]
- Matrix multiplication: AB = [Σa_ij * b_jk]
- Matrix transpose: A^T = [a_ji]
- Matrix scalar multiplication: cA = [ca_ij]
Determinants
- Determinant of a 2×2 matrix: |A| = ad – bc
- Determinant of a 3×3 matrix: |A| = a(ei – fh) – b(di – fg) + c(dh – eg)
- Determinant of a nxn matrix: |A| = Σ[(a_ij * cofactor(a_ij))]
- Cofactor expansion: |A| = Σ[a_ij * cofactor(a_ij)]
Adjoint and Inverse of Matrices
- Adjoint of a matrix: adj(A) = [cofactor(a_ij)]^T
- Inverse of a matrix: A^-1 = adj(A) / |A|
- Inverse of a 2×2 matrix: A^-1 = 1/(ad – bc) * [[d, -b], [-c, a]]
- a_ij represents the element in the ith row and jth column of matrix A.
- cofactor(a_ij) represents the cofactor of element a_ij.
- adj(A) represents the adjoint of matrix A.
- A^-1 represents the inverse of matrix A.
Candidates should Read the given formulas to remember them. It is extremely important to recall the needed formula at the moment of Solving the Maths Problem. Candidates can easily remember the NDA Maths formula by revising them sincerely.
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