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NDA Examination Mathematics Flashcards
56 question-and-answer cards covering Mathematics as it is examined in NDA Examination. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
Give the section formula for a point dividing the segment joining (x₁,y₁) and (x₂,y₂) in ratio m:n internally.
((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)).
What is the slope of a line and the condition for two lines to be perpendicular?
Slope m = tan θ = (y₂ − y₁)/(x₂ − x₁). Two lines are perpendicular if m₁·m₂ = −1; parallel if m₁ = m₂.
Give the perpendicular distance from point (x₁, y₁) to the line ax + by + c = 0.
d = |ax₁ + by₁ + c| / √(a² + b²).
Give the standard equations of a circle, parabola, ellipse, and hyperbola (centered/vertex at origin).
Circle: x² + y² = r²; Parabola: y² = 4ax; Ellipse: x²/a² + y²/b² = 1; Hyperbola: x²/a² − y²/b² = 1.
What is the eccentricity range for an ellipse, parabola, and hyperbola?
Ellipse: 0 < e < 1; Parabola: e = 1; Hyperbola: e > 1; Circle: e = 0.
Give the distance formula between two points in 3D space.
d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²].
How is the angle between two lines with direction ratios (a₁,b₁,c₁) and (a₂,b₂,c₂) found?
cos θ = |a₁a₂ + b₁b₂ + c₁c₂| / [√(a₁²+b₁²+c₁²)·√(a₂²+b₂²+c₂²)].
How is the angle between a line and a plane related to the angle between the line and the plane's normal?
If φ is the angle between the line and the normal, the angle between the line and the plane is θ = 90° − φ, so sin θ = cos φ.
What three conditions must hold for a function f(x) to be continuous at x = a?
(1) f(a) is defined; (2) lim(x→a) f(x) exists; (3) lim(x→a) f(x) = f(a).
State the two standard limits: lim(x→0) sin x / x and lim(x→0) (eˣ − 1)/x.
Both equal 1: lim(x→0) sin x / x = 1 and lim(x→0) (eˣ − 1)/x = 1.
State the product rule and quotient rule for differentiation.
Product: (uv)' = u'v + uv'. Quotient: (u/v)' = (u'v − uv')/v².
What does the first derivative test say about increasing/decreasing functions and maxima/minima?
f'(x) > 0 ⇒ increasing; f'(x) < 0 ⇒ decreasing. At a critical point, f' changing + to − gives a local maximum; − to + gives a local minimum.
Give the integrals ∫xⁿ dx (n ≠ −1) and ∫(1/x) dx.
∫xⁿ dx = x^(n+1)/(n+1) + C; ∫(1/x) dx = ln|x| + C.
State the fundamental theorem of calculus for a definite integral.
∫ₐᵇ f(x) dx = F(b) − F(a), where F is an antiderivative of f (F' = f).
What is the order and degree of a differential equation?
Order = highest derivative present; Degree = power of the highest-order derivative (after the equation is made polynomial/free of radicals in derivatives).
Define scalar (dot) product of vectors a and b and state when they are perpendicular.
a·b = |a||b| cos θ = a₁b₁ + a₂b₂ + a₃b₃. They are perpendicular when a·b = 0.
Define the vector (cross) product of a and b, including its magnitude and direction.
a × b has magnitude |a||b| sin θ and direction perpendicular to both a and b (right-hand rule). It is a vector; a × b = −(b × a). It is zero for parallel vectors.
What is the scalar triple product [a b c] and what does it represent geometrically?
[a b c] = a·(b × c); it equals the volume of the parallelepiped with edges a, b, c. If it is 0, the vectors are coplanar.
Give the formulas for mean, median, and mode (define each measure of central tendency).
Mean = (Σx)/n (arithmetic average); Median = middle value of ordered data; Mode = most frequently occurring value.
Define variance and standard deviation for a data set.
Variance σ² = Σ(xᵢ − x̄)²/n (mean of squared deviations); Standard deviation σ = √(variance).
State the classical (theoretical) definition of probability of an event E.
P(E) = (number of favourable outcomes) / (total number of equally likely outcomes), with 0 ≤ P(E) ≤ 1.
State the addition theorem of probability for events A and B.
P(A ∪ B) = P(A) + P(B) − P(A ∩ B). For mutually exclusive events, P(A ∩ B) = 0.
State Bayes' theorem and the conditional probability formula.
Conditional: P(A|B) = P(A ∩ B)/P(B). Bayes: P(Aᵢ|B) = [P(Aᵢ)P(B|Aᵢ)] / Σ P(Aⱼ)P(B|Aⱼ).
What does the Karl Pearson correlation coefficient r measure and what is its range?
It measures the strength and direction of a linear relationship between two variables; −1 ≤ r ≤ 1 (−1 perfect negative, +1 perfect positive, 0 no linear correlation).
What this deck covers
The Mathematics deck follows the NDA Examination Mathematics syllabus — 6 chapters and 34 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 9.3 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 91 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Mathematics flashcards FAQ
How many Mathematics flashcards are in this NDA Examination deck?
56 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these NDA Examination flashcards free?
Yes. The preview here is free to read with no signup, and the full 56-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the NDA Examination Mathematics syllabus — 6 chapters and 34 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.