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UPSC CDS (Combined Defence Services) Elementary Mathematics (Paper III, for IMA/INA/AFA) Flashcards
50 question-and-answer cards covering Elementary Mathematics (Paper III, for IMA/INA/AFA) as it is examined in UPSC CDS (Combined Defence Services). 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Elementary Mathematics (Paper III, for IMA/INA/AFA) deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
For 2 years, what is the difference between CI and SI on principal P at rate R%?
Difference = P × (R/100)². (For 1 year CI and SI are equal.)
At rate R%, in how many years does a sum double under simple interest?
T = 100 / R years (since the interest must equal the principal: P = P·R·T/100).
State the basic relationship between Speed, Distance and Time.
Speed = Distance / Time; Distance = Speed × Time; Time = Distance / Speed.
How do you convert km/hr to m/s and vice versa?
km/hr to m/s: multiply by 5/18. m/s to km/hr: multiply by 18/5.
What is the relative speed for two objects moving in the same direction vs opposite directions?
Same direction: relative speed = difference of speeds (|a − b|). Opposite directions: relative speed = sum of speeds (a + b).
A train of length L crossing a pole/man covers what distance, and crossing a platform of length P?
Crossing a pole/man: distance = L (train's own length). Crossing a platform: distance = L + P (train length plus platform length).
If A does a work in x days and B in y days, how long do they take working together?
Together they take xy/(x + y) days; their combined one-day work = 1/x + 1/y.
State the average (arithmetic mean) formula.
Average = (Sum of all observations) / (Number of observations).
What is the average speed for a round trip at speeds x and y over equal distances?
Average speed = 2xy / (x + y) (the harmonic mean), NOT the simple average of x and y.
State the Rule of Alligation.
(Quantity of cheaper)/(Quantity of dearer) = (Price of dearer − Mean price)/(Mean price − Price of cheaper).
If the average of n numbers is A, what is their total sum, and what happens if each is increased by k?
Sum = n × A. If each number increases by k, the new average becomes A + k.
State the identity for (a + b)².
(a + b)² = a² + 2ab + b².
State the identity for (a − b)² and the value of (a+b)² − (a−b)².
(a − b)² = a² − 2ab + b²; and (a + b)² − (a − b)² = 4ab.
State the difference of squares identity.
a² − b² = (a + b)(a − b).
State the identities for (a + b)³ and (a − b)³.
(a + b)³ = a³ + b³ + 3ab(a + b); (a − b)³ = a³ − b³ − 3ab(a − b).
State the factorisation identities for a³ + b³ and a³ − b³.
a³ + b³ = (a + b)(a² − ab + b²); a³ − b³ = (a − b)(a² + ab + b²).
State the identity for a³ + b³ + c³ − 3abc.
a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca). If a + b + c = 0, then a³ + b³ + c³ = 3abc.
For polynomials, how are HCF and LCM related to their product?
For two polynomials, HCF × LCM = product of the two polynomials (analogous to numbers).
How do you find the HCF of two polynomials?
Factorise each polynomial completely; the HCF is the product of all common factors taken with the lowest powers.
How many solutions does a linear equation in one variable (ax + b = 0) have, and what is the solution?
Exactly one solution: x = −b/a (provided a ≠ 0).
For a pair of linear equations a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0, what condition gives a unique solution?
Unique solution when a₁/a₂ ≠ b₁/b₂ (lines intersect at one point — consistent and independent).
For two linear equations, what ratio condition means no solution, and what means infinitely many?
No solution (parallel lines): a₁/a₂ = b₁/b₂ ≠ c₁/c₂. Infinitely many (coincident lines): a₁/a₂ = b₁/b₂ = c₁/c₂.
State the quadratic formula for ax² + bx + c = 0.
x = [−b ± √(b² − 4ac)] / (2a).
What is the discriminant of a quadratic, and what do its sign cases indicate about the roots? Also give the sum and product of roots.
Discriminant D = b² − 4ac. D > 0: two distinct real roots; D = 0: two equal real roots; D < 0: no real (complex) roots. Sum of roots = −b/a, Product of roots = c/a.
What this deck covers
The Elementary Mathematics (Paper III, for IMA/INA/AFA) deck follows the UPSC CDS (Combined Defence Services) Elementary Mathematics (Paper III, for IMA/INA/AFA) syllabus — 6 chapters and 27 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 8.3 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 80 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.
Elementary Mathematics (Paper III, for IMA/INA/AFA) flashcards FAQ
How many Elementary Mathematics (Paper III, for IMA/INA/AFA) flashcards are in this UPSC CDS (Combined Defence Services) deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these UPSC CDS (Combined Defence Services) flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Elementary Mathematics (Paper III, for IMA/INA/AFA) cards cover?
They follow the UPSC CDS (Combined Defence Services) Elementary Mathematics (Paper III, for IMA/INA/AFA) syllabus — 6 chapters and 27 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.