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Agniveer (Agnipath Scheme) Quantitative Aptitude and Mathematics Flashcards
63 question-and-answer cards covering Quantitative Aptitude and Mathematics as it is examined in Agniveer (Agnipath Scheme). 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Quantitative Aptitude and Mathematics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
For a pair of linear equations a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0, when is the system consistent or inconsistent?
Unique solution (consistent): a₁/a₂ ≠ b₁/b₂. Infinitely many (consistent, dependent): a₁/a₂ = b₁/b₂ = c₁/c₂. No solution (inconsistent): a₁/a₂ = b₁/b₂ ≠ c₁/c₂.
State the quadratic formula for ax² + bx + c = 0.
x = [−b ± √(b² − 4ac)] / (2a), provided a ≠ 0.
What does the discriminant of a quadratic equation tell you?
D = b² − 4ac. If D > 0: two distinct real roots. If D = 0: two equal real roots. If D < 0: no real roots (complex conjugates).
For ax² + bx + c = 0, what are the sum and product of the roots?
Sum of roots = −b/a; Product of roots = c/a.
What are complementary, supplementary, and vertically opposite angles?
Complementary: two angles summing to 90°. Supplementary: two angles summing to 180°. Vertically opposite angles (formed by two intersecting lines) are equal.
State the angle sum properties of a triangle and the exterior angle theorem.
Sum of interior angles of a triangle = 180°. Exterior angle = sum of the two interior opposite (remote) angles.
State the Pythagoras theorem.
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: hypotenuse² = base² + perpendicular².
What is the sum of interior angles of a polygon with n sides, and the measure of each interior angle of a regular polygon?
Sum of interior angles = (n − 2) × 180°. Each interior angle of a regular polygon = (n − 2) × 180° / n. Sum of exterior angles = 360°.
State the formulas for circumference and area of a circle.
Circumference = 2πr (or πd); Area = πr², where r = radius, d = diameter.
State the area and perimeter formulas for a rectangle, square, triangle, and circle.
Rectangle: Area = l×b, Perimeter = 2(l+b). Square: Area = a², Perimeter = 4a. Triangle: Area = ½×base×height. Circle: Area = πr², Circumference = 2πr.
State Heron's formula for the area of a triangle with sides a, b, c.
Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2 is the semi-perimeter.
State the surface area and volume formulas for a cube and a cuboid.
Cube (side a): Volume = a³, Total Surface Area = 6a². Cuboid (l,b,h): Volume = l×b×h, TSA = 2(lb + bh + hl).
State the volume and surface area formulas for a cylinder and a sphere.
Cylinder (r,h): Volume = πr²h, Curved SA = 2πrh, TSA = 2πr(r+h). Sphere (r): Volume = (4/3)πr³, Surface Area = 4πr².
State the volume and surface area formulas for a cone.
Cone (radius r, height h, slant height l): Volume = (1/3)πr²h, Curved SA = πrl, TSA = πr(r+l), where l = √(r²+h²).
Define the six trigonometric ratios in a right triangle.
sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse, tanθ = opposite/adjacent, cosecθ = 1/sinθ, secθ = 1/cosθ, cotθ = 1/tanθ.
State the fundamental Pythagorean trigonometric identities.
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
Give the values of sin, cos, and tan at 0°, 30°, 45°, 60°, and 90°.
sin: 0, 1/2, 1/√2, √3/2, 1. cos: 1, √3/2, 1/√2, 1/2, 0. tan: 0, 1/√3, 1, √3, undefined.
In heights and distances, what are the angle of elevation and angle of depression?
Angle of elevation: the angle above the horizontal when looking up at an object. Angle of depression: the angle below the horizontal when looking down at an object. Both are measured from the horizontal line of sight.
How do you find the height of an object using the angle of elevation θ from distance d?
Height = d × tanθ (object height above eye/base level), since tanθ = height/distance. Add observer's eye height if measured from eye level.
What is data interpretation and what are common chart types used?
Data interpretation is analyzing given data (tables, charts) to answer questions. Common forms: tables, bar graphs, line graphs, pie charts, and histograms.
How do you read a pie chart to find a quantity, and how many degrees equal the whole?
The whole circle = 360° (or 100%). A sector's value = (sector angle/360°) × total, or (sector percent/100) × total.
Define mean, median, and mode.
Mean = sum of observations / number of observations. Median = the middle value when data is arranged in order. Mode = the most frequently occurring value.
How do you find the median when the number of observations is even vs odd?
Arrange data in ascending order. Odd n: median = the ((n+1)/2)th value. Even n: median = average of the (n/2)th and (n/2 + 1)th values.
State the empirical relationship between mean, median, and mode.
Mode = 3 × Median − 2 × Mean. (Equivalently: Mean − Mode = 3(Mean − Median).)
What this deck covers
The Quantitative Aptitude and Mathematics deck follows the Agniveer (Agnipath Scheme) Quantitative Aptitude and Mathematics syllabus — 6 chapters and 23 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.5 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 118 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.
Quantitative Aptitude and Mathematics flashcards FAQ
How many Quantitative Aptitude and Mathematics flashcards are in this Agniveer (Agnipath Scheme) deck?
63 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these Agniveer (Agnipath Scheme) flashcards free?
Yes. The preview here is free to read with no signup, and the full 63-card deck is free inside the Examius app.
What do the Quantitative Aptitude and Mathematics cards cover?
They follow the Agniveer (Agnipath Scheme) Quantitative Aptitude and Mathematics syllabus — 6 chapters and 23 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.