Advanced Engineering Mathematics Certification Evaluation Exams Set Full Questions And Complete Solution

ADVANCED ENGINEERING MATHEMATICS
CERTIFICATION EVALUATION EXAMS SET
FULL QUESTIONS AND COMPLETE
SOLUTION

●● Circular Ring
Answer: V = ∫ π(R^2 - r^2) dy


●● Propositions of Pappus
Answer: First Proposition: A = 2πR * S; Second Theorem: V = 2πR * A


●● Length of an Arc
Answer: L = ∫ √(1 + (dy/dx)^2) dx


●● Number of Diagonal in Polygons
Answer: Nd = nC2 - n


●● Interior Angle of Polygon
Answer: Interior angle = (n - 2) * 180° / n


●● Area of n-sided Polygon

,Answer: Area = (1/2) * n * b * sin(θ)


●● Trapezium Area
Answer: Area = (1/2) * (a + b) * h


●● Frustum of Cone
Answer: V = (1/3) * πh * (R^2 + Rr + r^2)


●● Cyclic Quadrilateral
Answer: Bramagupta's Formula: Area = √(s(s-a)(s-b)(s-c)(s-d))


●● Arc Length of Circle
Answer: Arc length = r * θ


●● Sector Area of Circle
Answer: Sector Area = (1/2) * r^2 * θ


●● Spherical Segment Area
Answer: Area = 2πRh


●● SOH CAH TOA

, Answer: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse,
Tangent = Opposite/Adjacent


●● Ptolemy's Theorem
Answer: For a cyclic quadrilateral, the sum of the products of the
opposite sides is equal.


●● Ellipse
Answer: Eccentricity e = √(1 - (b^2/a^2))


●● Sine Law
Answer: a/sin(A) = b/sin(B) = c/sin(C)


●● Cosine Law
Answer: c^2 = a^2 + b^2 - 2ab * cos(C)


●● Tangent Law
Answer: tan(A/2) = (s - a)/(s)


●● Volume of Regular Polyhedron
Answer: V = (F + V - 2)


●● Napier's Rule I