AFCAT (Air Force Common Admission Test) Engineering Knowledge Test (EKT) - Common Engineering Core Syllabus

Engineering Knowledge Test (EKT) - Common Engineering Core syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Engineering Knowledge Test (EKT) - Common Engineering Core in AFCAT (Air Force Common Admission Test), not a summary of it.

1. 1

   Engineering Mathematics

   4 topics

   • Calculus and differential equations
     • Differentiation and integration
     • First and second order ODEs
   • Matrices and determinants
   • Complex variables and Laplace transforms
   • Probability and statistics
2. 2

   Engineering Physics

   3 topics

   • Mechanics and properties of matter
   • Optics and waves
   • Modern physics
     • Lasers and semiconductors
3. 3

   Engineering Drawing

   3 topics

   • Orthographic and isometric projections
   • Sectional views and dimensioning
   • Conventions and standards
4. 4

   Basic Engineering Concepts

   3 topics

   • Engineering mechanics (statics and dynamics)
   • Thermodynamics fundamentals
   • Material science basics

Engineering Knowledge Test (EKT) - Common Engineering Core flashcards for AFCAT (Air Force Common Admission Test)

25 of 59 cards from the Engineering Knowledge Test (EKT) - Common Engineering Core deck — real questions with worked answers.

1. What is the derivative of a function f(x) defined as, using the limit (first principle) definition?

   f'(x) = lim(h→0) [f(x+h) - f(x)] / h

2. State the formula for integration by parts.

   ∫u dv = uv - ∫v du

3. What is the order and degree of a differential equation?

   Order = the highest derivative present; Degree = the power of the highest-order derivative after the equation is made free of radicals and fractions in derivatives.

4. What is the general solution form of a first-order linear ODE dy/dx + Py = Q?

   y·(I.F.) = ∫Q·(I.F.) dx + C, where the integrating factor I.F. = e^(∫P dx).

5. State Leibniz's rule for the nth derivative of a product (uv).

   (uv)^(n) = Σ [nCr · u^(n-r) · v^(r)] for r = 0 to n.

6. What is the value of the determinant of a 2×2 matrix [[a, b],[c, d]]?

   ad - bc

7. When does the inverse of a square matrix A exist, and what is its formula?

   It exists when A is non-singular (det A ≠ 0). A⁻¹ = adj(A) / det(A).

8. What is a symmetric matrix and a skew-symmetric matrix?

   Symmetric: Aᵀ = A (a_ij = a_ji). Skew-symmetric: Aᵀ = -A (a_ij = -a_ji, with zero diagonal).

9. State Cramer's rule for solving a system of linear equations.

   For AX = B, each variable x_i = D_i / D, where D = det(A) and D_i is the determinant with the i-th column replaced by B (valid when D ≠ 0).

10. What is the rank of a matrix?

    The order of the largest non-zero minor, i.e., the number of linearly independent rows or columns.

11. What are eigenvalues and eigenvectors of a matrix A?

    For Av = λv (v ≠ 0), λ is an eigenvalue and v is the corresponding eigenvector; eigenvalues are roots of det(A - λI) = 0.

12. State the Cauchy-Riemann equations for a function f(z) = u(x,y) + iv(x,y) to be analytic.

    ∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x.

13. What is the definition of the Laplace transform of a function f(t)?

    L{f(t)} = ∫₀^∞ e^(-st) f(t) dt = F(s).

14. What is the Laplace transform of e^(at)?

    L{e^(at)} = 1/(s - a), for s > a.

15. What are the Laplace transforms of sin(at) and cos(at)?

    L{sin at} = a/(s² + a²); L{cos at} = s/(s² + a²).

16. State the Laplace transform of the derivative f'(t).

    L{f'(t)} = sF(s) - f(0).

17. State Cauchy's integral theorem for an analytic function.

    If f(z) is analytic everywhere inside and on a simple closed curve C, then ∮_C f(z) dz = 0.

18. What is the probability of an event using the classical (a priori) definition?

    P(E) = (number of favourable outcomes) / (total number of equally likely outcomes).

19. State Bayes' theorem.

    P(A|B) = [P(B|A)·P(A)] / P(B), where P(B) = Σ P(B|A_i)·P(A_i).

20. What is the mean (expected value) and variance of a binomial distribution B(n, p)?

    Mean = np; Variance = npq, where q = 1 - p.

21. What is the mean and variance of a Poisson distribution with parameter λ?

    Both the mean and variance equal λ.

22. Define standard deviation in terms of variance.

    Standard deviation σ = √(variance); it is the square root of the mean of squared deviations from the mean.

23. For mutually exclusive events A and B, what is the addition rule P(A ∪ B)?

    P(A ∪ B) = P(A) + P(B), since P(A ∩ B) = 0.

24. State Newton's second law of motion in equation form.

    F = ma (force equals mass times acceleration), or more generally F = dp/dt (rate of change of momentum).

25. What is the difference between stress and strain?

    Stress = force per unit area (N/m²); Strain = change in dimension per original dimension (dimensionless ratio).

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