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

The Engineering Knowledge Test (EKT) - Common Engineering Core syllabus for AFCAT (Air Force Common Admission Test) in full: 4 chapters, 13 topics and 3 sub-topics, every one listed below, plus 59 Engineering Knowledge Test (EKT) - Common Engineering Core flashcards with answers.

4Chapters
13Topics
3Sub-topics
59Flashcards

Engineering Knowledge Test (EKT) - Common Engineering Core syllabus: all 4 chapters

Expand any chapter to see its topics and sub-topics.

  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. Engineering Physics

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

  3. Engineering Drawing

     3 topics
    • Orthographic and isometric projections
    • Sectional views and dimensioning
    • Conventions and standards

  4. Basic Engineering Concepts

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

AFCAT (Air Force Common Admission Test) Engineering Knowledge Test (EKT) - Common Engineering Core flashcards — 59 questions with 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.

Show the other 39 Engineering Knowledge Test (EKT) - Common Engineering Core flashcards

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

    Both the mean and variance equal λ.

  2. 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.

  3. 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.

  4. 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).

  5. What is the difference between stress and strain?

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

  6. State Hooke's law and define Young's modulus.

    Within the elastic limit, stress ∝ strain. Young's modulus E = longitudinal stress / longitudinal strain.

  7. What is the moment of inertia, and what is it for a solid sphere about its diameter?

    Moment of inertia is the rotational analogue of mass (Σmr²). For a solid sphere about a diameter, I = (2/5)MR².

  8. State the principle of conservation of linear momentum.

    In the absence of external forces, the total linear momentum of a system remains constant.

  9. What is the relation between surface tension and excess pressure inside a soap bubble?

    Excess pressure P = 4T/r (two surfaces); for a liquid drop it is P = 2T/r, where T is surface tension and r is radius.

  10. State Bernoulli's equation for steady, incompressible, non-viscous flow.

    P + ½ρv² + ρgh = constant along a streamline.

  11. What is the laws of refraction (Snell's law)?

    n₁ sinθ₁ = n₂ sinθ₂; the ratio sin(incidence)/sin(refraction) = constant = relative refractive index.

  12. State the lens maker's formula.

    1/f = (n - 1)(1/R₁ - 1/R₂), where f is focal length, n the refractive index, and R₁, R₂ the radii of curvature.

  13. What is the condition for constructive and destructive interference of light?

    Constructive: path difference = nλ (integer multiples). Destructive: path difference = (2n+1)λ/2 (odd half-wavelengths).

  14. What is the relationship between velocity, frequency, and wavelength of a wave?

    v = fλ (velocity = frequency × wavelength).

  15. Differentiate between transverse and longitudinal waves.

    Transverse: particle vibration perpendicular to propagation (e.g., light). Longitudinal: particle vibration parallel to propagation (e.g., sound).

  16. State Einstein's photoelectric equation.

    hf = W₀ + KE_max, i.e., hf = φ + ½mv²_max, where φ is the work function.

  17. What is the de Broglie wavelength of a particle?

    λ = h/p = h/(mv), where h is Planck's constant and p is momentum.

  18. State Heisenberg's uncertainty principle.

    Δx·Δp ≥ h/4π; position and momentum cannot both be measured with arbitrary precision simultaneously.

  19. What is the mass-energy equivalence relation?

    E = mc², where c is the speed of light in vacuum.

  20. In orthographic projection, what are the three principal views typically shown?

    Front view (elevation), top view (plan), and side view (end view/profile).

  21. What is the difference between first-angle and third-angle projection?

    First-angle: object between observer and plane; top view below front view (used in India/Europe). Third-angle: plane between observer and object; top view above front view (used in USA).

  22. What is an isometric projection and its standard axis angles?

    A pictorial 3D representation where the three axes are equally inclined at 120° to each other (drawn at 30° to the horizontal).

  23. What is the isometric scale factor compared to true length?

    Isometric lengths are about 0.816 (√(2/3)) times the true length; isometric drawing often uses true lengths for simplicity.

  24. What is a sectional view and why is hatching used?

    A view showing the interior of an object as if cut by a cutting plane; hatching (section lines) indicates the solid material that the plane cuts through.

  25. What is the standard hatching angle and convention for adjacent parts in a section?

    Hatching lines are drawn at 45° to the principal axis; adjacent parts are hatched in opposite directions or different angles/spacing to distinguish them.

  26. What is the difference between a full section and a half section?

    Full section: cutting plane passes entirely through the object. Half section: removes one quarter, showing half in section and half in external view (for symmetric objects).

  27. Name the main systems of placing dimensions on a drawing.

    Aligned system (dimensions read parallel to the dimension line) and Unidirectional system (all dimensions read horizontally from the bottom).

  28. What type of line is used for a centre line and for a hidden edge in engineering drawing?

    Centre line: thin long-short dash (chain) line; Hidden edge: thin/medium dashed (short dash) line.

  29. Which Indian standard governs engineering drawing conventions?

    IS:696 / SP:46 (Bureau of Indian Standards code of practice for general engineering drawing).

  30. What is the difference between statics and dynamics in engineering mechanics?

    Statics deals with bodies at rest or in equilibrium under forces; Dynamics deals with bodies in motion, including kinematics (motion) and kinetics (forces causing motion).

  31. State the conditions of equilibrium for a coplanar force system.

    ΣFx = 0, ΣFy = 0, and ΣM = 0 (sum of horizontal forces, vertical forces, and moments all equal zero).

  32. State the first law of thermodynamics.

    Energy cannot be created or destroyed: Q = ΔU + W (heat added equals change in internal energy plus work done by the system).

  33. State the second law of thermodynamics (Kelvin-Planck statement).

    It is impossible to construct a device operating in a cycle that converts all absorbed heat completely into work (no 100% efficient heat engine).

  34. What is the efficiency of a Carnot engine operating between temperatures T_H and T_C?

    η = 1 - (T_C / T_H), with temperatures in kelvin; it is the maximum possible efficiency.

  35. What is the difference between ductility, malleability, and brittleness?

    Ductility: ability to be drawn into wires (tension). Malleability: ability to be hammered into sheets (compression). Brittleness: tendency to fracture without significant plastic deformation.

  36. What are the main types of crystal structures in metals?

    Body-Centred Cubic (BCC), Face-Centred Cubic (FCC), and Hexagonal Close-Packed (HCP).

  37. What is the difference between ferrous and non-ferrous metals, with examples?

    Ferrous metals contain iron as the main constituent (e.g., steel, cast iron); non-ferrous metals do not (e.g., aluminium, copper, brass).

  38. What distinguishes elastic deformation from plastic deformation?

    Elastic deformation is recoverable when load is removed (within elastic limit); plastic deformation is permanent (beyond the yield point).

  39. What is the chain rule for differentiating a composite function y = f(g(x))?

    dy/dx = f'(g(x)) · g'(x), i.e., (dy/du)·(du/dx).

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

What is in the AFCAT (Air Force Common Admission Test) Engineering Knowledge Test (EKT) - Common Engineering Core syllabus?

AFCAT (Air Force Common Admission Test) Engineering Knowledge Test (EKT) - Common Engineering Core is split into 4 chapters: Engineering Mathematics, Engineering Physics, Engineering Drawing and Basic Engineering Concepts. Together they contain 13 topics and 3 sub-topics.

How many chapters are in AFCAT (Air Force Common Admission Test) Engineering Knowledge Test (EKT) - Common Engineering Core?

4 chapters, containing 13 topics and 3 sub-topics. The largest chapter is Engineering Mathematics, with 4 topics.

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

Yes — a 59-card Engineering Knowledge Test (EKT) - Common Engineering Core deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.