FE CIVIL: FUNDAMENTALS OF ENGINEERING EXAM READY - VERIFIED QUESTIONS AND EXPLAINED ANSWERS - COMPREHENSIVE LATEST VERSION 2026/2027

FE CIVIL: FUNDAMENTALS OF ENGINEERING EXAM READY - VERIFIED

QUESTIONS AND EXPLAINED ANSWERS - COMPREHENSIVE LATEST

VERSION 2026/2027




Question 1. What is the derivative of sin(x)?
A. cos(x)
B. -cos(x)
C. -sin(x)
D. tan(x)
ANSWER : A
Explanation: The derivative of sin(x) with respect to x is cos(x).

Question 2. What is the integral of e^x dx?
A. e^x + C
B. xe^x + C
C. e^x/x + C
D. ln(x) + C
ANSWER : A
Explanation: The integral of e^x is e^x + C, since the exponential function is its own
derivative.

Question 3. If f(x) = 3x² + 2x – 5, what is f'(x)?
A. 6x + 2
B. 3x + 2
C. 6x
D. 6x² + 2
ANSWER : A
Explanation: Using the power rule: d/dx(3x²) = 6x and d/dx(2x) = 2, so f'(x) = 6x + 2.

Question 4. What is the determinant of matrix [[3,1],[2,4]]?
A. 10
B. 12

, C. 8
D. 14
ANSWER : A
Explanation: det = (3)(4) – (1)(2) = 12 – 2 = 10.

Question 5. Solve for x: 2x + 6 = 14
A. 4
B. 3
C. 5
D. 10
ANSWER : A
Explanation: 2x = 14 – 6 = 8, so x = 4.

Question 6. What is the Laplace transform of a constant c?
A. c/s
B. c·s
C. 1/s
D. c
ANSWER : A
Explanation: L{c} = c/s for s > 0.

Question 7. What is log₂(32)?
A. 5
B. 4
C. 6
D. 3
ANSWER : A
Explanation: 2⁵ = 32, so log₂(32) = 5.

Question 8. The dot product of vectors A = (1,2,3) and B = (4,5,6) is:
A. 32
B. 28
C. 30
D. 34
ANSWER : A
Explanation: (1)(4)+(2)(5)+(3)(6) = 4+10+18 = 32.

Question 9. What is the eigenvalue equation?

, A. Av = λv
B. Av = λ
C. A + v = λ
D. Av = v/λ
ANSWER : A
Explanation: The eigenvalue equation is Av = λv where v is an eigenvector and λ is its
corresponding eigenvalue.

Question 10. The Fourier series of a periodic function uses which functions as basis?
A. Sines and cosines
B. Polynomials
C. Exponentials only
D. Logarithms
ANSWER : A
Explanation: Fourier series represent periodic functions as infinite sums of sines and
cosines.

Question 11. What is the limit of (sin x)/x as x→0?
A. 1
B. 0
C. ∞
D. Undefined
ANSWER : A
Explanation: By L'Hôpital's rule or the standard limit, lim(x→0) sin(x)/x = 1.
Question 12. What does the mean value theorem state?
A. There exists c in (a,b) where f'(c) = [f(b)–f(a)]/(b–a)
B. f(a) = f(b) for all functions
C. f'(x) = 0 at maxima
D. The integral equals the area under the curve
ANSWER : A
Explanation: The MVT guarantees at least one point c where the instantaneous rate
equals the average rate.

Question 13. Which series converges according to the ratio test if lim|aₙ₊₁/aₙ| < 1?
A. Absolutely converges
B. Diverges
C. Conditionally converges

, D. Test is inconclusive
ANSWER : A
Explanation: If the ratio test limit is less than 1, the series converges absolutely.
Question 14. The cross product of A × B is:
A. A vector perpendicular to both A and B
B. A scalar quantity
C. The same as A · B
D. The sum of A and B
ANSWER : A
Explanation: The cross product produces a vector perpendicular to both input vectors.

Question 15. What is the solution to the ODE dy/dx = ky?
A. y = Ce^(kx)
B. y = Cx + k
C. y = kx²/2 + C
D. y = k·ln(x) + C
ANSWER : A
Explanation: Separating variables and integrating gives y = Ce^(kx), the exponential
growth/decay equation.

Question 16. If a 3×3 matrix has a determinant of 0, it is:
A. Singular
B. Invertible
C. Orthogonal
D. Symmetric
ANSWER : A
Explanation: A matrix with det = 0 is singular (non-invertible).

Question 17. The Taylor series expansion of e^x about x=0 begins:
A. 1 + x + x²/2! + x³/3! + ...
B. x + x²/2 + x³/3 + ...
C. 1 – x + x² – x³ + ...
D. x – x³/6 + x⁵/120 + ...
ANSWER : A
Explanation: The Maclaurin series for e^x = Σ xⁿ/n! = 1 + x + x²/2! + ...
Question 18. What is the value of the integral ∫₀¹ x² dx?