FUNDAMENTALS OF ENGINEERING EXAM (FE) | ULTIMATE ENGINEERING EXAM WITH CORRECT VERIFIED ANSWERS AND RATIONALES

FUNDAMENTALS OF ENGINEERING EXAM
(FE) | ULTIMATE ENGINEERING EXAM
WITH CORRECT VERIFIED ANSWERS AND
RATIONALES

1. A force of 50 N acts at 30° above the horizontal. What is
the horizontal component?
A. 25 N
B. 43.3 N
C. 50 N
D. 35.4 N
✅ Correct Answer: B
Rationale: Fx=Fcos⁡θ=50cos⁡30∘=43.3 NF_x = F \cos \theta
= 50 \cos 30^\circ = 43.3\text{ N}Fx
=Fcosθ=50cos30∘=43.3 N.


2. The derivative of f(x)=3x2−5x+2f(x)=3x^2-
5x+2f(x)=3x2−5x+2 is:
A. 6x−56x-56x−5
B. 3x−53x-53x−5
C. 6x2−56x^2-56x2−5
D. 3x2−53x^2-53x2−5
✅ Correct Answer: A
Rationale: Apply power rule: derivative of 3x23x^23x2 is
6x6x6x; derivative of −5x-5x−5x is −5-5−5.

,3. A simply supported beam with central point load
experiences maximum bending moment at:
A. Supports
B. Quarter span
C. Midspan
D. Anywhere equal
✅ Correct Answer: C
Rationale: For symmetric loading, maximum moment occurs
at the center.


4. Unit of electrical resistance:
A. Volt
B. Ampere
C. Coulomb
D. Ohm
✅ Correct Answer: D
Rationale: Resistance = voltage/current → Ohm.


5. If pressure doubles in an ideal gas at constant
temperature, volume:
A. Doubles
B. Remains constant
C. Halves
D. Quadruples
✅ Correct Answer: C
Rationale: Boyle’s Law: PV=constantPV =
\text{constant}PV=constant.

,6. Matrix determinant of
[2134]\begin{bmatrix}2&1\\3&4\end{bmatrix}[2314]:
A. 5
B. 8
C. 2
D. −5
✅ Correct Answer: A
Rationale: ad−bc=2(4)−1(3)=5ad-bc = 2(4)-
1(3)=5ad−bc=2(4)−1(3)=5.


7. Stress is defined as:
A. Force × area
B. Force / area
C. Area / force
D. Mass / volume
✅ Correct Answer: B
Rationale: Normal stress = force divided by cross-sectional
area.


8. First law of thermodynamics expresses conservation of:
A. Mass
B. Momentum
C. Charge
D. Energy
✅ Correct Answer: D
Rationale: Energy cannot be created or destroyed.


9. If velocity is constant, acceleration is:

, A. Increasing
B. Zero
C. Negative
D. Infinite
✅ Correct Answer: B
Rationale: Acceleration = rate of change of velocity.


10. SI unit of power:
A. Joule
B. Watt
C. Newton
D. Pascal
✅ Correct Answer: B
Rationale: Power = energy per time → Watt.


11. The integral of 2x2x2x is:
A. x2x^2x2
B. 2x22x^22x2
C. x2+Cx^2 + Cx2+C
D. 2x+C2x + C2x+C
✅ Correct Answer: C
Rationale: ∫2x dx=x2+C\int 2x\,dx = x^2 + C∫2xdx=x2+C.


12. A rigid body in equilibrium requires:
A. Net force ≠ 0
B. Net moment ≠ 0
C. Net force = 0 and moment ≠ 0
D. Net force = 0 and moment = 0