Fundamentals of Engineering (FE) Exam 1
Questions And Correct Answers (Verified
Answers) Plus Rationales 2025
1. A steel rod with a length of 2 m and a cross-sectional area of 0.01 m² is
subjected to an axial tensile force of 10,000 N. What is the normal stress in the
rod?
A) 500,000 Pa
B) 1,000,000 Pa
C) 100,000 Pa
D) 10,000 Pa
Answer: B) 1,000,000 Pa
Rationale: Stress, σ=ForceArea=10,0000.01=1,000,000 Pa\sigma = \frac{Force}{Area} =
\frac{10,000}{0.01} = 1,000,000 \, \text{Pa}σ=AreaForce=0.0110,000=1,000,000Pa. Stress is
force divided by cross-sectional area.
2. What is the derivative of f(x)=3x4−5x+2f(x) = 3x^4 - 5x + 2f(x)=3x4−5x+2?
A) 12x3−512x^3 - 512x3−5
B) 12x3−512x^3 - 512x3−5
C) 12x3+512x^3 + 512x3+5
D) 7x3−57x^3 - 57x3−5
Answer: B) 12x3−512x^3 - 512x3−5
Rationale: The derivative of 3x43x^43x4 is 12x312x^312x3, derivative of −5x-5x−5x is −5-
5−5, and derivative of constant 2 is 0.
3. A closed container holds 2 m³ of an ideal gas at 300 K and 100 kPa. If the
temperature is increased to 600 K while the volume remains constant, what is the
new pressure?
,A) 50 kPa
B) 100 kPa
C) 200 kPa
D) 400 kPa
Answer: C) 200 kPa
Rationale: Using Gay-Lussac’s Law for constant volume, P1/T1=P2/T2P_1/T_1 = P_2/T_2P1
/T1=P2/T2.
P2=P1×T2T1=100×600300=200 kPaP_2 = P_1 \times \frac{T_2}{T_1} = 100 \times
\frac{600}{300} = 200 \, \text{kPa}P2=P1×T1T2=100×300600=200kPa.
4. Which of the following is a scalar quantity?
A) Velocity
B) Acceleration
C) Displacement
D) Temperature
Answer: D) Temperature
Rationale: Scalars have only magnitude, no direction. Temperature is scalar; velocity,
acceleration, and displacement are vectors.
5. For a simply supported beam with a point load PPP applied at mid-span, what
is the maximum bending moment?
A) PL4\frac{PL}{4}4PL
B) PL4\frac{PL}{4}4PL
C) PL2\frac{PL}{2}2PL
D) PL\frac{P}{L}LP
Answer: B) PL4\frac{PL}{4}4PL
Rationale: The maximum bending moment in a simply supported beam with a mid-span point
load is PL4\frac{PL}{4}4PL.
6. The integral of ∫x3 dx\int x^3 \, dx∫x3dx is:
, A) 3x2+C3x^2 + C3x2+C
B) x44+C\frac{x^4}{4} + C4x4+C
C) 3x44+C\frac{3x^4}{4} + C43x4+C
D) x3+Cx^3 + Cx3+C
Answer: B) x44+C\frac{x^4}{4} + C4x4+C
Rationale: The integral of xnx^nxn is xn+1n+1+C\frac{x^{n+1}}{n+1} + Cn+1xn+1+C. For
n=3n=3n=3, ∫x3dx=x44+C\int x^3 dx = \frac{x^4}{4} + C∫x3dx=4x4+C.
7. A pump delivers water at a rate of 0.1 m³/s through a pipe with a velocity of 2
m/s. What is the cross-sectional area of the pipe?
A) 0.05 m²
B) 0.05 m²
C) 0.2 m²
D) 0.5 m²
Answer: B) 0.05 m²
Rationale: Flow rate Q=A×V⇒A=QV=0.12=0.05 m2Q = A \times V \Rightarrow A =
\frac{Q}{V} = \frac{0.1}{2} = 0.05 \, \text{m}^2Q=A×V⇒A=VQ=20.1=0.05m2.
8. Which law states that the current through a conductor between two points is
directly proportional to the voltage across the two points?
A) Newton’s Law
B) Ohm’s Law
C) Faraday’s Law
D) Hooke’s Law
Answer: B) Ohm’s Law
Rationale: Ohm’s Law states V=IRV = IRV=IR, voltage is proportional to current.
9. What is the unit of dynamic viscosity in SI units?
A) Pascal (Pa)
B) Pascal-second (Pa·s)
Questions And Correct Answers (Verified
Answers) Plus Rationales 2025
1. A steel rod with a length of 2 m and a cross-sectional area of 0.01 m² is
subjected to an axial tensile force of 10,000 N. What is the normal stress in the
rod?
A) 500,000 Pa
B) 1,000,000 Pa
C) 100,000 Pa
D) 10,000 Pa
Answer: B) 1,000,000 Pa
Rationale: Stress, σ=ForceArea=10,0000.01=1,000,000 Pa\sigma = \frac{Force}{Area} =
\frac{10,000}{0.01} = 1,000,000 \, \text{Pa}σ=AreaForce=0.0110,000=1,000,000Pa. Stress is
force divided by cross-sectional area.
2. What is the derivative of f(x)=3x4−5x+2f(x) = 3x^4 - 5x + 2f(x)=3x4−5x+2?
A) 12x3−512x^3 - 512x3−5
B) 12x3−512x^3 - 512x3−5
C) 12x3+512x^3 + 512x3+5
D) 7x3−57x^3 - 57x3−5
Answer: B) 12x3−512x^3 - 512x3−5
Rationale: The derivative of 3x43x^43x4 is 12x312x^312x3, derivative of −5x-5x−5x is −5-
5−5, and derivative of constant 2 is 0.
3. A closed container holds 2 m³ of an ideal gas at 300 K and 100 kPa. If the
temperature is increased to 600 K while the volume remains constant, what is the
new pressure?
,A) 50 kPa
B) 100 kPa
C) 200 kPa
D) 400 kPa
Answer: C) 200 kPa
Rationale: Using Gay-Lussac’s Law for constant volume, P1/T1=P2/T2P_1/T_1 = P_2/T_2P1
/T1=P2/T2.
P2=P1×T2T1=100×600300=200 kPaP_2 = P_1 \times \frac{T_2}{T_1} = 100 \times
\frac{600}{300} = 200 \, \text{kPa}P2=P1×T1T2=100×300600=200kPa.
4. Which of the following is a scalar quantity?
A) Velocity
B) Acceleration
C) Displacement
D) Temperature
Answer: D) Temperature
Rationale: Scalars have only magnitude, no direction. Temperature is scalar; velocity,
acceleration, and displacement are vectors.
5. For a simply supported beam with a point load PPP applied at mid-span, what
is the maximum bending moment?
A) PL4\frac{PL}{4}4PL
B) PL4\frac{PL}{4}4PL
C) PL2\frac{PL}{2}2PL
D) PL\frac{P}{L}LP
Answer: B) PL4\frac{PL}{4}4PL
Rationale: The maximum bending moment in a simply supported beam with a mid-span point
load is PL4\frac{PL}{4}4PL.
6. The integral of ∫x3 dx\int x^3 \, dx∫x3dx is:
, A) 3x2+C3x^2 + C3x2+C
B) x44+C\frac{x^4}{4} + C4x4+C
C) 3x44+C\frac{3x^4}{4} + C43x4+C
D) x3+Cx^3 + Cx3+C
Answer: B) x44+C\frac{x^4}{4} + C4x4+C
Rationale: The integral of xnx^nxn is xn+1n+1+C\frac{x^{n+1}}{n+1} + Cn+1xn+1+C. For
n=3n=3n=3, ∫x3dx=x44+C\int x^3 dx = \frac{x^4}{4} + C∫x3dx=4x4+C.
7. A pump delivers water at a rate of 0.1 m³/s through a pipe with a velocity of 2
m/s. What is the cross-sectional area of the pipe?
A) 0.05 m²
B) 0.05 m²
C) 0.2 m²
D) 0.5 m²
Answer: B) 0.05 m²
Rationale: Flow rate Q=A×V⇒A=QV=0.12=0.05 m2Q = A \times V \Rightarrow A =
\frac{Q}{V} = \frac{0.1}{2} = 0.05 \, \text{m}^2Q=A×V⇒A=VQ=20.1=0.05m2.
8. Which law states that the current through a conductor between two points is
directly proportional to the voltage across the two points?
A) Newton’s Law
B) Ohm’s Law
C) Faraday’s Law
D) Hooke’s Law
Answer: B) Ohm’s Law
Rationale: Ohm’s Law states V=IRV = IRV=IR, voltage is proportional to current.
9. What is the unit of dynamic viscosity in SI units?
A) Pascal (Pa)
B) Pascal-second (Pa·s)
