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#1. The moment of inertia of a rectangle (b×h) about its centroidal horizontal axis is:
#2. In an isentropic process for an ideal gas: Tv^(γ−1) =
#3. The natural frequency of a spring-mass system with k=400 N/m and m=1 kg is:
#4. The first law of thermodynamics for a closed system:
#5. Evaluate the definite integral: ∫₀^π sin(x) dx.
#7. Fourier’s law of heat conduction: q = −kA(dT/dx). The negative sign indicates:
#8. A flat belt drive has belt tensions T₁ (tight) and T₂ (slack). The power transmitted:
#9. The centroid of a right triangle of base b and height h is located at (from the right angle):
#10. In a feedback control system, the error signal is:
#11. The coefficient of static friction μs = 0.3. A 100-N block on a horizontal surface requires a horizontal push of at least __ to start sliding:
#12. The moment of a 200-N force about a point 3 m from the line of action is:
#13. In a two-force member, the forces must be:
#14. The head loss in a pipe (Darcy-Weisbach) is:
#15. A simply supported beam of span L with a central point load P has maximum bending moment of:
#16. Accuracy of a measurement refers to:
#17. The angular velocity of a wheel spinning at 3000 RPM is closest to:
#18. Specific heat at constant pressure cp minus specific heat at constant volume cv for an ideal gas:
#19. The thermal resistance of a plane wall of thickness L, area A, and conductivity k:
#20. Geometric Dimensioning and Tolerancing (GD&T) uses:
#21. The Otto cycle models:
#22. The kinetic energy of a 5-kg object moving at 6 m/s is:
#23. The Nusselt number represents:
#24. The Rankine cycle consists of:
#25. A strain gauge measures deformation based on:
#26. What is the determinant of the matrix [[3, 1], [2, 4]]?
#27. The modulus of elasticity (Young’s modulus) represents:
#28. The overall heat transfer coefficient U for a composite wall:
#29. A 500-N force acts at 30° above horizontal. Its horizontal component is:
#30. Work done during an isobaric (constant pressure) process:
#31. For binomial n=10, p=0.3, E[X] =
#32. The buoyant force on a submerged body equals:
#33. Galvanic corrosion occurs when:
#34. For laminar flow in a pipe, the friction factor f (Darcy) =
#35. According to NCEES Model Rules, an engineer’s primary obligation is to:
#36. The Stefan-Boltzmann law for blackbody radiation:
#37. The gradient of φ = x²y + yz³ at (1,1,1) is:
#38. A power screw with lead l and mean diameter d_m has efficiency η = tan λ / tan(λ+φ). Here λ is:
#39. The shear stress in a beam at the neutral axis is:
#41. Coefficient of variation is defined as:
#42. For a system in static equilibrium, which conditions must be satisfied?
#43. A disk of mass m and radius r rolling without slip has a total kinetic energy of:
#44. The maximum shear stress in a solid circular shaft under torsion T is:
#45. The general solution to y″ + 4y = 0 is:
#46. The period of a simple pendulum of length 1 m on Earth (g=9.81 m/s²) is closest to:
#48. The relationship between E, G, and ν is:
#49. Entropy of the universe for any real process:
#50. A thermocouple measures temperature by:
#51. A truss member in tension has:
#52. A steel rod (E=200 GPa) of 20-mm diameter and 2-m length carries 50 kN tensile load. The elongation is:
#53. A helical compression spring with n active coils, wire diameter d, and mean coil diameter D has spring rate:
#54. Austenite in steel is:
#55. The coefficient of restitution for a perfectly elastic collision is:
#56. The continuity equation for steady incompressible flow:
#57. A 2-kg ball moving at 5 m/s strikes a wall and rebounds at 3 m/s. The impulse is:
#58. A bar heated by ΔT with coefficient α and constrained at both ends develops stress:
#59. Principal stresses are stresses on planes where:
#60. In a stress-strain diagram, the area under the curve up to fracture represents:
#61. The pump power required to deliver flow Q at head H:
#62. A 10-kg mass is acted on by a net force of 40 N. The acceleration is:
#63. A projectile launched at 30° with v₀=20 m/s. The maximum height is closest to:
#64. In welding, the throat dimension of a fillet weld of size h is:
#65. The resultant of two concurrent forces of 3 kN and 4 kN at right angles is:
#66. The Mach number is defined as:
#67. Kirchhoff’s voltage law states that:
#68. The quality x of a wet steam mixture:
#69. The Laplace transform of f(t) = t·e^(−2t) is:
#70. A 120-V, 60-Hz AC source has a peak voltage of:
#71. A bolt in a bolted joint is typically designed to resist:
#72. The future worth of $5,000 invested at 8% compounded annually for 10 years is closest to:
#73. Turbulent flow in a pipe typically occurs when Re >
#74. Euler’s critical buckling load for a pinned-pinned column is:
#75. In transient conduction, the Biot number Bi = hL/k represents:
#76. A car accelerates from rest at 3 m/s². Its velocity after 8 s is:
#77. A die is rolled twice. P(sum = 7) =
#78. The von Mises (distortion energy) theory predicts failure when:
#79. The Reynolds number for pipe flow is defined as:
#80. The energy stored in a capacitor C charged to voltage V is:
#81. The bending stress formula σ = Mc/I applies to:
#82. Three 6-Ω resistors in parallel have an equivalent resistance of:
#83. A 12-V battery drives 2 A through a circuit. The power dissipated is:
#84. A machine costs $10,000 and generates $3,000/year for 5 years. At i=10%, the NPV is closest to:
#85. The maximum shear stress theory (Tresca) predicts yielding of a ductile material when:
#86. A normally distributed variable has μ=50, σ=5. The probability within ±1σ is approximately:
#87. Poisson’s ratio relates:
#88. The coefficient of performance (COP) of a refrigerator:
#89. Kinematic viscosity ν equals:
#90. A utility patent protects an invention for:
#91. The log mean temperature difference (LMTD) is used for:
#92. The drag coefficient C_D for a smooth sphere at Re ≈ 10⁵ is approximately:
#93. Find dy/dx if y = e^(3x)·sin(x).
#94. The AGMA bending stress formula for spur gears includes:
#95. A journal bearing operates in the hydrodynamic regime when:
#96. The Carnot efficiency between T_H=600 K and T_L=300 K:
#97. An engineer discovers a design flaw endangering public safety. They should:
#98. Dalton’s law for gas mixtures states:
#99. The pressure at a depth of 10 m in water (ρ=1000 kg/m³) is:
#100. The primary purpose of quenching steel is to:
#101. For an ideal gas, Pv = RT. If T is doubled at constant volume, P:
#102. Bernoulli’s equation assumes:
#103. The yield strength of a material is the stress at which:
#104. A composite material consists of:
#105. Mohr’s circle for a state of stress has center at:
#106. A first-order system response to a step input:
#107. Newton’s law of cooling states:
#108. The break-even point is where:
#109. The work done by a constant force of 50 N moving an object 4 m in the direction of the force is:
#110. Using Newton’s method with x₀ = 2, find x₁ for f(x) = x²−5.
#111. The moment of inertia of a rectangle (b×h) about its centroidal horizontal axis is:
#112. In an isentropic process for an ideal gas: Tv^(γ−1) =
#113. The natural frequency of a spring-mass system with k=400 N/m and m=1 kg is:
#114. The first law of thermodynamics for a closed system:
#115. Evaluate the definite integral: ∫₀^π sin(x) dx.
#117. A flat belt drive has belt tensions T₁ (tight) and T₂ (slack). The power transmitted:
#118. Fourier’s law of heat conduction: q = −kA(dT/dx). The negative sign indicates:
#119. The centroid of a right triangle of base b and height h is located at (from the right angle):
#120. In a feedback control system, the error signal is:
#121. The coefficient of static friction μs = 0.3. A 100-N block on a horizontal surface requires a horizontal push of at least __ to start sliding:
#122. The angular velocity of a wheel spinning at 3000 RPM is closest to:
#123. Accuracy of a measurement refers to:
#124. The kinetic energy of a 5-kg object moving at 6 m/s is:
#125. The thermal resistance of a plane wall of thickness L, area A, and conductivity k:
#126. Geometric Dimensioning and Tolerancing (GD&T) uses:
#127. In a two-force member, the forces must be:
#128. The moment of a 200-N force about a point 3 m from the line of action is:
#129. A strain gauge measures deformation based on:
#130. Specific heat at constant pressure cp minus specific heat at constant volume cv for an ideal gas:
#131. A simply supported beam of span L with a central point load P has maximum bending moment of:
#132. The head loss in a pipe (Darcy-Weisbach) is:
#133. What is the determinant of the matrix [[3, 1], [2, 4]]?
#134. The Rankine cycle consists of:
#135. The Otto cycle models:
#136. The modulus of elasticity (Young’s modulus) represents:
#137. The Nusselt number represents:
#138. A 500-N force acts at 30° above horizontal. Its horizontal component is:
#139. The overall heat transfer coefficient U for a composite wall:
#140. Work done during an isobaric (constant pressure) process:
#141. For binomial n=10, p=0.3, E[X] =
#142. The buoyant force on a submerged body equals:
#143. Galvanic corrosion occurs when:
#144. According to NCEES Model Rules, an engineer’s primary obligation is to:
#145. For laminar flow in a pipe, the friction factor f (Darcy) =
#147. The shear stress in a beam at the neutral axis is:
#148. The Stefan-Boltzmann law for blackbody radiation:
#149. The gradient of φ = x²y + yz³ at (1,1,1) is:
#150. A power screw with lead l and mean diameter d_m has efficiency η = tan λ / tan(λ+φ). Here λ is:
#151. Coefficient of variation is defined as:
#152. For a system in static equilibrium, which conditions must be satisfied?
#153. A disk of mass m and radius r rolling without slip has a total kinetic energy of:
#155. A steel rod (E=200 GPa) of 20-mm diameter and 2-m length carries 50 kN tensile load. The elongation is:
#156. Entropy of the universe for any real process:
#157. The maximum shear stress in a solid circular shaft under torsion T is:
#158. The relationship between E, G, and ν is:
#159. A truss member in tension has:
#160. A helical compression spring with n active coils, wire diameter d, and mean coil diameter D has spring rate:
#161. A thermocouple measures temperature by:
#162. The general solution to y″ + 4y = 0 is:
#163. The period of a simple pendulum of length 1 m on Earth (g=9.81 m/s²) is closest to:
#164. Austenite in steel is:
#165. The coefficient of restitution for a perfectly elastic collision is:
#166. The pump power required to deliver flow Q at head H:
#167. A bar heated by ΔT with coefficient α and constrained at both ends develops stress:
#168. Principal stresses are stresses on planes where:
#169. The continuity equation for steady incompressible flow:
#170. A 2-kg ball moving at 5 m/s strikes a wall and rebounds at 3 m/s. The impulse is:
#171. The resultant of two concurrent forces of 3 kN and 4 kN at right angles is:
#172. In welding, the throat dimension of a fillet weld of size h is:
#173. In a stress-strain diagram, the area under the curve up to fracture represents:
#174. A 10-kg mass is acted on by a net force of 40 N. The acceleration is:
#175. A projectile launched at 30° with v₀=20 m/s. The maximum height is closest to:
#176. Kirchhoff’s voltage law states that:
#177. The Mach number is defined as:
#178. Turbulent flow in a pipe typically occurs when Re >
#179. A bolt in a bolted joint is typically designed to resist:
#180. The Laplace transform of f(t) = t·e^(−2t) is:
#181. A die is rolled twice. P(sum = 7) =
#182. The quality x of a wet steam mixture:
#183. A 120-V, 60-Hz AC source has a peak voltage of:
#184. A car accelerates from rest at 3 m/s². Its velocity after 8 s is:
#185. The Reynolds number for pipe flow is defined as:
#186. Euler’s critical buckling load for a pinned-pinned column is:
#187. The future worth of $5,000 invested at 8% compounded annually for 10 years is closest to:
#188. The von Mises (distortion energy) theory predicts failure when:
#189. In transient conduction, the Biot number Bi = hL/k represents:
#190. A 12-V battery drives 2 A through a circuit. The power dissipated is:
#191. The maximum shear stress theory (Tresca) predicts yielding of a ductile material when:
#192. Three 6-Ω resistors in parallel have an equivalent resistance of:
#193. The bending stress formula σ = Mc/I applies to:
#194. A machine costs $10,000 and generates $3,000/year for 5 years. At i=10%, the NPV is closest to:
#195. A utility patent protects an invention for:
#196. A normally distributed variable has μ=50, σ=5. The probability within ±1σ is approximately:
#197. The energy stored in a capacitor C charged to voltage V is:
#198. Poisson’s ratio relates:
#199. The log mean temperature difference (LMTD) is used for:
#200. Kinematic viscosity ν equals:
#201. The coefficient of performance (COP) of a refrigerator:
#202. The AGMA bending stress formula for spur gears includes:
#203. The drag coefficient C_D for a smooth sphere at Re ≈ 10⁵ is approximately:
#204. The yield strength of a material is the stress at which:
#205. Bernoulli’s equation assumes:
#206. Find dy/dx if y = e^(3x)·sin(x).
#207. The Carnot efficiency between T_H=600 K and T_L=300 K:
#208. The pressure at a depth of 10 m in water (ρ=1000 kg/m³) is:
#209. For an ideal gas, Pv = RT. If T is doubled at constant volume, P:
#210. The primary purpose of quenching steel is to:
#211. An engineer discovers a design flaw endangering public safety. They should:
#212. A journal bearing operates in the hydrodynamic regime when:
#213. Dalton’s law for gas mixtures states:
#214. Mohr’s circle for a state of stress has center at:
#215. A composite material consists of:
#216. The break-even point is where:
#217. A first-order system response to a step input:
#218. Newton’s law of cooling states:
#219. The work done by a constant force of 50 N moving an object 4 m in the direction of the force is:
#220. Using Newton’s method with x₀ = 2, find x₁ for f(x) = x²−5.
