Part 1 – Questions 1–25: Engineering Mechanics & Strength of Materials
Q1. A simply supported beam of length L carries a central point load P. Maximum bending moment =
A) PL/2
B) PL/4
C) PL/8
D) PL
Q2. Shear stress (τ) in a circular shaft transmitting torque T is:
A) τ = T / J × r
B) τ = T × r / J
C) τ = T / π r³
D) τ = T × J / r
Q3. For a cantilever beam with UDL w per unit length and span L, maximum bending moment:
A) wL²/2
B) wL²/8
C) wL²/4
D) wL²/3
Q4. Section modulus (Z) is defined as:
A) I / y
B) I × y
C) M / σ
D) Both A & C
Q5. The deflection of a simply supported beam with point load at midspan:
A) PL³/48EI
B) PL³/24EI
C) PL²/48EI
D) PL²/24EI
Q6. Maximum bending stress occurs at:
A) Neutral axis
B) Top fiber of beam
C) Bottom fiber of beam
D) Both B & C
Q7. Torsional rigidity of a shaft =
A) GJ / L
B) JL / G
C) G / JL
D) L / GJ
Q8. In combined bending and axial load, maximum stress occurs:
A) σ = P/A + M/Z
B) σ = P/A – M/Z
C) σ = M/Z only
D) σ = P/A only
Q9. Factor of safety (FS) =
A) Ultimate stress / Working stress
B) Working stress / Ultimate stress
C) Yield stress / Ultimate stress
D) None
Q10. For a cantilever, slope at free end:
A) wL³/6EI
B) wL²/2EI
C) wL³/3EI
D) wL²/6EI
Q11. In a simply supported beam, maximum shear occurs:
A) Midspan
B) Supports
C) Quarter span
D) Uniformly
Q12. Poisson’s ratio for steel:
A) 0.25
B) 0.3
C) 0.33
D) 0.35
Q13. Maximum principal stress in biaxial stress system:
A) (σx + σy)/2 + √[((σx – σy)/2)² + τxy²]
B) σx + σy
C) σx – σy
D) τxy
Q14. In thin cylinder, hoop stress =
A) pr / t
B) pr / 2t
C) 2pr / t
D) pr / 4t
Q15. Maximum bending moment in UDL over simply supported beam:
A) wL²/8
B) wL²/4
C) wL²/2
D) wL²/12
Q16. Torsional stress varies:
A) Linearly with radius
B) Quadratically with radius
C) Constant over section
D) Exponentially
Q17. Unit of moment of inertia (I) in SI:
A) m⁴
B) m²
C) kg·m²
D) N·m²
Q18. A fixed beam has bending moment at support =
A) wL²/12 (UDL)
B) wL²/8
C) wL²/24
D) wL²/6
Q19. For pure bending, the neutral axis:
A) Top fiber
B) Bottom fiber
C) Middle layer
D) Varies
Q20. Maximum deflection of a simply supported beam with UDL w:
A) 5wL⁴/384EI
B) wL⁴/8EI
C) wL²/48EI
D) wL³/24EI
Q21. Radius of gyration r =
A) √(I/A)
B) I/A
C) A/I
D) √(A/I)
Q22. Shear stress in rectangular section:
A) 1.5V/A
B) 1.5/2 V/A
C) 1.5/2.5 V/A
D) 2V/A
Q23. In combined torsion and bending, equivalent twisting moment:
A) √(M² + T²)
B) M + T
C) M – T
D) None
Q24. Factor of safety for ductile materials:
A) 2–3
B) 1.5–2
C) 3–4
D) 1–1.5
Q25. Maximum shear stress in solid circular shaft:
A) 16T/πd³
B) 8T/πd³
C) 32T/πd³
D) 12T/πd³
Thermodynamics & Heat Transfer (Q26–35)
Q26. The first law of thermodynamics for a closed system:
A) ΔU = Q – W
B) ΔU = Q + W
C) ΔU = W – Q
D) ΔU = Q × W
Q27. In an ideal Rankine cycle, efficiency increases with:
A) Decreasing boiler pressure
B) Increasing boiler pressure
C) Increasing condenser pressure
D) Reducing superheat
Q28. Entropy change for an isothermal process:
A) ΔS = Q/T
B) ΔS = T/Q
C) ΔS = ΔU/T
D) ΔS = 0
Q29. In Otto cycle, maximum pressure occurs at:
A) Start of compression
B) End of compression
C) End of combustion
D) Start of expansion
Q30. Mean effective pressure (MEP) is:
A) Work per unit displacement volume
B) Total pressure in cylinder
C) Maximum cylinder pressure
D) Pressure at TDC
Q31. For a heat exchanger, effectiveness ε =
A) Actual heat transfer / Maximum possible heat transfer
B) Q / CpΔT
C) ΔT / Q
D) Q / ΔT
Q32. Thermal conductivity of a material is measured in:
A) W/m·K
B) J/s·m
C) J/K
D) W·s/m²
Q33. Stefan-Boltzmann law:
A) Q = σAT⁴
B) Q = σAT²
C) Q = kAΔT
D) Q = mcΔT
Q34. Conduction in a plane wall depends on:
A) Area, thickness, thermal conductivity
B) Only area
C) Only thickness
D) None
Q35. The Biot number (Bi) represents:
A) Ratio of conduction resistance to convection resistance
B) Ratio of convection to conduction
C) Ratio of heat capacity to conductivity
D) None
Fluid Mechanics & Hydraulic Machines (Q36–50)
Q36. Reynolds number indicates:
A) Laminar or turbulent flow
B) Flow velocity
C) Fluid density
D) Head loss
Q37. Flow is laminar when Re <
A) 2000
B) 3000
C) 4000
D) 5000
Q38. Bernoulli’s equation assumes:
A) Incompressible, inviscid, steady flow
B) Compressible, steady
C) Viscous, unsteady
D) None
Q39. Venturimeter measures:
A) Flow rate
B) Pressure
C) Velocity
D) Head loss
Q40. Hydraulic radius R =
A) Area of flow / Wetted perimeter
B) Wetted perimeter / Area
C) Diameter × velocity
D) Depth × width
Q41. Froude number indicates:
A) Flow regime in open channel
B) Pump efficiency
C) Turbulence in pipe
D) Viscosity
Q42. Darcy-Weisbach equation calculates:
A) Head loss in pipe
B) Pump power
C) Flow velocity
D) Efficiency
Q43. Specific speed of a pump is:
A) N√Q/H^3/4
B) N√H/Q^3/4
C) NQ/H^3/2
D) N√Q/H
Q44. Cavitation in pumps occurs when:
A) Pressure falls below vapor pressure
B) Velocity is low
C) Pump speed decreases
D) Fluid temperature falls
Q45. Pelton wheel is used for:
A) High head, low discharge
B) Low head, high discharge
C) Medium head
D) Both A & B
Q46. Francis turbine is suitable for:
A) Medium head, medium discharge
B) Low head
C) High head, low discharge
D) Low flow
Q47. Efficiency of a turbine =
A) Output power / Input power × 100
B) Input / Output × 100
C) Flow / Head × 100
D) None
Q48. Hydraulic gradient line shows:
A) Pressure head
B) Velocity head
C) Energy distribution
D) Flow rate
Q49. Losses in pipe flow include:
A) Friction
B) Minor losses
C) Both A & B
D) None
Q50. In open channel flow, specific energy E =
A) y + V²/2g
B) V²/2g
C) y – V²/2g
D) y × V²/2g
Machine Design & Theory of Machines (Q51–65)
Q51. In a simply supported shaft transmitting power, maximum torque occurs at:
A) Midspan
B) Supports
C) Quarter span
D) Uniformly
Q52. Factor of safety in machine design is generally based on:
A) Yield strength
B) Ultimate strength
C) Working stress
D) Material modulus
Q53. In a belt drive, the velocity ratio =
A) Diameter of driver / Diameter of driven
B) Diameter of driven / Diameter of driver
C) Speed of driver / Speed of driven
D) Both A & C
Q54. A flywheel is used to:
A) Store energy
B) Reduce speed fluctuations
C) Both A & B
D) Increase torque
Q55. For a helical gear, axial thrust arises due to:
A) Helix angle
B) Pressure angle
C) Tooth width
D) Pitch diameter
Q56. In a simple pin joint mechanism, degree of freedom =
A) 1
B) 2
C) 3
D) 0
Q57. In a slider-crank mechanism, maximum velocity of the slider occurs at:
A) Mid-stroke
B) End of stroke
C) Start of stroke
D) 1/4 stroke
Q58. In gear train, velocity ratio =
A) Number of teeth of driven / Number of teeth of driver
B) Driver / Driven
C) Sum of teeth / driver teeth
D) None
Q59. Bearing pressure =
A) Load / Projected area
B) Load / Surface area
C) Load × Area
D) None
Q60. In a screw jack, mechanical advantage =
A) πd / l tan α
B) 2πr / l
C) Load / Effort
D) None
Q61. In a spur gear, velocity ratio =
A) N2/N1
B) N1/N2
C) Z2/Z1
D) Z1/Z2
Q62. In a belt drive, slip decreases with:
A) Increasing tension
B) Decreasing pulley diameter
C) Increasing belt length
D) Reducing load
Q63. In a four-bar mechanism, Grashof condition determines:
A) Continuous rotation
B) Interference
C) Link lengths
D) None
Q64. In a helical spring, deflection δ =
A) 8WL³ / Gd⁴
B) 8WD³n / Gd⁴
C) 64WD³n / Gd⁴
D) 32WD³n / Gd⁴
Q65. In a clutch, torque transmitted =
A) μ × normal force × radius
B) Force / radius
C) μ × force²
D) μ × normal²
IC Engines & Refrigeration / Air Conditioning (Q66–75)
Q66. In Otto cycle, efficiency increases with:
A) Increasing compression ratio
B) Decreasing compression ratio
C) Increasing stroke length
D) Increasing bore
Q67. Diesel cycle efficiency > Otto cycle for same compression ratio because:
A) Higher cutoff ratio
B) Lower cutoff ratio
C) Same pressure
D) None
Q68. In IC engines, mean effective pressure (MEP) is:
A) Work per unit displacement volume
B) Maximum cylinder pressure
C) Torque × RPM
D) Pressure at TDC
Q69. Brake power =
A) Torque × Angular speed
B) Torque / Angular speed
C) Torque × RPM
D) Work / Time
Q70. Thermal efficiency of Carnot engine depends on:
A) T1 and T2 (high & low temperature reservoirs)
B) Compression ratio
C) Working fluid
D) Engine speed
Q71. Refrigeration effect is measured in:
A) kJ/kg
B) kW
C) BTU
D) J/s
Q72. Coefficient of Performance (COP) of a refrigerator =
A) QL / W
B) W / QL
C) QH / W
D) None
Q73. In vapor compression cycle, throttling occurs at:
A) Expansion valve
B) Compressor
C) Condenser
D) Evaporator
Q74. Superheating of refrigerant vapor:
A) Increases COP
B) Protects compressor
C) Reduces efficiency
D) Increases pressure
Q75. Air-conditioning latent load refers to:
A) Cooling sensible temperature
B) Moisture removal
C) Air circulation
D) Compressor work
Numerical Problems & Applied Mechanical Engineering (Q76–90)
Q76. A shaft transmits 50 kW at 150 rpm. Torque =
A) 3180 N·m
B) 3186 N·m
C) 3200 N·m
D) 3000 N·m
Q77. A simply supported beam 6 m long carries a point load of 10 kN at midspan. Maximum bending moment =
A) 15 kNm
B) 20 kNm
C) 30 kNm
D) 25 kNm
Q78. A solid shaft of 50 mm diameter is subjected to torque of 5 kN·m. Maximum shear stress =
A) 25.5 MPa
B) 31.8 MPa
C) 32.5 MPa
D) 28 MPa
Q79. In a helical spring, W = 500 N, mean diameter = 50 mm, wire diameter = 5 mm, deflection = 20 mm, find shear stress (G = 80 GPa)
A) 500 MPa
B) 510 MPa
C) 520 MPa
D) 530 MPa
Q80. A belt drive transmits 10 kW at 1000 rpm on driver pulley of 200 mm. Find belt velocity:
A) 10 m/s
B) 12 m/s
C) 15 m/s
D) 18 m/s
Q81. In a centrifugal pump, flow rate = 0.1 m³/s, head = 20 m, density = 1000 kg/m³, power =
A) 19.62 kW
B) 20 kW
C) 21 kW
D) 22 kW
Q82. A refrigeration system produces 20 kW refrigeration effect. Power input = 5 kW. COP =
A) 3
B) 4
C) 5
D) 2
Q83. Thermal efficiency of Otto cycle with compression ratio 8, γ = 1.4 =
A) 56%
B) 58%
C) 60%
D) 62%
Q84. In a Pelton turbine, jet velocity = 20 m/s, bucket velocity = 10 m/s. Velocity of water leaving bucket =
A) 10 m/s
B) 5 m/s
C) 0 m/s
D) 15 m/s
Q85. A shaft rotates at 120 rpm and transmits 50 kW. Find torque:
A) 3980 N·m
B) 3978 N·m
C) 4000 N·m
D) 3900 N·m
Q86. For a gas turbine, work ratio = Wnet / Wturbine. If Wnet = 500 kJ/kg, Wturbine = 1200 kJ/kg, work ratio =
A) 0.4
B) 0.42
C) 0.38
D) 0.5
Q87. In a slider-crank mechanism, crank length = 0.2 m, connecting rod = 0.8 m. Stroke =
A) 0.4 m
B) 0.3 m
C) 0.5 m
D) 0.6 m
Q88. Mass flow rate in pipe: ρ = 1000 kg/m³, Q = 0.05 m³/s. Mass flow rate =
A) 50 kg/s
B) 100 kg/s
C) 45 kg/s
D) 55 kg/s
Q89. In a belt drive, slip = 2%. Actual velocity ratio = 4:1. Find theoretical velocity ratio:
A) 3.92:1
B) 4.08:1
C) 4.00:1
D) 3.98:1
Q90. Mean effective pressure in a single-cylinder engine: 1 MPa, stroke 0.2 m, bore 0.1 m, work per stroke =
A) 1.57 kJ
B) 1.5 kJ
C) 1.6 kJ
D) 1.55 kJ
Fluid Machines, Misc. Mechanical Aptitude, & Mixed Numericals (Q91–100)
Q91. Centrifugal pump: head = 20 m, flow rate = 0.05 m³/s, efficiency = 80%, power required =
A) 12.25 kW
B) 13 kW
C) 12 kW
D) 11.5 kW
Q92. In a compressor, volumetric efficiency = 85%, swept volume = 0.05 m³, actual intake =
A) 0.0425 m³
B) 0.045 m³
C) 0.0475 m³
D) 0.050 m³
Q93. A flywheel stores 1000 kJ of energy, speed fluctuation = 10%. Maximum kinetic energy =
A) 1050 kJ
B) 1100 kJ
C) 1005 kJ
D) 1020 kJ
Q94. In a pin joint mechanism, velocity of point B on crank = 2 m/s, find speed of slider (crank length = 0.2 m, rod = 0.8 m)
A) 1.5 m/s
B) 1.6 m/s
C) 1.4 m/s
D) 1.3 m/s
Q95. In a refrigeration system, refrigerant absorbs 50 kJ/kg in evaporator, rejects 60 kJ/kg in condenser. Work input =
A) 10 kJ/kg
B) 12 kJ/kg
C) 8 kJ/kg
D) 15 kJ/kg
Q96. Hydraulic efficiency of a turbine = 90%, mechanical efficiency = 85%. Overall efficiency =
A) 76.5%
B) 75%
C) 77%
D) 78%
Q97. In gas turbine, pressure ratio = 10, γ = 1.4. Isentropic efficiency = 85%. Find outlet temperature (numerical setup)
A) 820 K
B) 800 K
C) 810 K
D) 830 K
Q98. In a helical spring, spring index C = 8, allowable shear stress = 500 MPa, wire diameter = 5 mm. Maximum load =
A) 500 N
B) 520 N
C) 510 N
D) 530 N
Q99. In a belt drive, driver speed = 1200 rpm, belt ratio = 3:1. Speed of driven pulley =
A) 400 rpm
B) 360 rpm
C) 380 rpm
D) 420 rpm
Q100. A single-cylinder IC engine: bore = 0.1 m, stroke = 0.12 m, MEP = 1.2 MPa. Work per stroke =
A) 1.13 kJ
B) 1.1 kJ
C) 1.2 kJ
D) 1.15 kJ
BPSC AEO Mechanical Preliminary Exam – Answer Key (Q1–Q100)
| Q.No | Answer | Q.No | Answer | Q.No | Answer | Q.No | Answer |
|---|---|---|---|---|---|---|---|
| 1 | B | 26 | A | 51 | C | 76 | B |
| 2 | B | 27 | B | 52 | A | 77 | C |
| 3 | A | 28 | A | 53 | D | 78 | B |
| 4 | D | 29 | C | 54 | C | 79 | C |
| 5 | B | 30 | A | 55 | A | 80 | B |
| 6 | D | 31 | A | 56 | A | 81 | A |
| 7 | A | 32 | A | 57 | A | 82 | A |
| 8 | A | 33 | A | 58 | A | 83 | A |
| 9 | A | 34 | A | 59 | A | 84 | C |
| 10 | A | 35 | A | 60 | A | 85 | B |
| 11 | B | 36 | A | 61 | A | 86 | A |
| 12 | B | 37 | A | 62 | A | 87 | A |
| 13 | A | 38 | A | 63 | A | 88 | B |
| 14 | A | 39 | A | 64 | B | 89 | A |
| 15 | A | 40 | A | 65 | A | 90 | A |
| 16 | A | 41 | A | 66 | A | 91 | A |
| 17 | A | 42 | A | 67 | A | 92 | A |
| 18 | A | 43 | A | 68 | A | 93 | A |
| 19 | C | 44 | A | 69 | A | 94 | B |
| 20 | A | 45 | A | 70 | A | 95 | A |
| 21 | A | 46 | A | 71 | A | 96 | A |
| 22 | A | 47 | A | 72 | A | 97 | C |
| 23 | A | 48 | C | 73 | A | 98 | A |
| 24 | A | 49 | C | 74 | B | 99 | A |
| 25 | A | 50 | A | 75 | B | 100 | A |