Mechanical Engineering Review Online

1. A 12,000 KW hydro-electric power plant has volumetric flow rate of 6 sec-m with 2.5% leakage loss. The head utilized in the turbine is 230 m. It has a generator efficiency of 95% and hydraulic efficiency of 83%. Determine its overall turbine efficiency.

a. 67.32%

b. 77.44%

c. 57.35%

d. 47.33%

2. A pump draws water from a reservoir at 5 kg/s. The suction side is located 12 m below the centerline of the pump, while the discharge side is 25 m above the centerline of the pump. Determine the hydraulic power needed if the head required to overcome friction is 1.8 m.

a. 2.30 kW

b. 1.90 hp

c. 1.90 kW

d. 2.30 hp

3. A gas turbine power plant operating as a Joule cycle, the compressor power needed 280 kW which is driven by a 1200 kW turbine. The compressor efficiency is 85% and that of the turbine is 90%. Determine the Back-work ratio

a. 30.5%

b. 28.1%

c. 34.3%

d. 38.2%

4. A 2.5 hp refrigerator of heat pump operates between -5oF and 110oF. The maximum theoretical heat that can be transferred from the reservoir is nearest to:

a. 26187.2 Btu/hr

b. 25179.2 Btu/hr

c. 30102.1 Btu/hr

d. 28310.3 Btu/hr

5. The effective head at the nozzle of an impulse turbine is 280 m. Water jet diameter is 130 mm and its coefficient due to turbulence is 95%. Determine the water jet power.

a. 2000.3 kW

b. 2035.9 kW

c. 2567.2 KW

d. 2699.3 kW

6. If PV is the power required for a vapor-compression refrigeration system, then what is the power required for an air refrigeration system, assuming that they have the same capacity?

a. 5PV

b. 2PV

c. PV/10

d. 1/PV

7. Gauge cock in the boiler is designed to determine

a. Level of steam

b. Specific heat

c. Level of water

d. Pressure

8. One mode of heat transfer that occurs in a material due to molecular motion in the material where a temperature gradient exists. The mode of heat transfer is called.

a. Conduction

b. Radiation

c. Convection

d. Transformation

9. What cycle is used for a vapor cycle in power plant?

a. Brayton cycle

b. Diesel cycle

c. Ericson cycle

d. Rankine cycle

10. For supersonic and subsonic divergent nozzle, what is the Mach number for supersonic

a. Greater than 1

b. Less than 1

c. 1

d. 0 

11. To obtain equilibrium in the condenser, what should be the range of the tower, in relation to the temperature difference in the condenser?

a. Should be higher

b. Indirectly proportional

c. Should be lesser

d. It should be equal

12. An energy conserved device which utilize air and water as a cooling medium, and used as a cooling tower and condenser as one

a. Shell and tube

b. Evaporative

c. Air cooled condenser

d. Water cooled

13. Exhaust steam from a turbine exhaust into a surface condenser at a mass flow rate of 1.3 kg/s, 15 kPa and 90% quality. Cooling water enters the condenser at 25^oC and leaves at the steam inlet temperature. What is the cooling water mass flow rate in kg/s? Steam properties: P=15 kPa (t=53.97^oC) hf=225.94 kJ/kg, hfg=2373.1 kJ/kg.

a. 14.3 kg/s

b. 15.8 kg/s

c. 17.6 kg/s

d. 13.0 kg/s

14. A 310 mm centrifugal pump needs a 60 m of head to deliver 0.8 m³/s of water. When speed is reduced from 600 rpm to 400 rpm, what is its new rate of discharge required?

a. 0.223 cu.m

b. 0.533 cu.m

c. 0.312 cu.m

d. 0.410 cu.m

15. 55,300 gallons of water passes through a heat exchanger and absorbs 29,550,000 kJ. The exit temperature is 50^oC. The entrance water temperature, in ^oC is nearest to:

a. 16.28

b. 13.89

c. 17.31

d. 15.11

16. The COP of a basic refrigeration system is 5.8. When operating as a heat pump, what is its efficiency?

a. 3.8

b. 2.8

c. 5.8

d. 6.8

17. The product leaves the dryer with 18% moisture content (wet basis). The initial mass of the wet feed is 28000 kg with 20% moisture content. Determine the amount of moisture extracted from the feed.

a. 581.3 kg

b. 682.9 kg

c. 763.1 kg

d. 603.1 kg

18. The refrigeration load of vapor compression refrigeration is system is 60 kJ/kg. The COP is 7. The enthalpy of the refrigerant leaving the compressor is 90 kJ/kg. Determine the enthalpy entering the compressor.

a. 81.43 kJ/kg

b. 73.21 kJ/kg

c. 69.31 kJ/kg

d. 88.73 kJ/kg

19. Wet feed at 30 MT enters the dryer with 35% moisture and the products leaves at 20 MT. Determine the regain in the products.

a. 43.2%

b. 53.9%

c. 58.3%

d. 40.3%

20. The operating high thermal level of a Reversed Carnot Cycle is 330 K and its COP is 7. Determine the temperature of the sink.

a. 268.3 K

b. 333.3 K

c. 288.8 K

d. 251.1 K

21. Find the height of the stack if it produces 30 m gas gage of theoretical draft. The temperature of the flue gas is 200^oC.

a. 38.3 m

b. 28.3 m

c. 59.3 m

d. 49.0 m

22. Water regulating valve should be located or installed in a refrigerating system

a. At the suction line to the compressor 

b. At a line to the condenser

c. Anywhere in the system

d. Water cooled

23. Where thus the percentage of moisture and refrigerant-vapor in the absorption last rejected?

a. Analyser

b. Condenser

c. Generator

d. Rectifier

24. What is that one main part of equipment, through the air movement of the ventilation, heating, refrigerating and also used to discharge to the ventilating outlet?

a. Duct

b. Dehumidifier

c. Blower

d.Strainer

25. Room air-conditioning needs abundant supply or air, because it uses what type of condenser?

a. Chilled water system

b. Water cooled

c. Shell and tube

d. Air cooled

26. What is the head developed if the pump that has a capacity Q1 and head H1 connected in series with another pump with a capacity Q2 and H2, if Q2 is less than Q1

a. H1 + H2

b. H1 – H2

c. H1 = H2

d. H1/H2

27. If the combustion chamber is concern. What will happen if the power output is increased?

a. Decrease the combustion time 

b. Increase the combustion chamber volume

c. Decrease combustion chamber volume

d. Increase the combustion time

28. Amount of heat surface to cooled, is the amount of heat absorbed by the cooling coils

a. Enthalpy

b. Compression

c. Refrigerating effect

d. Flow work

29. Helium is 50^oC and atmospheric pressure. What volume does it occupy? (Cv=3.0023 kJ/kg-K, k=1.555)

a. 5.311

b. 6.231

c. 4.821

d. 7.211

30. Determine the diameter of the stack if it produces 28 m gas gage of theoretical draft. The temperature of flue gas is 180^oC. The waste gases delivered is 5 kg/s. Molecular weight of the gases is 30.

a. 1.081 m

b. 0.917 m

c. 0.521 m

d. 0.771 m

31. An air compressor receives 0.18 m³/s at 98 kPa and discharges it to 400 kPa. The pressure drop at the discharge port is 5 kPa. What is the power required to drive the compressor if the overall efficiency is 0.80.

a. 28.17 kW

b. 30.21 kW

c. 38.17 kW

d. 40.31 kW

32. A 250 mm x 350 mm reciprocating compressor receives 0.80 kg/s air at 100 kPa and discharges it to an air receiver at 350 kPa. The rotative speed of the driving motor is 180 rpm. Determine the piston speed.

a. 1.1

b. 3.1

c. 4.1

d. 2.1

33. A Rankine cycle steam power plant receives 12 kg/s of superheated steam at 4.5 MPa, 550^oC and expands to an exhaust pressure of 100 kPa. The expansion efficiency in the turbine and pumping process efficiency in the boiler feed pump are 80% and 85%, respectively. Neglect the piping losses within the circuit, determine the power required to drive the pump. Note: v=0.001043 m³/kg at P=100 kPa.

a. 68.8 kW

b. 58.9 kW

c. 45.9 kW

d. 70.9 kW

34. A three stage reciprocating compressor receives 0.5 kg/s of air and discharge at 380 kPa. Determine the power needed by the compressor.

a. 69.3 kW

b. 59.4 kW

c. 66.3 kW

d. 46.1 kW

35. A 20 MW Diesel-generator uses 1.8 kg/s of fuel with a heating value of 35,000 kJ/kg. Determine the indicated thermal efficiency if the mechanical-electrical efficiency is 90%.

a. 25.2%

b. 30.8%

c. 35.3%

d. 38.2%

36. A waster heat recovery boiler has been installed at the exhaust of a Diesel engine which has a temperature of 850^oC and a mass flow rate of 50 kg/s. Feed water at 80^oC enters the boiler and leaves at 5 MPa. The steam produce is 12 kg/s. Determine the temperature of the exhaust gas that leaves the recovery boiler? Note: hg=2794.3 at P=5MPa.

a. 222.1 ^oC

b. 251.3 ^oC

c. 281.3 ^oC

d. 263.4 ^oC

37. A six cylinder, four stroke diesel engine with 220 mm x 250 mm with a rotative speed of 350 rpm. Its volumetric efficiency is 85%. Determine the amount of air needed for combustion at standard condition in kg per second.

a. 0.2615

b. 0.3121

c. 0.1696

d. 0.4112

38. An open Brayton Cycle has a compression ratio of 4.8. Determine the pressure ratio.

a. 10.21

b. 8.99

c. 9.12

d. 7.21

39. A double suction centrifugal operates against a head of 12 m with a specific speed of 380 rpm. The rotative speed of the impeller is 1300 rpm. Determine the rate of discharge.

a. 2.66 x 10^-3

b. 3.11 x 10^-3

c. 2.99 x 10^-3

d. 4.01 x 10^-3

40. An open Brayton cycle has a compression ratio of 6. It is operating at standard air condition. Determine the exit pressure of the compressor.

a. 2115.8 kPa

b. 1244.9 kPa

c. 1550.1 kPa

d. 1031.8 kPa

41. A wet cooling tower receives hot water at a rate of 80 kg/s at 40^oC and cools to 20^oC. Standard atmospheric air enters the tower at 25^oC and 60% relative humidity leaves at 30^oC. What is the mass flow rate of air into the cooling tower? At 3.169 kPa saturation pressure at t_d1=25^oC and 4.246 kPa saturation pressure at t_d2=30^oC.

a. 157.7 kg/s

b. 167.3 kg/s

c. 143.2 kg/s

d. 177.5 kg/s

42. Air enters the ACU at 90 kJ/kg. The refrigeration load is 18 TOR. The sensible and latent heat load are 28 kJ/s and 12 kJ/s, respectively. The enthalpy at the space to be conditioned is at 50 kJ/kg. Determine the amount of air to be conditioned.

a. 0.481 kg/s

b. 0.351 kg/s

c. 0.583 kg/s

d. 0.501 kg/s

43. A pump operating at 1900 rpm delivers 0.6 m³/s of water at 18^oC. Decreasing the impeller speed to 1300 rpm. What is the new rate of discharge?

a. 0.3721 cu.m

b. 0.4412 cu.m

c. 0.4105 cu.m

d. 0.1231 cu.m

44. A two stage reciprocating compressor operates at 0.5 kg/s air. The suction and discharge conditions are 100 kPa and 380 kPa, respectively. Determine the power required in the low pressure stage.

a. 35.2 kW

b. 32.1 kW

c. 39.8 kW

d. 30.7 kW

45. A room to be conditioned is supplied with air at 16^oC dry bulb and 80% relative humidity at standard pressure whose volumetric flow rate is 8 m³/s. The existing room specific enthalpy is 65 kJ/kg. Determine the total heat load. Note: 1.83188 kPa saturation pressure at t_d=16^oC.

a. 277.2 kW

b. 289.3 kW

c. 298.8 kW

d. 255.3 kW

46. The amount of moisture extracted from a wet feed that enters the dryer is 0.04 kg/s. The increase in moisture of the cooled and humidified air as it passes through the dryer is 0.01 kg water vapor per kg dry air. Determine the amount of air needed in the drying process, in kg/s.

a. 3

b. 4

c. 5

d. 6

47. Determine the thermal efficiency of a cycle with two isentropics and two isochorics process. The expansion ratio is 9.

a. 56.3%

b. 58.5%

c. 55.3%

d. 50.9%

48. A standard vapor compression refrigeration system requires a compressor work of 8 kW. The condenser releases 16 kW of heat. Determine the amount of air to be conditioned if the decrease in enthalpy at the air conditioning unit is 48 kJ/kg.

a. 0.1667 kg/s

b. 0.3371 kg/s

c. 0.1002 kg/s

d. 0.1991 kg/s

49. Determine the actual air-fuel ratio of C12H36 with 12% excess air.

a. 15.7

b. 16.3

c. 17.9

d. 19.0

50. The total heat load in the space to be conditioned is 110 kJ/s. It has a sensible heat load factor of 0.90. Determine the amount of sensible heat load due to temperature change.

a. 89 kW

b. 99 kW

c. 79 kW

d. 80 kW

51. The tower water is allowed to cool from 30^oC to 20^oC in a wet type cooling tower. The air enters the tower at a rate of 130 kg/s with a humidity ratio of 0.02 kg water vapor per kg dry air and leaves 0.03 kg water vapor per kg dry air. Determine the amount of make-up water.

a. 2.1 kg/s

b. 3.1 kg/s

c. 2.9 kg/s

d. 1.3 kg/s

52. An air compressor with a 330 mm bore operating at a piston speed of 8 m/min. The suction pressure is 100 kPa and discharges at 380 kPa. The clearance volume is 6%. What is the compressor power required, in kW. The compression and expansion polytropic constant is 1.29.

a. 0.7911

b. 0.7001

c. 0.7132

d. 0.7319

53. A 7,000 kW Rankine steam power plant has a combined heat rate of 11,000 kJ/kW-hr and brake steam rate of 8 kg/kW-hr. It has an efficiency of 95%. Determine the amount of energy chargeable to the system, in kJ/kg.

a. 1206.3

b. 1562.7

c. 1982.1

d. 1306.3

54. If a liquid is heated in a container, then it expands and become less dense and lighter. It rises upward to the container because of its reduced density and replaced by colder fluid. If the process continues, heat is transferred and distributed throughout. What is this mode of heat transfer?

a. Radiation

b. Condensation

c. Conduction

d. Convection

55. In steady flow of fluids, velocity at a section at the stream lines remains ____.

a. Uniform

b. Unsteady

c. Equal d

. Constant

56. An equipment used to cool the back pressure in the steam turbine generating steam and convert steam to water

a. Cooling tower

b. Condenser

c. Separator

d. Gas engine

57. Which of the following has a minimal effect n the penetration of the air in combustion chamber?

a. Jet velocity

b. Orifice size

c. Fuel viscosity

d. Air density

58. What is the part of an oil pressure governor that is used to continuously draw oil for as long as the turbine is working?

a. Speed governor

b. Servomotor

c. Governing device

d. Gear pump

59. When can a Francis turbine obtain a correct disposition of the moving blades and the guide?

a. At half the load

b. At full load only

c. At any load

d. At all loads

60. The volumetric efficiency of an engine normally decreases with

a. Higher fuel-viscosity

b. An increase in speed

c. A decrease in speed

d. A decrease in jet velocity

61. A single acting reciprocating compressor with 320 mm bore x 260 mm stroke has a 0.6 power stroke per cylinder per second. Determine the volumetric displacement.

a. 0.02413 m³/s

b. 0.03311 m³/s

c. 0.01255 m³/s

d. 0.04152 m³/s

62. Octane (C₈H₁₈) is burned with dry air. The volumetric analysis of the products on a dry basis: 10.02% CO₂; 5.62% O₂; 0.88% CO; 83.48% N₂. Determine the fraction of the H₂O that condenses as the product cooled to 25^oC at 100 kPa. Note: Saturation pressure at 25^oC:3.169 kPa.

a. 0.5311

b. 0.6141

c. 0.8136

d. 0.7331

63. A certain natural gas has the following volumetric analysis: 72% CH₄, 9% H₂; 14% N₂, 2% O₂; 3% CO₂. This gas is now burned with the stoichiometric amount of air which enters the combustion chamber at 20^oC, 1 atm, and 80% relative humidity. Assuming complete combustion and a total pressure of 1 atm, determine the dew point temperature of the products. Note: Saturation pressure at 20^oC: 2.339 kPa

Saturation temperature:

53.97^oC                    0.015 MPa

60.09^oC                    0.020 MPa

64.97^oC                    0.025 MPa

69.10^oC                    0.030 MPa

a. 55.8

b. 68.3.3

c. 65.4

d. 60.9

64. A room (9m x 8m x 3m) is held at 25^oC and 50% RH by an air conditioning unit, when ambient conditions are 32^oC and 80% RH. The room heating load (sensible and latent) is 9 kW and the room is provided with ten air changes per hour. Exhaust air leaves at room conditions and the ratio of return to make up air is 2:1. Determine the total air conditioning load. Note: at 32^oC and 80% RH (ambient): h=95 kJ/kg, v=0.898 m³/kg. At 25oC and 50% RH (room): h=50.5 kJ/kg, v=0.8575 m³/kg.

a. 11.4154 tons

b. 15.8411 tons

c. 18.3121 tons

d. 12.9913 tons

Performance values of a 2.8 MW Diesel generating set are as follows:

Fuel rate, 1.8 barrels for 850 kW-hr of 25 deg API fuel
Generator efficiency, 90 percent
Mechanical efficiency, 80 percent
Voltage, 440/220, three-phase, 60 hertz

65. Determine the fuel consumed for 850 kW-h energy produced.

a. 325.5 kg

b. 401.2 kg

c. 350.8 kg

d. 287.4 kg

66. Determine the engine-fuel rate in kg per kW-hr

a. 0.2436

b. 0.5421

c. 0.3447

d. 0.1182

67. Determine the brake thermal efficiency

a. 20.6%

b. 23.4%

c. 25.5%

d. 27.3%

68. Determine the indicated thermal efficiency

a. 38.9%

b. 29.3%

c. 25.1%

d. 35.9%

69. For pipes extending more than 1000 times the diameter, what are the major losses of hydraulic head due to?

a. Cross-sectional change

b. Friction

c. Velocity

d. Pressure

70. Which of the following is the preferred criterion for a high speed engine?

a. Higher internal stress

b. Low piston speed

c. High RPM

d. High mean piston speed

71. Which of the following pumps is recommended for high head and low discharge?

a. Bucket type

b. Plunger type

c. Single cylinder piston type

d. Piston type

72. The volumetric efficiency of an engine normally decreases with

a. Higher fuel-viscosity

b. An increase in speed

c. A decrease in speed

d. A decrease in jet velocity

73. What do bodies at a temperature above absolute zero emit?

a. Energy

b. Heat of convection

c. Thermal radiation

d. Heat of compression

74. A refrigerant control in a refrigeration system that is used to prevent the flow of refrigerant gas from the condenser back to the compressor during off cycles

a. Check valve

b. Solenoid valve

c. Hold-back valve

d. Safety valve

Magnolia Dairy Products plant must cool 3800 gallons of fresh milk received from the farm per day from an initial temperature of 75 deg F to temperature of 40 deg F in 5 hours. If the density of milk is 8.8 lbs per gallon, specific gravity is 1.05, and specific heat is 0.946 Btu per lb per deg F.

75. How much brine must be circulated of the refrigerating machine in tons?

a. 15.3

b. 16.2

c. 18.5

d. 17.3

76. How much brine must be circulated if the change in temperature is 16 deg R, specific gravity is 1.173, and the specific heat of brine is 0.715 Btu/lb-^oR?

a. 32 gpm

b. 38 gpm

c. 43 gpm

d. 28 gpm

Water substance at 70 bar and 65 deg C enters a boiler tube of constant inside diameter of 30 mm. The water leaves the boiler tube at 50 bar and 700 K at a velocity of 110 m/s. Water properties: At 70 bar and 65 deg C: v=0.001017 m³/kg. At 50 bar and 700 K: v=0.06081 m³/kg.

77. Calculate the inlet velocity

a. 2.8 m/s

b. 3.8 m/s

c. 1.8 m/s

d. 4.5 m/s

78. Calculate the inlet volume flow in liters per second.

a. 2.3

b. 1.9

c. 3.3

d. 1.3

255,000 kg/hr of water at 35^oC enters a cooling tower where it is to be cooled to 17.5^oC. The energy is to be exchanged with atmospheric entering the unit at 15^oC and leaving the unit at 30^oC. The air enters at 30% RH and leaves 85% RH. Air properties: At 15^oC and 30% RH: h=23 kJ/kg, SH=0.0032. At 30^oC and 85% RH: h=89 kJ/kg, SH=0.0232.

79. Determine the range of the tower.

a. 17.5

b. 15.6

c. 13.7

d. 19.9

80. Determine the mass flow rate of air required to cool the water in kg/hr.

a. 255.3

b. 283.1

c. 293.1

d. 278.1

81. Determine the amount of make-up water requirement, in kg/hr

a. 5661

b. 4661

c. 3661

d. 6661

82. What is the percentage of make-up water to the cooling water flow?

a. 2.22%

b. 3.33%

c. 4.44%

d. 5.55%

A circular fuel oil tank 50 ft long and 6 feet diameter is used for oil storage and supplying fuel oil at 34 deg API to a steam boiler. The steam flow is 2200 lbs per hour at 200 psia dry steam. Feed water is 230 deg F and boiler efficiency is 80%. Steam properties: At 200 psia (1.38 MPa): hg=2789.6 kJ/kg. At 230 deg F (110 deg C): hf=461.3 kJ/kg.
83. Determine the flow rate of fuel in kg per hour

a. 44.3

b. 63.4

c. 52.1

d. 61.2

84. Determine the density of fuel in kg per cu. meter

a. 655

b. 855

c. 765

d. 698

85. Calculate the number of days the supply tank can hold for continuous operation.

a. 10

b. 15

c. 22

d. 33

An air conditioning plant with a capacity of 450 kW or refrigeration has an evaporating temperature and condensing temperature of 3 deg C and 37 deg C, respectively. The plant is using R12 with properties at 3 deg C: hf=202.78 kJ/kg, hg=352.755 kJ/kg, vg=50.47 L/kg. At 37 deg C: hf=235.503 kJ/kg

86. What will be the mass of flash gas per kg of refrigerant circulated?

a. 0.111

b. 0.129

c. 0.218

d. 0.291 

87. What is the mass of R12 must be circulated per second?

a. 4.8

b. 6.8

c. 5.5

d. 3.8

88. What is the suction in m³/sec?

a. 0.289

b. 0.912

c. 0.713

d. 0.194

A two stage compressor with first stage piston displacement of 95200 m³/s is driven by a motor. Motor output is 35 hp, suction temperature is 23 deg C, volumetric efficiency is 88%, mechanical efficiency is 96%, the intercooler pressure is 32 psi gage, air temperature in and out of the intercooler are 108 and 45 deg C. Final discharge pressure is 110 psi gage, suction is estimated to be 14.58 psi.

89. Determine the volume flow at the suction in cu. m per second.

a. 0.08378

b. 0.09872

c. 0.05621

d. 0.07712

90. Find the mass flow rate at the suction in kg per second

a. 0.11970

b. 0.09911

c. 0.23011

d. 0.05561

91. What is the air power in the first stage in kW?

a. 9

b. 10

c. 11

d. 12

92. What is the compressor efficiency?

a. 77.3

b. 89.3

c. 65.3

d. 83.9

93. What is the power saved by intercooling?

a. 2.9 KW

b. 3.9 kW

c. 1.9 kW

d. 4.1 kW

94. Find the heat rejected in the intercooler, in kJ/sec.

a. 5.63 kW

b. 6.21 kW

c. 4.41 kW

d. 8.3 kW

95. In the absence of any irreversibilities, a thermoelectric generator, a device that incorporates both thermal and electric effects will have the efficiency of a _____.

a. Carnot cycle

b. Otto cycle

c. Diesel cycle

d. Rankine cycle

96. If the actual kinetic energy of a nozzle is Ka and Ki is the maximum value that can be attained by an isentropic expansion from initial to final state, then the efficiency of the nozzle is

a. Ka/Ki

b. Ki=Ka

c. Ka+Ki

d. Ki/Ka

97. Both Stirling and Ericson engines are

a. Internal combustion engines 

b. External combustion engines

c. Carnot engines

d. Brayton engines

98. Nozzles does not involve any work interaction, the fluid through this device experiences

a. No change in PE

b. Vacuum

c. No change in KE

d. No change in enthalpy

99. For a double acting reciprocating pump, there are two suction strokes for every revolution of the crank wheel. How many delivery strokes does it have?

a. 4

b. 3

c. 2

d. 1

100. What is commonly used/done to a system when the turbine has excessive moisture?

a. Frosting

b. Diffusing

c. Reheating

d. Dehumidiying

Answer Key (Handwritten)